AMS 2000 subject classifications: 60G70, 62H12, 62H15, 62F05, 62F12, 62F25.

We consider the relative merits of various saddlepoint approximations for the c.d.f. of a statistic with a possibly non-normal limit distribution. In addition to the usual Lugannani-Rice approximation we also consider approximations based on higher-order expansions, including the case where the...

We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence. Although our model is developed in a bivariate...

In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is proposed which is applicable under very weak assumptions. The new test is based on an empirical process formed from pseudo residuals, for which weak convergence to a Gaussian...