Bounds on generalized linear predictors with incomplete outcome data
type: Item
instance of: scholarly article
title: Bounds on generalized linear predictors with incomplete outcome data
zbMATH Open document ID: 1120.65007
author: Jörg Stoye
published in: Reliable Computing
publication date: 2007-04-19T00:00:00Z
review text: The generalized linear predictors for a response \(Y\) are considered of the form \(\widehat Y=G(X\vartheta)\), where \(X\) is the explanatory variables vector, \(G\) is some pre-assigned strictly increasing function, \(\vartheta\) is a vector of coefficients (to be determined). The best \(\vartheta\) (for the quadratic loss function) is \(\vartheta=(\mathbf{E}X'X)^{-1}\text\textbf{E}X'G^{-1}(X)\). The paper is devoted to the bounds for \(c'\vartheta\) (\(c\) being a fixed vector) in the case when lower and upper bounds \(\overline F\) and \(\underline{F}\) for the conditional CDF \(F_{Y| X}(y,x)\) are known, i.e., \(\underline{F}(y,x)\leq F_{Y| X}(y,x)\leq \overline F(y,x)\) for all \(x\) and \(y\). The obtained bounds are used for estimation of \(\vartheta\) in the case of missing values of \(Y\) in the sample. A real data example is presented.
Mathematics Subject Classification ID: 65C50
Mathematics Subject Classification ID: 60G25
Mathematics Subject Classification ID: 65C40
zbMATH DE Number: 5145086
zbMATH Keywords: instrumental variable estimator
zbMATH Keywords: square loss
zbMATH Keywords: missing outcome data
zbMATH Keywords: numerical examples
zbMATH Keywords: generalized linear predictors
reviewed by: R. E. Maiboroda
MaRDI profile type: Publication
full work available at URL: s11155-006-9030-5
OpenAlex ID: W2085395303
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DOI: 10.1007/S11155-006-9030-5
description: scientific article; zbMATH DE number 5145086