Linear least squares estimates and nonlinear means

Roger L. Berger; Naftali A. Langberg

doi:10.1016/0378-3758(84)90054-5

Linear least squares estimates and nonlinear means

Roger L. Berger, Naftali A. Langberg

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

The consistency and asymptotic normality of a linear least squares estimate of the form (X'X)^-X'Y when the mean is not Xβ is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not be the best linear approximation of the true mean function. Choices of designs which allow large sample inferences to be made about the best linear approximation of the true mean function are discussed.

Original language	English
Pages (from-to)	277-288
Number of pages	12
Journal	Journal of Statistical Planning and Inference
Volume	10
Issue number	3
DOIs	https://doi.org/10.1016/0378-3758(84)90054-5
State	Published - Oct 1984

Bibliographical note

Funding Information:
in part by Air Force Office of Scientific

Keywords

Asymptotic normality
Best linear approximation
Consistency
Model robustness

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/0378-3758(84)90054-5

Cite this

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title = "Linear least squares estimates and nonlinear means",

abstract = "The consistency and asymptotic normality of a linear least squares estimate of the form (X'X)-X'Y when the mean is not Xβ is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not be the best linear approximation of the true mean function. Choices of designs which allow large sample inferences to be made about the best linear approximation of the true mean function are discussed.",

keywords = "Asymptotic normality, Best linear approximation, Consistency, Model robustness",

author = "Berger, {Roger L.} and Langberg, {Naftali A.}",

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AU - Langberg, Naftali A.

N1 - Funding Information: in part by Air Force Office of Scientific

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N2 - The consistency and asymptotic normality of a linear least squares estimate of the form (X'X)-X'Y when the mean is not Xβ is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not be the best linear approximation of the true mean function. Choices of designs which allow large sample inferences to be made about the best linear approximation of the true mean function are discussed.

AB - The consistency and asymptotic normality of a linear least squares estimate of the form (X'X)-X'Y when the mean is not Xβ is investigated in this paper. The least squares estimate is a consistent estimate of the best linear approximation of the true mean function for the design chosen. The asymptotic normality of the least squares estimate depends on the design and the asymptotic mean may not be the best linear approximation of the true mean function. Choices of designs which allow large sample inferences to be made about the best linear approximation of the true mean function are discussed.

KW - Asymptotic normality

KW - Best linear approximation

KW - Consistency

KW - Model robustness

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ER -

Linear least squares estimates and nonlinear means

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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