Nonparametric series density estimation and testing
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 consisten...
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| Format: | Article |
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Springer
2018
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| Online Access: | https://eprints.nottingham.ac.uk/52926/ |
| _version_ | 1848798841647661056 |
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| author | Marsh, Patrick |
| author_facet | Marsh, Patrick |
| author_sort | Marsh, Patrick |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:26:11Z |
| format | Article |
| id | nottingham-52926 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:26:11Z |
| publishDate | 2018 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-529262020-05-04T19:45:38Z https://eprints.nottingham.ac.uk/52926/ Nonparametric series density estimation and testing Marsh, Patrick 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. Springer 2018-07-08 Article PeerReviewed Marsh, Patrick (2018) Nonparametric series density estimation and testing. Statistical Methods and Applications . ISSN 1618-2510 (In Press) Goodness-of-fit Nonparametric likelihood ratio Nuisance Parameters and Series Density Estimator |
| spellingShingle | Goodness-of-fit Nonparametric likelihood ratio Nuisance Parameters and Series Density Estimator Marsh, Patrick Nonparametric series density estimation and testing |
| title | Nonparametric series density estimation and testing |
| title_full | Nonparametric series density estimation and testing |
| title_fullStr | Nonparametric series density estimation and testing |
| title_full_unstemmed | Nonparametric series density estimation and testing |
| title_short | Nonparametric series density estimation and testing |
| title_sort | nonparametric series density estimation and testing |
| topic | Goodness-of-fit Nonparametric likelihood ratio Nuisance Parameters and Series Density Estimator |
| url | https://eprints.nottingham.ac.uk/52926/ |