Existence, Consistency and computer simulation for selected variants of minimum distance estimators
Václav Kůs, Domingo Morales, Jitka Hrabáková, Iva Frýdlová (2018)
Kybernetika
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The paper deals with sufficient conditions for the existence of general approximate minimum distance estimator (AMDE) of a probability density function on the real line. It shows that the AMDE always exists when the bounded -divergence, Kolmogorov, Lévy, Cramér, or discrepancy distance is used. Consequently, consistency rate in any bounded -divergence is established for Kolmogorov, Lévy, and discrepancy estimators under the condition that the degree of variations of the corresponding...