Pseudo-population bootstrap methods for imputed survey data

Chen, S; Haziza, David; Léger, Christian; Mashreghi, Zeinab

doi:10.1093/biomet/asz001

Cited by 16 publications

(6 citation statements)

References 37 publications

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“…Pseudo population procedures are not new. They are, for example, often used in the area of resampling variance estimation (see, for example, Gross (1980), Bickel and Freedman (1984) or Chen et al (2019)). In the present study, we apply the pseudo population approach to the estimation of cell population sizes that are, for example, needed for the MRP approach.…”

Section: General Proceduresmentioning

confidence: 99%

An Approximation of Joint Distributions of Weighting Variables Using a Pseudo Population Approach

Bruch,

Felderer

2024

Preprint

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Several weighting techniques require joint distributions of weighting variables on apopulation level in order to adjust for the selectivity in the participation process of the survey. Inpractical applications, joint distributions are frequently not available and population margins arethe only information available to inform the weighting procedure. We propose a novel approachto estimate the population sizes of weighting cells based on a pseudo population that was constructedusing a copula. The approach makes use of population margins of weighting variablesand their correlations. We show how the approach can be used for poststratification and multilevelregression and poststratification approaches and illustrate the usefulness in a simulationstudy and an empirical example. Using the copula pseudo population approach in combinationwith multilevel regression and poststratification for highly selective data strongly improves thesurvey estimation as compared to traditional raking and poststratification methods in our study.

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Section: General Proceduresmentioning

confidence: 99%

An Approximation of Joint Distributions of Weighting Variables Using a Pseudo Population Approach

Bruch,

Felderer

2024

Preprint

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“…Furthermore, on average, these residuals are similar in terms of variability if

{\overset{true^}{D}}_{0}^{2}

is approximately unbiased for

D_{0}^{2}

, or equivalently, if the estimator

{\overset{true^}{D}}_{E}^{2}

D_{E}^{2}

has little or no bias. Using

({},, {\overset{true^}{y}}_{k}^{0} : k = 1 \dots N)

and

({},, E_{k}^{*} : k = 1 \dots N)

, we define the

{y_{k}^{*}}^{'} normals

U^{*}

y_{k}^{*} goodbreak= {\overset{true^}{y}}_{k}^{0} goodbreak+ E_{k}^{*}, k goodbreak= 1, \dots, N .

Chen et al (2019) proposed a pseudo‐population bootstrap procedure for estimating the variance of imputed estimators. Their bootstrap population is based on Equation (20), where the set of residuals

({},, E_{k}^{*} : k = 1 \dots N)

represents an independent and identically distributed sample of size N selected from

({},, {\overset{true˜}{e}}_{ks} : k = 1 \dots n)

, and the

{\overset{e}{true}}_{italicks}^{'} normals

are some standardised centred versions of residuals

{e_{italicks}}^{'} normals

, for

k \in s

.…”

Section: Bootstrapping Proceduresmentioning

confidence: 99%

A Bootstrap Variance Procedure for the Generalised Regression Estimator

Stefan

Hidiroglou

2022

Int Statistical Rev

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SummaryThe generalised regression estimator (GREG) uses auxiliary data that are available from the finite population to improve the efficiency of the estimator of a total (mean). Estimators of the variance of GREG that have been proposed in the sampling literature include those based on Taylor linearisation and the jackknife techniques. Approximations based on Taylor expansions are reasonable for large samples. However, when the sample size is small, the Taylor‐based variance estimator has a large negative bias. The jackknife variance estimators overestimate the variance of GREG for small sample sizes. We offset these setbacks using a bootstrap procedure for estimating the variance of the GREG. The method uses a bootstrap population constructed with the model underlying the GREG estimator. Repeated samples are selected in the bootstrap population according to the design used to select the initial sample, and the variability associated with these bootstrap samples is used to compute the proposed bootstrap variance estimator. Simulations show that the new bootstrap estimator has a small bias for samples that have few observations.

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“…Sverchkov and Pfeffermann (2004) used a multinomial distribution to generate a fixed bootstrap finite population. Chen et al (2019) proposed two pseudo‐population bootstrap methods for handling missing data problems in survey sampling, and argued that their methods are widely applicable.…”

Section: Introductionmentioning

confidence: 99%

Bootstrap Inference for the Finite Population Mean under Complex Sampling Designs

Wang

Peng²,

Kim³

2022

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Bootstrap is a useful computational tool for statistical inference, but it may lead to erroneous analysis under complex survey sampling. In this paper, we propose a unified bootstrap method for stratified multi‐stage cluster sampling, Poisson sampling, simple random sampling without replacement and probability proportional to size sampling with replacement. In the proposed bootstrap method, we first generate bootstrap finite populations, apply the same sampling design to each bootstrap population to get a bootstrap sample, and then apply studentization. The second‐order accuracy of the proposed bootstrap method is established by the Edgeworth expansion. Simulation studies confirm that the proposed bootstrap method outperforms the commonly used Wald‐type method in terms of coverage, especially when the sample size is not large.

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Pseudo-population bootstrap methods for imputed survey data

Cited by 16 publications

References 37 publications

An Approximation of Joint Distributions of Weighting Variables Using a Pseudo Population Approach

An Approximation of Joint Distributions of Weighting Variables Using a Pseudo Population Approach

A Bootstrap Variance Procedure for the Generalised Regression Estimator

Bootstrap Inference for the Finite Population Mean under Complex Sampling Designs

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