Least empirical risk procedures in statistical inference

Wojciech Niemiro

Applicationes Mathematicae (1993)

  • Volume: 22, Issue: 1, page 55-67
  • ISSN: 1233-7234

Abstract

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We consider the empirical risk function Q n ( α ) = 1 n ∑ i = 1 n · 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.

How to cite

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Niemiro, Wojciech. "Least empirical risk procedures in statistical inference." Applicationes Mathematicae 22.1 (1993): 55-67. <http://eudml.org/doc/219083>.

@article{Niemiro1993,
abstract = {We consider the empirical risk function $Q_n(α)=\{1\over n\} \sum _\{i=1\}^n \cdot f(α,Z_i)$ (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.},
author = {Niemiro, Wojciech},
journal = {Applicationes Mathematicae},
keywords = {least distances; convex minimization; tests of significance; least absolute deviations; asymptotics; asymptotic representation; minimum of the empirical risk function; tests of significance for linear hypotheses; least distance; discriminant analysis},
language = {eng},
number = {1},
pages = {55-67},
title = {Least empirical risk procedures in statistical inference},
url = {http://eudml.org/doc/219083},
volume = {22},
year = {1993},
}

TY - JOUR
AU - Niemiro, Wojciech
TI - Least empirical risk procedures in statistical inference
JO - Applicationes Mathematicae
PY - 1993
VL - 22
IS - 1
SP - 55
EP - 67
AB - We consider the empirical risk function $Q_n(α)={1\over n} \sum _{i=1}^n \cdot f(α,Z_i)$ (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.
LA - eng
KW - least distances; convex minimization; tests of significance; least absolute deviations; asymptotics; asymptotic representation; minimum of the empirical risk function; tests of significance for linear hypotheses; least distance; discriminant analysis
UR - http://eudml.org/doc/219083
ER -

References

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  13. P. Milasevic and G. R. Ducharme (1987), Uniqueness of the spatial median, Ann. Statist. 15, 1332-1333. Zbl0631.62058
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