Model fitting in the presence of nuisance parameters

A basic problem in any statistical modeling of a scientific dataset is to provide the ‘best’ fit. Such inference is generally based on the empirical distribution function when the underlying process generating the data is not reasonably known. A computationally intensive resampling method called the bootstrap method are presented, to estimate the null distributions of various goodness of fit test statistics, when the underlying process is partially known. These results hold not only in the univariate case but also in the multivariate setting.