# 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 Forschungsbericht/Preprint Publikationsjahr 2020 Sprache Englisch Identifikator KITopen-ID: 1000126060 Umfang 27 S. Vorab online veröffentlicht am 28.10.2020 Nachgewiesen in arXiv Relationen in KITopen Verweist aufMinimum L$^{q}$-distance estimators for non-normalized parametric models [in press]. Betsch, Steffen; Ebner, Bruno; Klar, Bernhard (2020) Zeitschriftenaufsatz (1000126035)
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