Linear least squares estimates and nonlinear means

Roger L. Berger, Naftali A. Langberg

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)277-288
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume10
Issue number3
DOIs
StatePublished - 1984
Externally publishedYes

Fingerprint

Least Squares Estimate
Linear Least Squares
Linear Approximation
Best Approximation
Asymptotic Normality
Consistent Estimates
Least squares
Approximation
Design
Asymptotic normality

Keywords

  • Asymptotic normality
  • Best linear approximation
  • Consistency
  • Model robustness

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

Linear least squares estimates and nonlinear means. / Berger, Roger L.; Langberg, Naftali A.

In: Journal of Statistical Planning and Inference, Vol. 10, No. 3, 1984, p. 277-288.

Research output: Contribution to journalArticle

Berger, Roger L. ; Langberg, Naftali A. / Linear least squares estimates and nonlinear means. In: Journal of Statistical Planning and Inference. 1984 ; Vol. 10, No. 3. pp. 277-288.
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