Analysis

Description: This article examines the methodological complexities associated with the design of business surveys, with particular emphasis on sampling strategies implemented by National Statistical Offices (NSOs). It addresses the inherent challenges posed by the dynamic nature of the business population, which necessitates continual updates to the sampling frame to ensure representativeness and relevance. Critical design considerations include the determination of optimal sample sizes, stratification across key dimensions such as industry, geographic region, and enterprise size, as well as the treatment of business births and the exclusion of inactive (or “dead”) units. The article applies Bankier’s (1988) power allocation method to a two-way stratification scheme defined by industry and geography, evaluating its performance by comparing the resulting coefficients of variation with those obtained via a raking algorithm applied to the marginal coefficients. Furthermore, the approach is extended to a multivariate context to accommodate multiple estimation domains. The discussion also encompasses practical issues related to sample rotation and coordination, which are critical for maintaining data quality and minimizing respondent burden over time.

Description:

The synthetic estimator (SYN) has been traditionally used to estimate characteristics of small domains. Although it has the advantage of a small variance, it can be seriously biased in some small domains which depart in structure from the overall domains. Särndal (1981) introduced the regression estimator (REG) in the context of domain estimation. This estimator is nearly unbiased, however, it has two drawbacks; (i) its variance can be considerable in some small domains and (ii) it can take on negative values in situations that do not allow such values.

In this paper, we report on a compromise estimator which strikes a balance between the two estimators SYN and REG. This estimator, called the modified regression estimator (MRE), has the advantage of a considerably reduced variance compared to the REG estimator and has a smaller Mean Squared Error than the SYN estimator in domains where the latter is badly biased. The MRE estimator eliminates the drawback with negative values mentioned above. These results are supported by a Monte Carlo study involving 500 samples.

Description:

Goodness of fit tests, tests for independence in a two-way contingency table, log-linear models and logistic regression models are investigated in the context of samples which are obtained from complex survey designs. Suggested approximations to the null distributions are reviewed and some examples from the Canada Health Survey and Canadian Labour Force Survey are given. Software implementation for using these methods is briefly discussed.

Description: Statistics on sales of establishments classified as restaurants, caterers and taverns have been collected since 1951. The sample has not been updated for births since 1968 and as a result, it is not representative of the current universe. This paper reports on several methodological aspects of the redesign. The sampling unit, sample design, sample size and allocation, data collection methods, edits and imputations, accumulations and calculations, frame and sample maintenance are described. The new survey will reduce manual procedures wherever possible. Collection, editing, imputation, tabulation and updating procedures will be completely computerized. Data collection will be decentralized and will take place via telephone.

Description: Approximate cutoff rules for stratifying a population into a take-all and take-some universe have been given by Dalenius (1950) and Glasser (1962). They expressed the cutoff value (that value which delineates the boundary of the take-all and take-some) as a function of the mean, the sampling weight and the population variance. Their cutoff values were derived on the assumption that a single random sample of size n was to be drawn without replacement from the population of size N.

In the present context, exact and approximate cutoff rules have been worked out for a similar situation. Rather than providing the sample size of the sample, the precision (coefficient of variation) is given. Note that in many sampling situations, the sampler is given a set of objectives in terms of reliability and not sample size. The result is particularly useful for determining the take-all - take-some boundary for samples drawn from a known population. The procedure is also extended to ratio estimation.

Description: This article describes briefly the methodology of the Occupational Employment Survey, which has been conducted every second year since 1973. The article presents the scope of the survey, the sampling plan and the estimation procedure.

Description: In multi-stage sampling when selection is without replacement at the first stage, estimation of the variance of the estimate of the population total is often done assuming sampling with replacement. This estimate is biased and the degree of bias is not negligible. In this paper, a procedure which gives unbiased estimates of the variance making use of only estimated primary sampling unit totals is suggested for the case when sampling at the second and subsequent stages is simple random without replacement. This procedure is based on sub-samples drawn from the selected second and subsequent stage units.

Description: The problem considered is the estimation of population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators which alter the usual sampling weights have been considered. The efficiencies of these estimators have been worked out in terms of the ratio of the variance of the usual estimator of the population total to the mean square error of these estimators. An empirical study of these estimators is also discussed.

Description: The negative moments of the positive hypergeometric distribution are often approximated by the inverse of the positive moments of this distribution. In this paper, a suitable approximation to the positive hypergeometric distribution is used to obtain the negative moments.

Description: J.N.K. Rao (1975) derived a general formula for estimating the variance in multistage sample designs. This general formula extends the previous results by Des Raj (1966) to the case where the conditional variance from a given primary sampling unit is a random variable. The authors reviewed Rao's paper for its application to Horvitz-Thompson and Yates-Grundy variance estimators as well as the variance estimator for the random group method by Rao, Hartley and Cochran (1962). The authors present an altered version of the Yates-Grundy variance estimators as a result of Rao's paper.

Description: This article examines the methodological complexities associated with the design of business surveys, with particular emphasis on sampling strategies implemented by National Statistical Offices (NSOs). It addresses the inherent challenges posed by the dynamic nature of the business population, which necessitates continual updates to the sampling frame to ensure representativeness and relevance. Critical design considerations include the determination of optimal sample sizes, stratification across key dimensions such as industry, geographic region, and enterprise size, as well as the treatment of business births and the exclusion of inactive (or “dead”) units. The article applies Bankier’s (1988) power allocation method to a two-way stratification scheme defined by industry and geography, evaluating its performance by comparing the resulting coefficients of variation with those obtained via a raking algorithm applied to the marginal coefficients. Furthermore, the approach is extended to a multivariate context to accommodate multiple estimation domains. The discussion also encompasses practical issues related to sample rotation and coordination, which are critical for maintaining data quality and minimizing respondent burden over time.

Description:

The synthetic estimator (SYN) has been traditionally used to estimate characteristics of small domains. Although it has the advantage of a small variance, it can be seriously biased in some small domains which depart in structure from the overall domains. Särndal (1981) introduced the regression estimator (REG) in the context of domain estimation. This estimator is nearly unbiased, however, it has two drawbacks; (i) its variance can be considerable in some small domains and (ii) it can take on negative values in situations that do not allow such values.

In this paper, we report on a compromise estimator which strikes a balance between the two estimators SYN and REG. This estimator, called the modified regression estimator (MRE), has the advantage of a considerably reduced variance compared to the REG estimator and has a smaller Mean Squared Error than the SYN estimator in domains where the latter is badly biased. The MRE estimator eliminates the drawback with negative values mentioned above. These results are supported by a Monte Carlo study involving 500 samples.

Description:

Goodness of fit tests, tests for independence in a two-way contingency table, log-linear models and logistic regression models are investigated in the context of samples which are obtained from complex survey designs. Suggested approximations to the null distributions are reviewed and some examples from the Canada Health Survey and Canadian Labour Force Survey are given. Software implementation for using these methods is briefly discussed.

Description: Statistics on sales of establishments classified as restaurants, caterers and taverns have been collected since 1951. The sample has not been updated for births since 1968 and as a result, it is not representative of the current universe. This paper reports on several methodological aspects of the redesign. The sampling unit, sample design, sample size and allocation, data collection methods, edits and imputations, accumulations and calculations, frame and sample maintenance are described. The new survey will reduce manual procedures wherever possible. Collection, editing, imputation, tabulation and updating procedures will be completely computerized. Data collection will be decentralized and will take place via telephone.

Description: Approximate cutoff rules for stratifying a population into a take-all and take-some universe have been given by Dalenius (1950) and Glasser (1962). They expressed the cutoff value (that value which delineates the boundary of the take-all and take-some) as a function of the mean, the sampling weight and the population variance. Their cutoff values were derived on the assumption that a single random sample of size n was to be drawn without replacement from the population of size N.

In the present context, exact and approximate cutoff rules have been worked out for a similar situation. Rather than providing the sample size of the sample, the precision (coefficient of variation) is given. Note that in many sampling situations, the sampler is given a set of objectives in terms of reliability and not sample size. The result is particularly useful for determining the take-all - take-some boundary for samples drawn from a known population. The procedure is also extended to ratio estimation.

Description: This article describes briefly the methodology of the Occupational Employment Survey, which has been conducted every second year since 1973. The article presents the scope of the survey, the sampling plan and the estimation procedure.

Description: In multi-stage sampling when selection is without replacement at the first stage, estimation of the variance of the estimate of the population total is often done assuming sampling with replacement. This estimate is biased and the degree of bias is not negligible. In this paper, a procedure which gives unbiased estimates of the variance making use of only estimated primary sampling unit totals is suggested for the case when sampling at the second and subsequent stages is simple random without replacement. This procedure is based on sub-samples drawn from the selected second and subsequent stage units.

Description: The problem considered is the estimation of population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators which alter the usual sampling weights have been considered. The efficiencies of these estimators have been worked out in terms of the ratio of the variance of the usual estimator of the population total to the mean square error of these estimators. An empirical study of these estimators is also discussed.

Description: The negative moments of the positive hypergeometric distribution are often approximated by the inverse of the positive moments of this distribution. In this paper, a suitable approximation to the positive hypergeometric distribution is used to obtain the negative moments.

Description: J.N.K. Rao (1975) derived a general formula for estimating the variance in multistage sample designs. This general formula extends the previous results by Des Raj (1966) to the case where the conditional variance from a given primary sampling unit is a random variable. The authors reviewed Rao's paper for its application to Horvitz-Thompson and Yates-Grundy variance estimators as well as the variance estimator for the random group method by Rao, Hartley and Cochran (1962). The authors present an altered version of the Yates-Grundy variance estimators as a result of Rao's paper.