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  • Articles and reports: 12-001-X202300100009
    Description: In this paper, with and without-replacement versions of adaptive proportional to size sampling are presented. Unbiased estimators are developed for these methods and their properties are studied. In the two versions, the drawing probabilities are adapted during the sampling process based on the observations already selected. To this end, in the version with-replacement, after each draw and observation of the variable of interest, the vector of the auxiliary variable will be updated using the observed values of the variable of interest to approximate the exact selection probability proportional to size. For the without-replacement version, first, using an initial sample, we model the relationship between the variable of interest and the auxiliary variable. Then, utilizing this relationship, we estimate the unknown (unobserved) population units. Finally, on these estimated population units, we select a new sample proportional to size without-replacement. These approaches can significantly improve the efficiency of designs not only in the case of a positive linear relationship, but also in the case of a non-linear or negative linear relationship between the variables. We investigate the efficiencies of the designs through simulations and real case studies on medicinal flowers, social and economic data.
    Release date: 2023-06-30

  • Articles and reports: 12-001-X202200100010
    Description:

    This study combines simulated annealing with delta evaluation to solve the joint stratification and sample allocation problem. In this problem, atomic strata are partitioned into mutually exclusive and collectively exhaustive strata. Each partition of atomic strata is a possible solution to the stratification problem, the quality of which is measured by its cost. The Bell number of possible solutions is enormous, for even a moderate number of atomic strata, and an additional layer of complexity is added with the evaluation time of each solution. Many larger scale combinatorial optimisation problems cannot be solved to optimality, because the search for an optimum solution requires a prohibitive amount of computation time. A number of local search heuristic algorithms have been designed for this problem but these can become trapped in local minima preventing any further improvements. We add, to the existing suite of local search algorithms, a simulated annealing algorithm that allows for an escape from local minima and uses delta evaluation to exploit the similarity between consecutive solutions, and thereby reduces the evaluation time. We compared the simulated annealing algorithm with two recent algorithms. In both cases, the simulated annealing algorithm attained a solution of comparable quality in considerably less computation time.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X201900300007
    Description:

    Finding the optimal stratification and sample size in univariate and multivariate sample design is hard when the population frame is large. There are alternative ways of modelling and solving this problem, and one of the most natural uses genetic algorithms (GA) combined with the Bethel-Chromy evaluation algorithm. The GA iteratively searches for the minimum sample size necessary to meet precision constraints in partitionings of atomic strata created by the Cartesian product of auxiliary variables. We point out a drawback with classical GAs when applied to the grouping problem, and propose a new GA approach using “grouping” genetic operators instead of traditional operators. Experiments show a significant improvement in solution quality for similar computational effort.

    Release date: 2019-12-17

  • Articles and reports: 12-001-X201800154929
    Description:

    The U.S. Census Bureau is investigating nonrespondent subsampling strategies for usage in the 2017 Economic Census. Design constraints include a mandated lower bound on the unit response rate, along with targeted industry-specific response rates. This paper presents research on allocation procedures for subsampling nonrespondents, conditional on the subsampling being systematic. We consider two approaches: (1) equal-probability sampling and (2) optimized allocation with constraints on unit response rates and sample size with the objective of selecting larger samples in industries that have initially lower response rates. We present a simulation study that examines the relative bias and mean squared error for the proposed allocations, assessing each procedure’s sensitivity to the size of the subsample, the response propensities, and the estimation procedure.

    Release date: 2018-06-21

  • Articles and reports: 12-001-X201600214660
    Description:

    In an economic survey of a sample of enterprises, occupations are randomly selected from a list until a number r of occupations in a local unit has been identified. This is an inverse sampling problem for which we are proposing a few solutions. Simple designs with and without replacement are processed using negative binomial distributions and negative hypergeometric distributions. We also propose estimators for when the units are selected with unequal probabilities, with or without replacement.

    Release date: 2016-12-20

  • Articles and reports: 12-001-X201500214237
    Description:

    Careful design of a dual-frame random digit dial (RDD) telephone survey requires selecting from among many options that have varying impacts on cost, precision, and coverage in order to obtain the best possible implementation of the study goals. One such consideration is whether to screen cell-phone households in order to interview cell-phone only (CPO) households and exclude dual-user household, or to take all interviews obtained via the cell-phone sample. We present a framework in which to consider the tradeoffs between these two options and a method to select the optimal design. We derive and discuss the optimum allocation of sample size between the two sampling frames and explore the choice of optimum p, the mixing parameter for the dual-user domain. We illustrate our methods using the National Immunization Survey, sponsored by the Centers for Disease Control and Prevention.

    Release date: 2015-12-17

  • Articles and reports: 12-001-X201400214090
    Description:

    When studying a finite population, it is sometimes necessary to select samples from several sampling frames in order to represent all individuals. Here we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. We apply the Hartley (1962), Bankier (1986) and Kalton and Anderson (1986) methods, and we show that these methods can be applied conditional on first-stage selection. We also compare the performance of several estimators as part of a simulation study. Our results suggest that the estimator should be chosen carefully when there are multiple sampling frames, and that a simple estimator is sometimes preferable, even if it uses only part of the information collected.

    Release date: 2014-12-19

  • Articles and reports: 12-001-X201100211607
    Description:

    This paper describes recent developments in adaptive sampling strategies and introduces new variations on those strategies. Recent developments described included targeted random walk designs and adaptive web sampling. These designs are particularly suited for sampling in networks; for example, for finding a sample of people from a hidden human population by following social links from sample individuals to find additional members of the hidden population to add to the sample. Each of these designs can also be translated into spatial settings to produce flexible new spatial adaptive strategies for sampling unevenly distributed populations. Variations on these sampling strategies include versions in which the network or spatial links have unequal weights and are followed with unequal probabilities.

    Release date: 2011-12-21

  • Articles and reports: 12-001-X201100211609
    Description:

    This paper presents a review and assessment of the use of balanced sampling by means of the cube method. After defining the notion of balanced sample and balanced sampling, a short history of the concept of balancing is presented. The theory of the cube method is briefly presented. Emphasis is placed on the practical problems posed by balanced sampling: the interest of the method with respect to other sampling methods and calibration, the field of application, the accuracy of balancing, the choice of auxiliary variables and ways to implement the method.

    Release date: 2011-12-21

  • Articles and reports: 12-001-X201000211385
    Description:

    In this short note, we show that simple random sampling without replacement and Bernoulli sampling have approximately the same entropy when the population size is large. An empirical example is given as an illustration.

    Release date: 2010-12-21
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  • Articles and reports: 12-001-X202300100009
    Description: In this paper, with and without-replacement versions of adaptive proportional to size sampling are presented. Unbiased estimators are developed for these methods and their properties are studied. In the two versions, the drawing probabilities are adapted during the sampling process based on the observations already selected. To this end, in the version with-replacement, after each draw and observation of the variable of interest, the vector of the auxiliary variable will be updated using the observed values of the variable of interest to approximate the exact selection probability proportional to size. For the without-replacement version, first, using an initial sample, we model the relationship between the variable of interest and the auxiliary variable. Then, utilizing this relationship, we estimate the unknown (unobserved) population units. Finally, on these estimated population units, we select a new sample proportional to size without-replacement. These approaches can significantly improve the efficiency of designs not only in the case of a positive linear relationship, but also in the case of a non-linear or negative linear relationship between the variables. We investigate the efficiencies of the designs through simulations and real case studies on medicinal flowers, social and economic data.
    Release date: 2023-06-30

  • Articles and reports: 12-001-X202200100010
    Description:

    This study combines simulated annealing with delta evaluation to solve the joint stratification and sample allocation problem. In this problem, atomic strata are partitioned into mutually exclusive and collectively exhaustive strata. Each partition of atomic strata is a possible solution to the stratification problem, the quality of which is measured by its cost. The Bell number of possible solutions is enormous, for even a moderate number of atomic strata, and an additional layer of complexity is added with the evaluation time of each solution. Many larger scale combinatorial optimisation problems cannot be solved to optimality, because the search for an optimum solution requires a prohibitive amount of computation time. A number of local search heuristic algorithms have been designed for this problem but these can become trapped in local minima preventing any further improvements. We add, to the existing suite of local search algorithms, a simulated annealing algorithm that allows for an escape from local minima and uses delta evaluation to exploit the similarity between consecutive solutions, and thereby reduces the evaluation time. We compared the simulated annealing algorithm with two recent algorithms. In both cases, the simulated annealing algorithm attained a solution of comparable quality in considerably less computation time.

    Release date: 2022-06-21

  • Articles and reports: 12-001-X201900300007
    Description:

    Finding the optimal stratification and sample size in univariate and multivariate sample design is hard when the population frame is large. There are alternative ways of modelling and solving this problem, and one of the most natural uses genetic algorithms (GA) combined with the Bethel-Chromy evaluation algorithm. The GA iteratively searches for the minimum sample size necessary to meet precision constraints in partitionings of atomic strata created by the Cartesian product of auxiliary variables. We point out a drawback with classical GAs when applied to the grouping problem, and propose a new GA approach using “grouping” genetic operators instead of traditional operators. Experiments show a significant improvement in solution quality for similar computational effort.

    Release date: 2019-12-17

  • Articles and reports: 12-001-X201800154929
    Description:

    The U.S. Census Bureau is investigating nonrespondent subsampling strategies for usage in the 2017 Economic Census. Design constraints include a mandated lower bound on the unit response rate, along with targeted industry-specific response rates. This paper presents research on allocation procedures for subsampling nonrespondents, conditional on the subsampling being systematic. We consider two approaches: (1) equal-probability sampling and (2) optimized allocation with constraints on unit response rates and sample size with the objective of selecting larger samples in industries that have initially lower response rates. We present a simulation study that examines the relative bias and mean squared error for the proposed allocations, assessing each procedure’s sensitivity to the size of the subsample, the response propensities, and the estimation procedure.

    Release date: 2018-06-21

  • Articles and reports: 12-001-X201600214660
    Description:

    In an economic survey of a sample of enterprises, occupations are randomly selected from a list until a number r of occupations in a local unit has been identified. This is an inverse sampling problem for which we are proposing a few solutions. Simple designs with and without replacement are processed using negative binomial distributions and negative hypergeometric distributions. We also propose estimators for when the units are selected with unequal probabilities, with or without replacement.

    Release date: 2016-12-20

  • Articles and reports: 12-001-X201500214237
    Description:

    Careful design of a dual-frame random digit dial (RDD) telephone survey requires selecting from among many options that have varying impacts on cost, precision, and coverage in order to obtain the best possible implementation of the study goals. One such consideration is whether to screen cell-phone households in order to interview cell-phone only (CPO) households and exclude dual-user household, or to take all interviews obtained via the cell-phone sample. We present a framework in which to consider the tradeoffs between these two options and a method to select the optimal design. We derive and discuss the optimum allocation of sample size between the two sampling frames and explore the choice of optimum p, the mixing parameter for the dual-user domain. We illustrate our methods using the National Immunization Survey, sponsored by the Centers for Disease Control and Prevention.

    Release date: 2015-12-17

  • Articles and reports: 12-001-X201400214090
    Description:

    When studying a finite population, it is sometimes necessary to select samples from several sampling frames in order to represent all individuals. Here we are interested in the scenario where two samples are selected using a two-stage design, with common first-stage selection. We apply the Hartley (1962), Bankier (1986) and Kalton and Anderson (1986) methods, and we show that these methods can be applied conditional on first-stage selection. We also compare the performance of several estimators as part of a simulation study. Our results suggest that the estimator should be chosen carefully when there are multiple sampling frames, and that a simple estimator is sometimes preferable, even if it uses only part of the information collected.

    Release date: 2014-12-19

  • Articles and reports: 12-001-X201100211607
    Description:

    This paper describes recent developments in adaptive sampling strategies and introduces new variations on those strategies. Recent developments described included targeted random walk designs and adaptive web sampling. These designs are particularly suited for sampling in networks; for example, for finding a sample of people from a hidden human population by following social links from sample individuals to find additional members of the hidden population to add to the sample. Each of these designs can also be translated into spatial settings to produce flexible new spatial adaptive strategies for sampling unevenly distributed populations. Variations on these sampling strategies include versions in which the network or spatial links have unequal weights and are followed with unequal probabilities.

    Release date: 2011-12-21

  • Articles and reports: 12-001-X201100211609
    Description:

    This paper presents a review and assessment of the use of balanced sampling by means of the cube method. After defining the notion of balanced sample and balanced sampling, a short history of the concept of balancing is presented. The theory of the cube method is briefly presented. Emphasis is placed on the practical problems posed by balanced sampling: the interest of the method with respect to other sampling methods and calibration, the field of application, the accuracy of balancing, the choice of auxiliary variables and ways to implement the method.

    Release date: 2011-12-21

  • Articles and reports: 12-001-X201000211385
    Description:

    In this short note, we show that simple random sampling without replacement and Bernoulli sampling have approximately the same entropy when the population size is large. An empirical example is given as an illustration.

    Release date: 2010-12-21
Reference (2)

Reference (2) ((2 results))

  • Surveys and statistical programs – Documentation: 89-631-X
    Description:

    This report highlights the latest developments and rationale behind recent cycles of the General Social Survey (GSS). Starting with an overview of the GSS mandate and historic cycle topics, we then focus on two recent cycles related to families in Canada: Family Transitions (2006) and Family, Social Support and Retirement (2007). Finally, we give a summary of what is to come in the 2008 GSS on Social Networks, and describe a special project to mark 'Twenty Years of GSS'.

    The survey collects data over a twelve month period from the population living in private households in the 10 provinces. For all cycles except Cycles 16 and 21, the population aged 15 and older has been sampled. Cycles 16 and 21 sampled persons aged 45 and older.

    Cycle 20 (GSS 2006) is the fourth cycle of the GSS to collect data on families (the first three cycles on the family were in 1990, 1995 and 2001). Cycle 20 covers much the same content as previous cycles on families with some sections revised and expanded. The data enable analysts to measure conjugal and fertility history (chronology of marriages, common-law unions, and children), family origins, children's home leaving, fertility intentions, child custody as well as work history and other socioeconomic characteristics. Questions on financial support agreements or arrangements (for children and the ex-spouse or ex-partner) for separated and divorced families have been modified. Also, sections on social networks, well-being and housing characteristics have been added.

    Release date: 2008-05-27

  • Surveys and statistical programs – Documentation: 11-522-X19980015022
    Description:

    This article extends and further develops the method proposed by Pfeffermann, Skinner and Humphreys (1998) for the estimation of gross flows in the presence of classification errors. The main feature of that method is the use of auxiliary information at the individual level which circumvents the need for validation data for estimating the misclassification rates. The new developments in this article are the establishment of conditions for model identification, a study of the properties of a model goodness of fit statistic and modifications to the sample likelihood to account for missing data and informative sampling. The new developments are illustrated by a small Monte-Carlo simulation study.

    Release date: 1999-10-22
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