On Score-Functions and Goodness-of-Fit Tests for Stochastic Processes

2014/03/30 by Yury A. Kutoyants, Kutoyants, Yury A.
Mathematics · #62G10 #62G20 #62M02 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62G10 #msc:62G20 #msc:62M02 #stat.TH

paper · pdf · doi:10.48550/arxiv.1403.7715

32 pages

arxiv created 2014/03/30 · arxiv updated 2014/04/01

Abstract

The problems of the construction of the asymptotically distribution free goodness-of-fit tests for three models of stochastic processes are considered. The null hypothesis for all models is composite parametric. All tests are based on the score-function processes, where the unknown parameter is replaced by the MLE. We show that a special change of time transforms the limit score-function processes into the Brownian bridge. This property allows us to construct the asymptotically distribution free tests for the following three models of stochastic processes : dynamical systems with small noise, ergodic diffusion processes, inhomogeneous Poisson processes and nonlinear AR time series.

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