A truncated Cramér–von Mises test of normality

Asymptotic normality of randomly truncated stochastic algorithms

A Modified Kolmogorov-Smirnov Test for Normality

In this paper we propose an improvement of the Kolmogorov-Smirnov test for normality. In the current implementation of the Kolmogorov-Smirnov test, a sample is compared with a normal distribution where the sample mean and the sample variance are used as parameters of the distribution. We propose to select the mean and variance of the normal distribution that provide the closest fit to the data....

Asymptotic normality of Hill Estimator for truncated data

The problem of estimating the tail index from truncated data is addressed in ?. In that paper, a sample based (and hence random) choice of k is suggested, and it is shown that the choice leads to a consistent estimator of the inverse of the tail index. In this paper, the second order behavior of the Hill estimator with that choice of k is studied, under some additional assumptions. In the untru...

A new test for multivariate normality

We propose a new class of rotation invariant and consistent goodness-of-fit tests for multivariate distributions based on Euclidean distance between sample elements. The proposed test applies to any multivariate distribution with finite second moments. In this article we apply the new method for testing multivariate normality when parameters are estimated. The resulting test is affine invariant...

Asymptotic Distribution of the Hermite Normality Test

This paper presents some asymptotical results of the Hermite Normality test previously introduced. We show that the Hermite statistic S H is distributed under the null hypothesis as a quadratic form of normal variates and under the nonnull hypothesis as normal. The special case of tests with two polynomials is studied in details. Finally, we give some considerations for the choice of a best Her...