Approximate optimal allocation in repeated sampling from a finite population
type: Item
instance of: scholarly article
title: Approximate optimal allocation in repeated sampling from a finite population
zbMATH Open document ID: 0579.62008
DOI: 10.1016/0378-3758(85)90001-1
published in: Journal of Statistical Planning and Inference
publication date: 1985-01-01T00:00:00Z
review text: Consider a finite population of size N. Let samples of size n be drawn on each of two occasions. On the first occasion, an auxiliary variable x is measured and on the second occasion the study variable y is measured. Let \(\bar Y\) be the population mean of y. For estimating \(\bar Y\), one considers the best linear unbiased combination of means for the matched and unmatched samples by minimising V(\(\hat{\bar Y})\) with respect to the sampling design on the second occasion. This optimum allocation depends on the population correlation coefficient \(\rho\) which is usually assumed to be known from past experience or pilot studies. The author estimates \(\rho\) from an initial matched sample and then an approximately optimum allocation is obtained for which the corresponding estimator is suggested. Under a bivariate normal superpopulation model assumption, this suggested estimator has model expected m.s.e. equal to the minimum model m.s.e. of any linear unbiased estimate apart from an error of order \(n^{-2}\).
Mathematics Subject Classification ID: 62D05
zbMATH DE Number: 3928077
zbMATH Keywords: repeated sampling
zbMATH Keywords: simple random sampling
zbMATH Keywords: mean square error
zbMATH Keywords: finite population
zbMATH Keywords: best linear unbiased combination of means
zbMATH Keywords: optimum allocation
zbMATH Keywords: population correlation coefficient
zbMATH Keywords: matched sample
zbMATH Keywords: bivariate normal superpopulation model
author: Peter M. Robinson
reviewed by: T. J. Rao
MaRDI profile type: Publication
full work available at URL: 0378-3758(85)90001-1
OpenAlex ID: W2082306615
cites work: Q5819795
cites work: Q3227961
cites work: Q3957768
cites work: Q5823902
cites work: Some Problems of Optimum Allocation for Sampling on Two Occasions
cites work: Q3889908
cites work: Q5649819
Wikidata QID: Q128040210
description: scientific article; zbMATH DE number 3928077