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PMC Theorems on PCR–Ridge Class Estimators

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Abstract

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.

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Authors and Affiliations

  1. University of Texas at San Antonio, San Antonio, USA

    Yuanhan Li & Jerome P. Keating

  2. McMaster University, Hamilton, Canada

    Narayanaswamy Balakrishnan

Authors
  1. Yuanhan Li
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  2. Jerome P. Keating
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  3. Narayanaswamy Balakrishnan
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Correspondence to Yuanhan Li.

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This article is part of the topical collection “Celebrating the Centenary of Professor C. R. Rao” guest edited by , Ravi Khattree, Sreenivasa Rao Jammalamadaka, and M. B. Rao.

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Li, Y., Keating, J.P. & Balakrishnan, N. PMC Theorems on PCR–Ridge Class Estimators. J Stat Theory Pract 15, 17 (2021). https://doi.org/10.1007/s42519-020-00150-3

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  • DOI: https://doi.org/10.1007/s42519-020-00150-3

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