Nonparametric series density estimation and testing

Marsh, Patrick

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.

Citation

Marsh, P. (2019). Nonparametric series density estimation and testing. Statistical Methods and Applications, 28(1), 77–99. https://doi.org/10.1007/s10260-018-00432-y

• Journal Article Type: Article
• Acceptance Date: Jul 8, 2018
• Online Publication Date: Aug 1, 2018
• Publication Date: 2019-03
• Deposit Date: Jul 12, 2018
• Publicly Available Date: Aug 2, 2019
• Journal: Statistical Methods and Applications
• Print ISSN: 1618-2510
• Electronic ISSN: 1618-2510
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 28
• Issue: 1
• Pages: 77–99
• DOI: https://doi.org/10.1007/s10260-018-00432-y
• Keywords: Goodness-of-fit, Nonparametric likelihood ratio, Nuisance Parameters and Series Density Estimator
• Public URL: https://nottingham-repository.worktribe.com/output/945798
• Publisher URL: https://link.springer.com/article/10.1007/s10260-018-00432-y
• Additional Information: This is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10260-018-00432-y