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Least empirical risk procedures in statistical inference. (English) Zbl 0797.62021

The author considers the asymptotic representation of the minimum of the empirical risk function under the assumption of convexity. The tests of significance for linear hypotheses are derived. Procedures of the type of least absolute deviations (LAD) and least distance are considered. In particular, an application of LAD-related methods to discriminant analysis is discussed.

MSC:

62F12 Asymptotic properties of parametric estimators
62F05 Asymptotic properties of parametric tests
62H30 Classification and discrimination; cluster analysis (statistical aspects)
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