Estimating the total of a continuous population
type: Item
instance of: scholarly article
title: Estimating the total of a continuous population
zbMATH Open document ID: 0603.62005
DOI: 10.1016/0378-3758(86)90119-9
author: Roy F. Bartlett
published in: Journal of Statistical Planning and Inference
publication date: 1986-01-01T00:00:00Z
review text: A continuous population on the real line may be considered as the realization y(t) of a random process Y(t) with a trend function and a covariance function. On the basis of sample values \(y(t_ 1),...,y(t_ n)\) it is natural to choose the estimator \(\hat T\) of the toal \(T=\int^{a}_{0}y(t)dt\) so that \(E[(\hat T-T)^ 2]\) is minimized. Various criteria for choosing the sample ofpoints and the estimator are discussed in this paper. One result is that for a constant trend and triangular covariance function \(\gamma (t)=C\cdot (1-| t| /a)\), the centered systematic sample and \(\hat T=a\sum y(t_ i)/n\) provide the optimal choice. A similar result is also given for the case of a quadratic trend.
Mathematics Subject Classification ID: 62D05
zbMATH DE Number: 3974034
zbMATH Keywords: estimation of the population total
zbMATH Keywords: predictive mean square error
zbMATH Keywords: minimum Xi-bias
zbMATH Keywords: survey sampling
zbMATH Keywords: superpopulation
zbMATH Keywords: systematic sampling
zbMATH Keywords: continuous population
zbMATH Keywords: constant trend
zbMATH Keywords: triangular covariance function
zbMATH Keywords: centered systematic sample
zbMATH Keywords: quadratic trend
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90119-9
OpenAlex ID: W2063940132
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description: scientific article; zbMATH DE number 3974034