On predicting the finite population distribution function
type: Item
instance of: scholarly article
title: On predicting the finite population distribution function
zbMATH Open document ID: 0802.62010
DOI: 10.1016/0167-7152(94)90187-2
author: Heleno Bolfarine
author: Mônica C. Sandoval
published in: Statistics \& Probability Letters
publication date: 1994-12-12T00:00:00Z
review text: Consider a finite population of size \(N\) with \(y_ 1, y_ 2, \dots, y_ N\) as values of a study variable \(y\). The finite population distribution function is defined by \[ F_ n(t)= N^{-1} \sum_{j=1}^ N \Delta(t- y_ j) \quad \text{where} \quad \Delta(x)=1 \text{ if } x\geq 0 \text{ and 0 otherwise}. \] The authors discuss the problem of optimal prediction of \(F_ N(t)\) under general linear regression models with normally distributed errors when the error variance is unknown and derive its best unbiased predictor as well as the asymptotic distribution. Under a simple location model the asymptotic relative efficiency of this predictor, relative to that of the ordinary sample empirical distribution function, is derived. Further, for some important special cases, large sample approximations for the prediction variances are obtained for the best unbiased predictors.
Mathematics Subject Classification ID: 62D05
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62E20
zbMATH DE Number: 571644
zbMATH Keywords: finite population
zbMATH Keywords: optimal prediction
zbMATH Keywords: normally distributed errors
zbMATH Keywords: error variance
zbMATH Keywords: best unbiased predictor
zbMATH Keywords: location model
zbMATH Keywords: asymptotic relative efficiency
zbMATH Keywords: ordinary sample empirical distribution function
zbMATH Keywords: sample approximations
zbMATH Keywords: prediction variances
reviewed by: T. J. Rao
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)90187-2
OpenAlex ID: W2037476274
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description: scientific article; zbMATH DE number 571644