The problems of application of nonparametric Kolmogorov, Cramer-von MisesSmirnov, Anderson-Darling goodness-of-fit tests for discrete, grouped and censored data have been considered in this paper. The use of these tests for grouped and censored data as well as samples of discrete random variables is based on Smirnov transformation. The convergence of statistic distributions to the corresponding...

We develop a new consistent conditional moment test of functional form based on nuisance parameter indexed sample moments. We reduce the nuisance parameter space to known countable sets, provide a new vantage into why existing parametric moment condition tests work, and uncover a new class of revealing weights. These results are exploited to construct a weighted average conditional moment test,...

BACKGROUND A recent paper found that terminal digits of statistical values in Nature deviated significantly from an equiprobable distribution, indicating errors or inconsistencies in rounding. This finding, as well as the discovery that a large percentage of p values were inconsistent with reported test statistics, led to a great deal of concern in the popular press and scientific community. Th...

1 Some Basic Theory 1 1.1 Consistency and Unbiasedness at a Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Kolmogorov–Smirnov Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Order Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Proof of the Kolmogorov–Smirnov Theorem . . ....