Generalised regression estimation via the bootstrap. (8th April 2020)

• Record Type: Journal Article
• Authors: Booth, James G.; Welsh, Alan H.
• Is Part Of: Australian & New Zealand journal of statistics. Volume 62:Number 1(2020)
• Page Start: 5
• Page End: 24
• Publication Date: 2020-04-08
• Subjects: Bahadur expansion -- covariance -- double bootstrap -- Gini coefficient -- quantile estimation -- survey data; Statistics -- Periodicals; 519.5
• DOI: 10.1111/anzs.12282
• Languages: English
• ISSNs: 1369-1473

Abstract

Summary: A generalised regression estimation procedure is proposed that can lead to much improved estimation of population characteristics, such as quantiles, variances and coefficients of variation. The method involves conditioning on the discrepancy between an estimate of an auxiliary parameter and its known population value. The key distributional assumption is joint asymptotic normality of the estimates of the target and auxiliary parameters. This assumption implies that the relationship between the estimated target and the estimated auxiliary parameters is approximately linear with coefficients determined by their asymptotic covariance matrix. The main contribution of this paper is the use of the bootstrap to estimate these coefficients, which avoids the need for parametric distributional assumptions. First‐order correct conditional confidence intervals based on asymptotic normality can be improved upon using quantiles of a conditional double bootstrap approximation to the distribution of the studentised target parameter estimate. Abstract : The classical regression estimation method widely used in survey sampling for estimating a population mean is extended to general population characteristics.