Mynbayev, Kairat and Aipenova, Aziza
(2013):
*Testing a differential condition and local normality of densities.*
Published in: News of the National Academy of Sciences of the Republic of Kazakhstan, physico-mathematical series
, Vol. 5, No. 297
(2014): pp. 42-47.

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## Abstract

In this paper, we consider testing if a density satisfies a differential equation. This result can be applied to see if a density belongs to a particular family of distributions. For example, the standard normal density f(t) satisfies the differential equation f'(t)+tf(t)=0. If a density satisfies this equation at that point t, then it is called locally standard normal at that point. Thus, there is a practical need to test whether a density satisfies a certain differential equation. We consider a more general differential equation F(x)=0 involving f(x). We can test the null hypothesis H0: f satisfies the equation F(x)=0 against the alternative hypothesis Ha: F(x)≠0. The testing procedure is accompanied by an asymptotic normality statement.

Item Type: | MPRA Paper |
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Original Title: | Testing a differential condition and local normality of densities |

Language: | English |

Keywords: | testing; local normality test; alternative hypothesis; null hypothesis; asymptotic normality |

Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General |

Item ID: | 87045 |

Depositing User: | Kairat Mynbaev |

Date Deposited: | 02 Jun 2018 14:42 |

Last Modified: | 01 Oct 2019 04:35 |

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URI: | https://mpra.ub.uni-muenchen.de/id/eprint/87045 |