Approximation of Stochastic Integrals with Applications to Goodness-of-Fit Tests

Abstract

In this paper stochastic integrals with respect to the basic martingale are approximated by Gaussian processes. The probability inequalities governing this approximation are used to study goodness-of-fit tests based on sublinear functionals of weighted versions of these stochastic integrals. As special cases of these tests, generalized rank and supremum-type tests are considered.