Least empirical risk procedures in statistical inference

Wojciech Niemiro

ArticleOriginal scientific text

Title

Least empirical risk procedures in statistical inference

Authors ¹

Affiliations

Institute of Applied Mathematics, Department of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Abstract

We consider the empirical risk function

Q_{n} (α) = {1 o v e r n} \sum_{i = 1}^{n} \cdot f (α, Z_{i})

(for iid

Z_{i}

's) under the assumption that f(α,z) is convex with respect to α. Asymptotics of the minimum of

Q_{n} (α)

is investigated. Tests for linear hypotheses are derived. Our results generalize some of those concerning LAD estimators and related tests.

Keywords

ENG

least distances, convex minimization, tests of significance, least absolute deviations, asymptotics

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Title

Least empirical risk procedures in statistical inference

Affiliations

Abstract

Keywords

Bibliography