# Minimum L$^{q}$-distance estimators for non-normalized parametric models [in press]

Betsch, Steffen; Ebner, Bruno; Klar, Bernhard

##### Abstract:
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.

 Zugehörige Institution(en) am KIT Institut für Stochastik (STOCH) Publikationstyp Zeitschriftenaufsatz Publikationsjahr 2020 Sprache Englisch Identifikator ISSN: 0319-5724, 1708-945X KITopen-ID: 1000126035 Erschienen in The Canadian journal of statistics 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 ScopusWeb of Science Relationen in KITopen Verweist aufMinimum L$^{q}$-distance estimators for non-normalized parametric models [in press]. Betsch, Steffen; Ebner, Bruno; Klar, Bernhard (2020) Forschungsbericht/Preprint (1000126060)
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