Minimum \(L^q\)-distance estimators for non-normalized parametric models

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...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Betsch, Steffen, Ebner, Bruno, Klar, Bernhard
Format: Article
Language:English
Subjects:
Asymptotic methods
Computer simulation
Economic models
Estimating techniques
Maximum likelihood estimators
Monte Carlo simulation
Parameter estimation
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1909.00002