Nonparametric series density estimation and testing

Marsh, Patrick (2018) Nonparametric series density estimation and testing. Statistical Methods and Applications . ISSN 1618-2510 (In Press)

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Abstract

This paper .rst establishes consistency of the exponential series density estimator when nuisance parameters are estimated as a preliminary step. Convergence in relative entropy of the density estimator is preserved, which in turn implies that the quantiles of the population density can be consistently estimated. The density estimator can then be employed to provide a test for the specification of fitted density functions. Commonly, this testing problem has utilized statistics based upon the empirical distribution function (edf), such as the Kolmogorov-Smirnov or Cramér von-Mises, type. However, the tests of this paper are shown to be asymptotically pivotal having limiting standard normal distribution, unlike those based on the edf. For comparative purposes with those tests, the numerical properties of both the density estimator and test are explored in a series of experiments. Some general superiority over commonly used edf based tests is evident, whether standard or bootstrap critical values are used.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/945798
Keywords: Goodness-of-fit, Nonparametric likelihood ratio, Nuisance Parameters and Series Density Estimator
Schools/Departments: University of Nottingham, UK > Faculty of Social Sciences > School of Economics
Depositing User: Eprints, Support
Date Deposited: 12 Jul 2018 14:08
Last Modified: 04 May 2020 19:45
URI: http://eprints.nottingham.ac.uk/id/eprint/52926

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