Murray D. Burke - Model checking and estimation: A large sample approach

A brief survey of some models used in statistical analysis is given. Estimation and tests of fit considerations often lead to distribution-free or asymptotically distribution-free statistics. However, in many types of situations (e.g. multivariate, semiparametric models), the resulting processes depend on the underlying distribution function or family of distribution functions. Weighted bootstrap methods are considered as an omnibus way of approximating the limiting distribution of test statistics. Since percentage points of the resulting statistics do not need to be calculated explicitly, one can be flexible in the choice of statistic and achieve greater power against particular alternatives.