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Minimum L$^{q}$-distance estimators for non-normalized parametric models

Betsch, Steffen; Ebner, Bruno; Klar, Bernhard

We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective probability distributions, and is to be classified as a minimum distance estimator, incorporating as a distance function the L$^{q}$‐norm. Throughout, we deal rigorously with issues of existence and measurability of these implicitly defined estimators. Moreover, we provide consistency results in a common asymptotic setting, and compare our new method with classical estimators for the exponential, the Rayleigh and the Burr Type XII distribution in Monte Carlo simulation studies. We also assess the performance of different estimators for non‐normalized models in the context of an exponential‐polynomial family.

Verlagsausgabe §
DOI: 10.5445/IR/1000126035
Veröffentlicht am 12.11.2020
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH)
Publikationstyp Zeitschriftenaufsatz
Publikationsmonat/-jahr 06.2021
Sprache Englisch
Identifikator ISSN: 0319-5724, 1708-945X
KITopen-ID: 1000126035
Erschienen in The Canadian journal of statistics
Verlag John Wiley and Sons
Band 49
Heft 2
Seiten 514-548
Vorab online veröffentlicht am 28.10.2020
Schlagwörter Burr Type XII distribution; empirical processes; exponential-polynomial models; measurable selections; minimum distance estimators; Rayleigh distribution; Stein discrepancies
Nachgewiesen in Scopus
Web of Science
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