Weighting and estimation

Results

All (638)

All (638) (570 to 580 of 638 results)

571. Estimates based on randomly rounded data Archived
Articles and reports: 12-001-X198700214515
Description:
Methods are given to estimate functions of the cell probabilities associated with a table of multinomial data that has been randomly rounded to multiples of a given number, say l. We show that: (i) random rounding causes only second order effects on bias and variance; (ii) the loss of efficiency in using the natural estimates of cell probability is negligible provided that the cell entry is large compared with (l^2 - 1) / (6R) where R is the number of cells in the table; and (iii) estimates of apparently exponentially small bias are available for moments of these natural estimates and for polynomials in the cell probabilities.
Release date: 1987-12-15
572. Variance estimation for the Canadian Labour Force Survey Archived
Articles and reports: 12-001-X198700214516
Description:
The biases and stabilities of alternative variance estimators for the two stage random group design (Rao et al. 1962) are evaluated in a Monte Carlo study in the context of Canadian Labour Force Survey. The variance formula for raking ratio estimation procedure is derived using Taylor linearization method. The properties of the variance formula are investigated by a Monte Carlo simulation.
Release date: 1987-12-15
573. An alternative method of controlling Current Population Survey estimates to population counts Archived
Articles and reports: 12-001-X198700214605
Description:
The CPS uses raking ratio estimation in post-stratification estimation to adjust sample estimates of population to census-based estimates of the population. An alternative procedure, using generalized least squares, is compared to the current procedure.
Release date: 1987-12-15
574. A class of methods for using person controls in household weighting Archived
Articles and reports: 12-001-X198700214606
Description:
A class of “constrained minimum distance” methods is considered for constraining household weights to be consistent with auxiliary information on the number of persons in various age x race x sex cells. The constrained weights are as close as possible to the initial weights based on the inverse probability of selection. This class of methods includes raking and generalized least square methods, as well as multinomial maximum likelihood, (where the cells of the distribution are household types.) The properties of the methods in the presence of systematic undercoverage of the household types are studied through some simple models for coverage. Comparisons with the principal person method are made and the paper concludes with the observation that it is necessary to know more about the nature of survey undercoverage before deciding on which of the constrained minimum distance or principal person methods is to be preferred in applications.
Release date: 1987-12-15
575. An integrated method for weighting persons and families Archived
Articles and reports: 12-001-X198700214607
Description:
Household surveys generally use separate procedures for estimating characteristics of persons and those of families. An integrated procedure is proposed and a least-squares estimator introduced to achieve this end. The estimator is shown to be unbiased under certain general conditions. Using data from the Canadian Labour Force Survey, variances for the estimator are calculated and shown to compare favourably to those from current procedures.
Release date: 1987-12-15
576. Modified raking ratio estimation Archived
Articles and reports: 12-001-X198700214608
Description:
A hybrid technique is described that employs both conventional and raking ratio estimation to handle the case when the population frequencies N_ij in a two-dimensional table are known, but some of the observed frequencies n_ij are small (or zero). Results are provided on the approach taken as it has evolved in the Corporate Statistics of Income Program over the last several years. Changes are still being considered and these will be discussed as well.
Release date: 1987-12-15
577. Statistical properties of crop production estimators Archived
Articles and reports: 12-001-X198700114468
Description:
The National Agricultural Statistics Service, U.S. Department of Agriculture, conducts yield surveys for a variety of field crops in the United States. While field sampling procedures for various crops differ, the same basic survey design is used for all crops. The survey design and current estimators are reviewed. Alternative estimators of yield and production and of the variance of the estimators are presented. Current estimators and alternative estimators are compared, both theoretically and in a Monte Carlo simulation.
Release date: 1987-06-15
578. On efficient estimation of unemployment rates from Labour Force Survey Data Archived
Articles and reports: 12-001-X198700114510
Description:
The method of minimum Q^(T) estimation for complex survey designs proposed by Singh (1985) provides asymptotically efficient estimates of model parameters analogous to Neyman’s (1949) min X^2 estimation procedure for simple random samples. The Q^(T) can be viewed as a X^2 type statistic for categorical survey data, and min Q^(T) estimates provide a robust alternative to Weighted Least Squares estimates, which often display unstable behaviour for complex surveys. In this paper, the min Q^(T) method is first described and then illustrated for the problem of estimating parameters of a logit model for survey estimates of unemployment rates which are obtained from the October 1980 Canadian LFS data cross-classified according to age-education covariate categories. It is seen that the trace efficiency of smoothed estimates obtained by Kumar and Rao (1986), who applied the method of pseudo maximum likelihood estimates (pseudo mle) to the same problem can be slightly improved by the min Q^(T) method. Interestingly enough, pseudo mle for individual cells behave much the same way as the efficient min Q^(T) estimates for the particular LFS example.
Release date: 1987-06-15
579. A sampling procedure with inclusion probabilities proportional to size Archived
Articles and reports: 12-001-X198700114511
Description:
A new unequal probability sampling scheme for selecting n(> 2) units without replacement from a finite population is proposed. This scheme ensures that the inclusion probabilities are proportional to sizes. It has the advantage of simplicity in selection and estimation and also provides a non-negative variance estimator. The variance of the Horvitz-Thompson (H-T) estimator under the proposed scheme is shown to be smaller than that of the customary estimator in probability proportional to size sampling with replacement. The proposed scheme also compares favourably with the without replacement scheme suggested by Sampford (1967) in an empirical study on a few natural populations.
Release date: 1987-06-15
580. Comparison of estimators of population total in two-stage successive sampling using auxiliary information Archived
Articles and reports: 12-001-X198700114513
Description:
Singh and Srivastava (1973) proposed a linear unbiased estimator of the population mean when sampling on successive occasions using several auxiliary variables whose known population means remain unchanged for all occasions. In this paper, three composite estimators T_1, T_2 and T_3, each utilising an auxiliary variable whose known population mean changes from one occasion to the next, are presented for the estimation of the current population total. The proposed estimators are compared with the ordinary estimator, T_0, and the usual successive sampling estimator, T \prime, of the current population total without the use of auxiliary information. We find that using auxiliary information in conjunction with successive sampling does not always uniformly produce a gain in efficiency over T_0 or T \prime. However, when applied to a survey of teak plantations to estimate the mean height of teak trees, T_1, T_2 and T_3 proved more efficient than T_0 and T \prime.
Release date: 1987-06-15

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Analysis (610)

Analysis (610) (0 to 10 of 610 results)

1. Exact and approximation formulas for second-order inclusion probabilities in randomized systematic sampling with unequal probabilities and without replacement
Articles and reports: 12-001-X202600100003
Description: Probability-proportional-to-size sampling is widely used by national statistical offices. Here population units are selected with probabilities proportional to an auxiliary variable. Variance formulas in such designs require both first- and second-order inclusion probabilities. The computation of second-order inclusion probabilities is particularly challenging for large populations, and has been the subject of extensive research. This article presents some new exact and approximation formulas for second-order inclusion probabilities in randomized systematic sampling with unequal probabilities and without replacement.
Release date: 2026-06-29
2. Improving the coverage of confidence intervals with respect to degrees of freedom: Application to the Canadian Census
Articles and reports: 12-001-X202600100005
Description: Confidence intervals are very often constructed based on a probability distribution that uses a certain number of degrees of freedom as a parameter. This is the case with the Student and the modified Wilson confidence intervals, discussed in this article, which use quantiles from the Student distribution where the number of degrees of freedom is generally unknown. For the length of a confidence interval to be representative of the reliability of an estimate, the actual coverage rate must match the nominal rate. To that end, the number of degrees of freedom in the probability distribution used in practice to calculate the confidence interval must be estimated as precisely as possible. An approximate rule is often used, although it tends to overestimate the actual number of degrees of freedom. In this article, a more precise version of degrees of freedom, derived from the Satterthwaite approximation, is obtained in the context of the Canadian Census of Population. The sampling design is equivalent to a simple random design without replacement, cluster-stratified, and the variance estimation method is an adaptation of the balanced repeated replication method. An explicit expression of the degrees of freedom is obtained under these conditions, enabling the factors influencing them to be identified. For comparison, the degree of freedom formula is also established for the conventional variance estimator. A simulation study shows that using this version of degrees of freedom corrects the undercoverage problem observed with the approximate rule, showing the importance of accurately assessing this number.
Release date: 2026-06-29
3. The inverse-variance trap: A simple ratio fix for combining skewed data
Articles and reports: 12-001-X202600100009
Description: Combining estimates from independent surveys via inverse-variance weights can lead to negative bias when unknown variances are estimated and the target variable is non-negative and positively skewed. In such cases, strong positive correlations typically arise between the estimators and their corresponding variance estimators, causing standard linear combinations with inverse-variance weights to exhibit negative bias. We introduce a strikingly simple method to reduce bias: replace the standard weight with the ratio of the estimator to the variance estimator. Under a linear model linking the two, we show that the new ratio-weighted estimator is approximately unbiased, whereas the conventional inverse-variance combination exhibits downward bias. Through simulations, we demonstrate that the new method brings both the bias and the mean squared error closer to the optimum for a wide range of different target variables. As our method uses only standardly reported summary statistics, it can be immediately adopted to reduce this widespread bias and improve the reliability of scientific findings in various fields.
Release date: 2026-06-29
4. Variance of the generalized regression estimator under measurement error
Articles and reports: 12-001-X202600100010
Description: With the exception of two-phase sampling, the standard variance approximation of the generalized regression (GREG) estimator assumes that the population totals in the weighting scheme are observed without error. If the weighting model of the GREG estimator contains population totals that are observed with measurement error sources other than the sampling error of first-phase estimates, then this uncertainty will be ignored by the variance approximation of the GREG estimator. This paper proposes a variance approximation for the GREG estimator that accounts for additional uncertainty arising from measurement error in one or more of the population totals used in the weighting scheme. This approach has been developed for, and is being applied to, the Dutch Labour Force Survey (DLFS). The monthly publications of the DLFS are obtained with a time series model, which corrects for rotation group bias and discontinuities caused by major redesigns and the loss of face-to-face interviews during COVID-19. The GREG estimates for the quarterly figures are benchmarked to the average of the monthly publications to enforce numerical consistency between monthly and quarterly publication tables. The standard variance approximation of the GREG estimator assumes that these population totals are observed without error. This results in an underestimation of the variance of the GREG estimator. The variance approximation proposed in this paper results in more realistic standard errors for the quarterly GREG estimates.
Release date: 2026-06-29
5. Bayesian differential privacy for small counties and individual commodities
Articles and reports: 12-001-X202600100011
Description: We construct a hybrid Bayesian method, which includes a differentially private mechanism, to mask Census county totals for a U.S. state on acreage of a commodity. We use surrogates for data collected at the farm level from a past U.S. Census of Agriculture to illustrate our procedure. We use two Bayesian small area models (parametric and mixture) to accommodate the smaller counties with fewer farms and some counties with large acres. In these models, the Laplace distribution provides a differentially private mechanism. In pre-processing, we also incorporate the Census weights to form the observed total acreage, a scaling factor to the Laplace mechanism for each county, a square-root transformation of the observed total acreage to avoid negative masked estimates especially for small counties, and the p-percent rule and the 3+ rule to partition the counties into suppressed counties, non-sensitive counties and sensitive counties. Because of difficulties in specifying and tuning the privacy budget (an unknown parameter), to balance security and utility, we specify a prior for the privacy budget, where the values are not specified, and the Gibbs sampler is used to fit the hierarchical Bayesian models. In post-processing, we use Bayesian predictive inference to obtain masked county acreages, and this includes a benchmarking so that the masked state total matches the observed state total. As a measure of reliability of the Bayesian procedure, we use the posterior coefficients of variation for the masked posterior means of the counties. As a measure of utility, we use the absolute relative errors for the individual counties, together with other global measures. For the sensitive counties, there are some differences between the two small area models but both are much better than an individual area model; the mixture model being the best compromise for security and utility.
Release date: 2026-06-29
6. Small area estimation of general indicators in off-census years
Articles and reports: 12-001-X202600100012
Description: We propose small area estimators of general indicators in off-census years, which avoid the use of deprecated census microdata, but are nearly optimal in census years. The procedure is based on replacing the obsolete census file with a larger unit-level survey that adequately covers the areas of interest and contains the values of useful auxiliary variables. However, the minimal data requirement of the proposed method is a single survey with microdata on the target variable and suitable auxiliary variables for the period of interest. We also develop an estimator of the mean squared error (MSE) that accounts for the uncertainty introduced by the large survey used to replace the census of auxiliary information. Our empirical results indicate that the proposed predictors perform clearly better than the alternative predictors when census data are outdated, and are very close to optimal ones when census data are correct. They also illustrate that the proposed total MSE estimator corrects for the bias of purely model-based MSE estimators that do not account for the large survey uncertainty.
Release date: 2026-06-29
7. Effects of model misspecification on small area estimators
Articles and reports: 12-001-X202500200001
Description: Nested error regression models are commonly used to incorporate unit specific auxiliary variables to improve small area estimates. When the mean structure of the model is misspecified, the design-based mean squared prediction error (MSPE) of Empirical Best Linear Unbiased Predictors (EBLUP) generally increases. The Observed Best Prediction (OBP) method has been proposed with the intent to improve on the design-based MSPE over EBLUP. In this paper, we conduct a Monte Carlo simulation experiments to understand the effect of misspsecification of mean structures on different small area estimators. Our findings suggest that the OBP using unit-level auxiliary variables does not outperform the EBLUP in terms of design-based MSPE, unless the number of small areas m is extremely large. Conversely, the performance of OBP significantly improves when area-level auxiliary variables are employed. This paper includes both analytical and numerical evidence to demonstrate these observations, providing practical insights for addressing model misspecification in small area estimation (SAE).
Release date: 2025-12-23
8. Estimating monthly indicators for Consumer Confidence using Structural Time Series Models
Articles and reports: 12-001-X202500200003
Description: In this paper a model-based inference procedure based on a multivariate structural time series model is developed for the production of monthly figures about consumer confidence. The input for the model are five series of direct estimates for the indices that measure consumer confidence, which are derived from the Dutch Consumer Survey. The model improves the accuracy of the direct estimates, since it provides a better separation of measurement errors and sampling errors from estimated target parameters. The standard errors for the month-to-month changes are clearly smaller under the time series model. A second problem addressed in this paper is related to the transition to a new survey process in 2017. Structural time series models in combination with a parallel run are applied to estimate discontinuities induced by the redesign. An algorithm designed for the consumer confidence variables is developed to construct uninterrupted input series for the aforementioned structural time series model. This inference method facilitated a smooth transition to a new survey design and resulted in uninterrupted series about consumer confidence that date back to 1986. The method is implemented for the production of official monthly figures on consumer confidence in the Netherlands.
Release date: 2025-12-23
9. Quantile balancing inverse probability weighting for non-probability samples
Articles and reports: 12-001-X202500200005
Description: The use of non-probability data sources for statistical purposes and for official statistics has become increasingly popular in recent years. However, statistical inference based on non-probability samples is made more difficult by nature of their biasedness and lack of representativity. In this paper we propose quantile balancing inverse probability weighting estimator (QBIPW) for non-probability samples. We apply the idea of Harms and Duchesne (2006) allowing the use of quantile information in the estimation process to reproduce known totals and the distribution of auxiliary variables. We discuss the estimation of the QBIPW probabilities and its variance. Our simulation study has demonstrated that the proposed estimators are robust against model mis-specification and, as a result, help to reduce bias and mean squared error. Finally, we applied the proposed methods to estimate the share of job vacancies aimed at Ukrainian workers in Poland using an integrated set of administrative and survey data about job vacancies.
Release date: 2025-12-23
10. Improved small area inference from data integration using global-local priors
Articles and reports: 12-001-X202500200009
Description: We present and apply methodology to improve inference for small area parameters by using data from several sources. This work extends Cahoy and Sedransk (2023) who showed how to integrate summary statistics from several sources. Our methodology uses hierarchical global-local prior distributions to make inferences for the proportion of individuals in Florida’s counties who do not have health insurance. Results from an extensive simulation study show that this methodology will provide improved inference by using several data sources. Among the five model variants evaluated the ones using horseshoe priors for all variances have better performance than the ones using lasso priors for the local variances.
Release date: 2025-12-23

Reference (28)

Reference (28) (20 to 30 of 28 results)

21. Sampling and Weighting (Reference Products: Technical Reports: 1996 Census of Population) Archived
Surveys and statistical programs – Documentation: 92-371-X
Description:
This report deals with sampling and weighting, a process whereby certain characteristics are collected and processed for a random sample of dwellings and persons identified in the complete census enumeration. Data for the whole population are then obtained by scaling up the results for the sample to the full population level. The use of sampling may lead to substantial reductions in costs and respondent burden, or alternatively, can allow the scope of a census to be broadened at the same cost.
Release date: 1999-12-07
22. Random effects models for longitudinal data from complex samples Archived
Surveys and statistical programs – Documentation: 11-522-X19980015017
Description:
Longitudinal studies with repeated observations on individuals permit better characterizations of change and assessment of possible risk factors, but there has been little experience applying sophisticated models for longitudinal data to the complex survey setting. We present results from a comparison of different variance estimation methods for random effects models of change in cognitive function among older adults. The sample design is a stratified sample of people 65 and older, drawn as part of a community-based study designed to examine risk factors for dementia. The model summarizes the population heterogeneity in overall level and rate of change in cognitive function using random effects for intercept and slope. We discuss an unweighted regression including covariates for the stratification variables, a weighted regression, and bootstrapping; we also did preliminary work into using balanced repeated replication and jackknife repeated replication.
Release date: 1999-10-22
23. Weighting versus modeling in adjusting for non-response in the British Labour Force Survey: An application to gross flows estimation Archived
Surveys and statistical programs – Documentation: 11-522-X19980015019
Description:
The British Labour Force Survey (LFS) is a quarterly household survey with a rotating sample design that can potentially be used to produce longitudinal data, including estimates of labour force gross flows. However, these estimates may be biased due to the effect of non-response. Weighting adjustments are a commonly used method to account for non-response bias. We find that weighting may not fully account for the effect of non-response bias because non-response may depend on the unobserved labour force flows, i.e., the non-response is non-ignorable. To adjust for the effects of non-ignorable non-response, we propose a model for the complex non-response patterns in the LFS which controls for the correlated within-household non-response behaviour found in the survey. The results of modelling suggest that non-response may be non-ignorable in the LFS, causing the weighting estimates to be biased.
Release date: 1999-10-22
24. Calculation of weights for the European panel of households: A comparison of some indicators based on variables selected to correct for homogenous categorical non-response Archived
Surveys and statistical programs – Documentation: 11-522-X19980015020
Description:
At the end of 1993, Eurostat lauched a 'community' panel of households. The first wave, carried out in 1994 in the 12 countries of the European Union, included some 7,300 households in France, and at least 14,000 adults 17 years or over. Each individual was then followed up and interviewed each year, even if they had moved. The individuals leaving the sample present a particular profile. In the first part, we present a sketch of how our sample evolves and an analysis of the main characteristics of the non-respondents. We then propose 2 models to correct for non-response per homogeneous category. We then describe the longitudinal weight distribution obtained from the two models, and the cross-sectional weights using the weight share method. Finally, we compare some indicators calculated using both weighting methods.
Release date: 1999-10-22
25. Mobility matrices and computation of associated precision Archived
Surveys and statistical programs – Documentation: 11-522-X19980015023
Description:
The study of social mobility, between labour market statuses or between income levels, for example, is often based on the analysis of mobility matrices. When comparing these transition matrices, with a view to evaluating behavioural changes, one often forgets that the data derive from a sample survey and are therefore affected by sampling variances. Similarly, it is assumed that the responses collected correspond to the ' true value.'
Release date: 1999-10-22
26. Evaluating nonresponse adjustment in the Current Population Survey (CPS) using longitudinal data Archived
Surveys and statistical programs – Documentation: 11-522-X19980015026
Description:
The purpose of the present study is to utilize panel data from the Current Population Survey (CPS) to examine the effects of unit nonresponse. Because most nonrespondents to the CPS are respondents during at least one month-in-sample, data from other months can be used to compare the characteristics of complete respondents and panel nonrespondents and to evaluate nonresponse adjustment procedures. In the current paper we present analyses utilizing CPS panel data to illustrate the effects of unit nonresponse. After adjusting for nonresponse, additional comparisons are also made to evaluate the effects of nonresponse adjustment. The implications of the findings and suggestions for further research are discussed.
Release date: 1999-10-22
27. Variance estimation in longitudinal studies of income dynamics Archived
Surveys and statistical programs – Documentation: 11-522-X19980015028
Description:
We address the problem of estimation for the income dynamics statistics calculated from complex longitudinal surveys. In addition, we compare two design-based estimators of longitudinal proportions and transition rates in terms of variability under large attrition rates. One estimator is based on the cross-sectional samples for the estimation of the income class boundaries at each time period and on the longitudinal sample for the estimation of the longitudinal counts; the other estimator is entirely based on the longitudinal sample, both for the estimation of the class boundaries and the longitudinal counts. We develop Taylor linearization-type variance estimators for both the longitudinal and the mixed estimator under the assumption of no change in the population, and for the mixed estimator when there is change.
Release date: 1999-10-22
28. Weighting and variance estimation for the exploration of possible time trends in data from the U.S. Third National Health and Nutrition Examination Survey Archived
Surveys and statistical programs – Documentation: 11-522-X19980015031
Description:
The U.S. Third National Health and Nutrition Examination Survey (NHANES III) was carried out from 1988 to 1994. This survey was intended primarily to provide estimates of cross-sectional parameters believed to be approximately constant over the six-year data collection period. However, for some variable (e.g., serum lead, body mass index and smoking behavior), substantive considerations suggest the possible presence of nontrivial changes in level between 1988 and 1994. For these variables, NHANES III is potentially a valuable source of time-change information, compared to other studies involving more restricted populations and samples. Exploration of possible change over time is complicated by two issues. First, there was of practical concern because some variables displayed substantial regional differences in level. This was of practical concern because some variables displayed substantial regional differences in level. Second, nontrivial changes in level over time can lead to nontrivial biases in some customary NHANES III variance estimators. This paper considers these two problems and discusses some related implications for statistical policy.
Release date: 1999-10-22

Date modified:: 2026-09-12