Pitman closest equivariant estimators and predictors under location-scale models

Haojin Zhou, Tapan K. Nayak*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

For location, scale and location-scale models, which are common in practical applications, we derive optimum equivariant estimators and predictors using the Pitman closeness criterion. This approach is very robust with respect to the choice of the loss function as it only requires the loss function to be strictly monotone. We also prove that, in general, the Pitman closeness comparison of any two equivariant predictors depends on the unknown parameter only through a maximal invariant, and hence it is independent of the parameter when the parameter space is transitive. We present several examples illustrating applications of our theoretical results.

Original languageEnglish
Pages (from-to)1367-1377
Number of pages11
JournalJournal of Statistical Planning and Inference
Volume142
Issue number6
DOIs
Publication statusPublished - Jun 2012
Externally publishedYes

Keywords

  • Invariance
  • Loss function
  • Maximal invariant
  • Quantile
  • Transformation group

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