Goodness of Fit Tests Based on Kernel Density Estimators

Article type: Research Article

Authors: Rudzkis, Rimantas^; | Bakshaev, Aleksej

Affiliations: Vilnius University, Institute of Mathematics and Informatics, Akademijos 4, LT-08663 Vilnius, Lithuania, e-mail: rimantas.rudzkis@mii.vu.lt, aleksej.bakshaev@gmail.com

Note: [] Corresponding author.

Abstract: The paper is devoted to goodness of fit tests based on probability density estimates generated by kernel functions. The test statistic is considered in the form of maximum of the normalized deviation of the estimate from its expected value or a hypothesized distribution density function. A comparative Monte Carlo power study of the investigated criterion is provided. Simulation results show that the proposed test is a powerful competitor to the existing classical criteria testing goodness of fit against a specific type of alternative hypothesis. An analytical way for establishing the asymptotic distribution of the test statistic is proposed, using the theory of high excursions of close to Gaussian random processes and fields introduced by Rudzkis (1992, 2012).

Keywords: goodness of fit test, Gaussian processes, high excursions

Journal: Informatica, vol. 24, no. 3, pp. 447-460, 2013