Abstract
This chapter discusses empirical and quantile processes with the help of strong approximation methods. The chapter reviews the law of iterated logarithm for the empirical process, and the distance between the empirical and the quantile processes. Various theorems are proved in the chapter. The law of iterated logarithm for the quantile process is reviewed. The asymptotic distribution results for some classical functionals of the empirical process, and the asymptotic distribution results for some classical functionals of the quantile process are discussed. The chapter reviews the asymptotic distribution results for some classical functional of some k-sample empirical and quantile processes. Approximations of the empirical process when parameters are estimated, and the asymptotic quadratic quantile tests for composite goodness-of-fit are discussed.
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