Plane sampling
type: Item
instance of: scholarly article
title: Plane sampling
zbMATH Open document ID: 0592.62013
DOI: 10.1016/0167-7152(85)90054-9
author: Ronaldo Iachan
published in: Statistics \& Probability Letters
publication date: 1985-01-01T00:00:00Z
review text: Consider a population of \(N=N_ 1\cdot N_ 2\) units arranged in a grid of \(N_ 1=n_ 1\cdot k_ 1\) rows and \(N_ 2=n_ 2\cdot k_ 2\) columns. The population mean is estimated by the sample mean and the efficiency of various sample designs is compared when the population size N and the sample size n tend to infinity in such a way that the ratio N/n is constant. Samples aligned in both directions and unaligned samples are studied. The population values are assumed to arise as a realization of a spatial process, stationary in the wide sense with a non-negative autocorrelation function \(\rho\) being non-increasing in both arguments. Assuming that the correlation function \(\rho\) satisfies \[ \sum_{u}\sum_{v}\rho (| u|,| v|)<\infty \] it is shown, both for unaligned and aligned designs, that systematic sampling is at least as good as stratified sampling which is at least as good as simple random sampling. Under an additional assumption about weak dependence of the spatial process generating the population, asymptotic normality of the aligned systematic sample mean is shown.
Mathematics Subject Classification ID: 62D05
zbMATH DE Number: 3951779
zbMATH Keywords: plane sampling
zbMATH Keywords: spatial process
zbMATH Keywords: systematic sampling
zbMATH Keywords: stratified sampling
zbMATH Keywords: simple random sampling
zbMATH Keywords: asymptotic normality
describes a project that uses: spatial
MaRDI profile type: Publication
full work available at URL: 0167-7152(85)90054-9
OpenAlex ID: W4234604552
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description: scientific article; zbMATH DE number 3951779