Estimating coefficient distributions in random coefficient regressions
type: Item
instance of: scholarly article
title: Estimating coefficient distributions in random coefficient regressions
zbMATH Open document ID: 0774.62068
author: Rudolf Beran
author: Peter Hall
published in: The Annals of Statistics
publication date: 1993-05-16T00:00:00Z
review text: The model is \(Y_ j=a+(b+j)x_ j+e_ j\), \(j=1,2,\dots\) where \(E(b_ j)=E(e_ j)=0\), the \(b_ 1,e_ 1,b_ 2,e_ 2,\dots\) are independent and \(\{b_ 1,b_ 2,\dots\}\) as well as \(\{e_ 1,e_ 2,\dots\}\) are i.i.d. The authors study the estimation of the distribution of \(b_ j\) and \(e_ j\), respectively, for resampling purposes. At first questions of identifiability and consistent estimability of the distributions are discussed. A variety of methods, among them least squares and ``efficient'' estimation are put forward in order to estimate a finite number of moments of \(b_ j\) and \(e_ j\), respectively. From the estimated moments four methods of estimating the distributions are proposed, among them two methods due to Hausdorff (1923). This leads to a computational algorithm. A numerical example is given; proofs are deferred to the appendix. Two critical remarks: The reference Pollard (1984) is not contained in the bibliography. The authors claim that \(a\) and \(b\) can be estimated ``under very general circumstances'' consistently by least squares. But these ``general circumstances'' include necessary and sufficient conditions on the asymptotic behaviour of the regression matrices.
reviewed by: Hilmar Drygas
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62G07
zbMATH DE Number: 166848
zbMATH Keywords: resampling
zbMATH Keywords: identifiability
zbMATH Keywords: consistent estimability
zbMATH Keywords: least squares
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176348898
OpenAlex ID: W2050852339
DOI: 10.1214/AOS/1176348898
description: scientific article; zbMATH DE number 166848