A Bootstrap Variance Procedure for the Generalised Regression Estimator

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-10-19 DOI:10.1111/insr.12528

Marius Stefan, Michael A. Hidiroglou

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Abstract

The 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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广义回归估计量的自举方差法

广义回归估计器(GREG)使用从有限总体中可用的辅助数据来提高总(均值)估计器的效率。在抽样文献中提出的方差估计包括基于泰勒线性化和刀切技术的方差估计。基于泰勒展开的近似对于大样本是合理的。然而，当样本量较小时，基于泰勒的方差估计量具有较大的负偏差。对于小样本量，折刀方差估计器高估了GREG的方差。我们使用自举方法来估计GREG的方差来抵消这些挫折。该方法使用基于GREG估计器的模型构造的自举总体。根据用于选择初始样本的设计，在自举总体中选择重复样本，并使用与这些自举样本相关的可变性来计算提出的自举方差估计量。仿真结果表明，对于观测值较少的样本，新的自举估计器具有较小的偏差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.