Least empirical risk procedures in statistical inference

Volume 22 / 1993

Wojciech Niemiro Applicationes Mathematicae 22 (1993), 55-67 DOI: 10.4064/am-22-1-55-67


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.


  • Wojciech Niemiro

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