Statistical Papers

, Volume 39, Issue 2, pp 125–134

# Simultaneous equivariant estimation of the parameters of linear models

• S. Kalpana Bai
• T. M. Durairajan
Articles

## Abstract

Consider a family of distributions which is invariant under a group of transformations. In this paper, we define an optimality criterion with respect to an arbitrary convex loss function and we prove a characterization theorem for an equivariant estimator to be optimal. Then we consider a linear model Y=Xβ+ε, in which ε has a multivariate distribution with mean vector zero and has a density belonging to a scale family with scale parameter σ. Also we assume that the underlying family of distributions is invariant with respect to a certain group of transformations. First, we find the class of all equivariant estimators of regression parameters and the powers of σ. By using the characterization theorem we discuss the simultaneous equivariant estimation of the parameters of the linear model.

## Key words and Phrases

Convex loss function equivariant estimators characterization linear model regression parameters

## AMS Subject Classification

Primary 62A05 Secondary 62J05

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