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- Articles and reports: 12-001-X202300200011Description: The article considers sampling designs for populations that can be represented as a N × M matrix. For instance when investigating tourist activities, the rows could be locations visited by tourists and the columns days in the tourist season. The goal is to sample cells (i, j) of the matrix when the number of selections within each row and each column is fixed a priori. The ith row sample size represents the number of selected cells within row i; the jth column sample size is the number of selected cells within column j. A matrix sampling design gives an N × M matrix of sample indicators, with entry 1 at position (i, j) if cell (i, j) is sampled and 0 otherwise. The first matrix sampling design investigated has one level of sampling, row and column sample sizes are set in advance: the row sample sizes can vary while the column sample sizes are all equal. The fixed margins can be seen as balancing constraints and algorithms available for selecting such samples are reviewed. A new estimator for the variance of the Horvitz-Thompson estimator for the mean of survey variable y is then presented. Several levels of sampling might be necessary to account for all the constraints; this involves multi-level matrix sampling designs that are also investigated.Release date: 2024-01-03
- 2. Using balanced sampling in creel surveys ArchivedArticles and reports: 12-001-X201800254954Description:
These last years, balanced sampling techniques have experienced a recrudescence of interest. They constrain the Horvitz Thompson estimators of the totals of auxiliary variables to be equal, at least approximately, to the corresponding true totals, to avoid the occurrence of bad samples. Several procedures are available to carry out balanced sampling; there is the cube method, see Deville and Tillé (2004), and an alternative, the rejective algorithm introduced by Hájek (1964). After a brief review of these sampling methods, motivated by the planning of an angler survey, we investigate using Monte Carlo simulations, the survey designs produced by these two sampling algorithms.
Release date: 2018-12-20 - Articles and reports: 12-001-X201100111447Description:
This paper introduces a R-package for the stratification of a survey population using a univariate stratification variable X and for the calculation of stratum sample sizes. Non iterative methods such as the cumulative root frequency method and the geometric stratum boundaries are implemented. Optimal designs, with stratum boundaries that minimize either the CV of the simple expansion estimator for a fixed sample size n or the n value for a fixed CV can be constructed. Two iterative algorithms are available to find the optimal stratum boundaries. The design can feature a user defined certainty stratum where all the units are sampled. Take-all and take-none strata can be included in the stratified design as they might lead to smaller sample sizes. The sample size calculations are based on the anticipated moments of the survey variable Y, given the stratification variable X. The package handles conditional distributions of Y given X that are either a heteroscedastic linear model, or a log-linear model. Stratum specific non-response can be accounted for in the design construction and in the sample size calculations.
Release date: 2011-06-29 - 4. A generalization of the Lavallée and Hidiroglou algorithm for stratification in business Surveys ArchivedArticles and reports: 12-001-X20020026432Description:
This paper suggests stratification algorithms that account for a discrepancy between the stratification variable and the study variable when planning a stratified survey design. Two models are proposed for the change between these two variables. One is a log-linear regression model; the other postulates that the study variable and the stratification variable coincide for most units, and that large discrepancies occur for some units. Then, the Lavallée and Hidiroglou (1988) stratification algorithm is modified to incorporate these models in the determination of the optimal sample sizes and of the optimal stratum boundaries for a stratified sampling design. An example illustrates the performance of the new stratification algorithm. A discussion of the numerical implementation of this algorithm is also presented.
Release date: 2003-01-29 - Articles and reports: 12-001-X20000015179Description:
This paper suggests estimating the conditional mean squared error of small area estimators to evaluate their accuracy. This mean squared error is conditional in the sense that it measures the variability with respect to the sampling design for a particular realization of the smoothing model underlying the small area estimators. An unbiased estimators for the conditional mean squared error is easily constructed using Stein's Lemma for the expectation of normal random variables.
Release date: 2000-08-30 - Articles and reports: 12-001-X199500214399Description:
This paper considers the winsorized mean as an estimator of the mean of a positive skewed population. A winsorized mean is obtained by replacing all the observations larger than some cut-off value R by R before averaging. The optimal cut-off value, as defined by Searls (1966), minimizes the mean square error of the winsorized estimator. Techniques are proposed for the evaluation of this optimal cut-off in several sampling designs including simple random sampling, stratified sampling and sampling with probability proportional to size. For most skewed distributions, the optimal winsorization strategy is shown, on average, to modify the value of about one data point in the sample. Closed form approximations to the efficiency of Searls’ winsorized mean are derived using the theory of extreme order statistics. Various estimators reducing the impact of large data values are compared in a Monte Carlo experiment.
Release date: 1995-12-15
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Articles and reports (6)
Articles and reports (6) ((6 results))
- Articles and reports: 12-001-X202300200011Description: The article considers sampling designs for populations that can be represented as a N × M matrix. For instance when investigating tourist activities, the rows could be locations visited by tourists and the columns days in the tourist season. The goal is to sample cells (i, j) of the matrix when the number of selections within each row and each column is fixed a priori. The ith row sample size represents the number of selected cells within row i; the jth column sample size is the number of selected cells within column j. A matrix sampling design gives an N × M matrix of sample indicators, with entry 1 at position (i, j) if cell (i, j) is sampled and 0 otherwise. The first matrix sampling design investigated has one level of sampling, row and column sample sizes are set in advance: the row sample sizes can vary while the column sample sizes are all equal. The fixed margins can be seen as balancing constraints and algorithms available for selecting such samples are reviewed. A new estimator for the variance of the Horvitz-Thompson estimator for the mean of survey variable y is then presented. Several levels of sampling might be necessary to account for all the constraints; this involves multi-level matrix sampling designs that are also investigated.Release date: 2024-01-03
- 2. Using balanced sampling in creel surveys ArchivedArticles and reports: 12-001-X201800254954Description:
These last years, balanced sampling techniques have experienced a recrudescence of interest. They constrain the Horvitz Thompson estimators of the totals of auxiliary variables to be equal, at least approximately, to the corresponding true totals, to avoid the occurrence of bad samples. Several procedures are available to carry out balanced sampling; there is the cube method, see Deville and Tillé (2004), and an alternative, the rejective algorithm introduced by Hájek (1964). After a brief review of these sampling methods, motivated by the planning of an angler survey, we investigate using Monte Carlo simulations, the survey designs produced by these two sampling algorithms.
Release date: 2018-12-20 - Articles and reports: 12-001-X201100111447Description:
This paper introduces a R-package for the stratification of a survey population using a univariate stratification variable X and for the calculation of stratum sample sizes. Non iterative methods such as the cumulative root frequency method and the geometric stratum boundaries are implemented. Optimal designs, with stratum boundaries that minimize either the CV of the simple expansion estimator for a fixed sample size n or the n value for a fixed CV can be constructed. Two iterative algorithms are available to find the optimal stratum boundaries. The design can feature a user defined certainty stratum where all the units are sampled. Take-all and take-none strata can be included in the stratified design as they might lead to smaller sample sizes. The sample size calculations are based on the anticipated moments of the survey variable Y, given the stratification variable X. The package handles conditional distributions of Y given X that are either a heteroscedastic linear model, or a log-linear model. Stratum specific non-response can be accounted for in the design construction and in the sample size calculations.
Release date: 2011-06-29 - 4. A generalization of the Lavallée and Hidiroglou algorithm for stratification in business Surveys ArchivedArticles and reports: 12-001-X20020026432Description:
This paper suggests stratification algorithms that account for a discrepancy between the stratification variable and the study variable when planning a stratified survey design. Two models are proposed for the change between these two variables. One is a log-linear regression model; the other postulates that the study variable and the stratification variable coincide for most units, and that large discrepancies occur for some units. Then, the Lavallée and Hidiroglou (1988) stratification algorithm is modified to incorporate these models in the determination of the optimal sample sizes and of the optimal stratum boundaries for a stratified sampling design. An example illustrates the performance of the new stratification algorithm. A discussion of the numerical implementation of this algorithm is also presented.
Release date: 2003-01-29 - Articles and reports: 12-001-X20000015179Description:
This paper suggests estimating the conditional mean squared error of small area estimators to evaluate their accuracy. This mean squared error is conditional in the sense that it measures the variability with respect to the sampling design for a particular realization of the smoothing model underlying the small area estimators. An unbiased estimators for the conditional mean squared error is easily constructed using Stein's Lemma for the expectation of normal random variables.
Release date: 2000-08-30 - Articles and reports: 12-001-X199500214399Description:
This paper considers the winsorized mean as an estimator of the mean of a positive skewed population. A winsorized mean is obtained by replacing all the observations larger than some cut-off value R by R before averaging. The optimal cut-off value, as defined by Searls (1966), minimizes the mean square error of the winsorized estimator. Techniques are proposed for the evaluation of this optimal cut-off in several sampling designs including simple random sampling, stratified sampling and sampling with probability proportional to size. For most skewed distributions, the optimal winsorization strategy is shown, on average, to modify the value of about one data point in the sample. Closed form approximations to the efficiency of Searls’ winsorized mean are derived using the theory of extreme order statistics. Various estimators reducing the impact of large data values are compared in a Monte Carlo experiment.
Release date: 1995-12-15
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