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

摘要

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