This paper derives asymptotic approximations to the power of Cramer-von Mises (CvM) style tests for inference on a finite dimensional parameter defined by conditional moment inequalities in the case where the parameter is set identified. Combined with power results for Kolmogorov-Smirnov (KS) tests, these results can be used to choose the optimal test statistic, weighting function and, for test...

We present a systematic study of the dynamical scaling process leading to the establishment of the Kolmogorov-Zakharov (KZ) spectrum in weak three-wave turbulence. In the finite-capacity case, in which the transient spectrum reaches infinite frequency in finite time, the dynamical scaling exponent is anomalous in the sense that it cannot be determined from dimensional considerations. As a conse...

We propose a way to construct consistent generalizations of the Cram er-von Mises test on the line, and the Watson U 2 n test on the circle, based on classes of partitions invariant under various group actions. The framework developed extends our earlier work generalizing the Kolmogorov-Smirnov and Kuiper goodness-oft tests, and provides a conceptually unifying description. Many goodness-oft te...

While performing statistical tests [7] the first question is which statistical test, parametric or non-parametric, is suitable. It is well known that parametric tests have much more power (probability that a statistical test will correctly reject a false null hypothesis, or a probability of avoiding a Type II error) than a non-parametric test. Hence, we should use parametric tests whenever allo...

In this chapter, we consider some chi-square-type goodness-of-fit tests for right AQ1 censored samples, viz. the Nikulin–Rao–Robson (NRR) test and generalized Pearson–Fisher (GPF) test. We compare these tests in terms of power in the case of testing composite hypotheses by randomly censored and Type II censored samples. Various grouping methods are considered, including equifrequent grouping, g...

In this paper we study stochastic processes which enable monitoring the possible changes of probability distributions over time. These processes may in particular be used to test the null hypothesis of no change. The monitoring processes are bivariate functions, of time and position at the measurement scale, and are approximated with zero mean Gaussian processes under the constancy hypothesis. ...

This paper make an overview of the copula theory from a practical side. We consider different methods of copula estimation and different Goodness-of-Fit tests for model selection. In the GoF section we apply Kolmogorov-Smirnov and Cramer-von-Mises type tests and calculate power of these tests under different assumptions. Novating in this paper is that all the procedures are done in dimensions h...

We consider the goodness of fit testing problem for stochastic differential equation with small diffusion coefficient. The basic hypothesis is always simple and it is described by the known trend coefficient. We propose several tests of the type of Cramer-von Mises, Kolmogorov-Smirnov and Chi-Square. The power functions of these tests we study for a special classes of close alternatives. We dis...