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arXiv · 1403.7715

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

Yury A. Kutoyants
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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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Yury A. Kutoyants. 2014-03-30. On Score-Functions and Goodness-of-Fit Tests for Stochastic Processes. https://arxiv.org/abs/1403.7715

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