PMC Theorems on PCR–Ridge Class Estimators

After presenting the basic linear model and some definitions, the PMC superiority for a class of biased estimators is discussed. One objective of this paper is to develop such a methodology for the case when the squared statistical distance between the estimator and the parameter is used as the loss...

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Bibliographic Details
Published inJournal of statistical theory and practice Vol. 15; no. 1
Main Authors Li, Yuanhan, Keating, Jerome P., Balakrishnan, Narayanaswamy
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2021
Subjects
Celebrating the Centenary of Professor C. R. Rao
Mathematics and Statistics
Original Article
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Statistics
class estimators
Pitman’s measure of closeness
Multicollinearity
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Summary:After presenting the basic linear model and some definitions, the PMC superiority for a class of biased estimators is discussed. One objective of this paper is to develop such a methodology for the case when the squared statistical distance between the estimator and the parameter is used as the loss function, and that the estimators to be compared are linear combinations of common statistics having a multivariate normal distribution. To demonstrate the usefulness of the methodology, it is applied for the comparison of r - k class estimators with unbiased least squares estimator of regression coefficients.
ISSN:1559-8608
1559-8616
DOI:10.1007/s42519-020-00150-3