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Existence, Consistency and computer simulation for selected variants of minimum distance estimators

Václav Kůs; Domingo Morales; Jitka Hrabáková; Iva Frýdlová — 2018

Kybernetika

The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function $f_{0}$ on the real line. It shows that the AMDE always exists when the bounded $φ$ -divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, $n^{- 1 / 2}$ consistency rate in any bounded $φ$ -divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding family...

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