The optimal bandwidth of the d-dimensional kernel estimator of a density is well known to have order n-1/(4+d. In this note, the multivariate distribution function F(x) is estimated by integrating a kernel estimator of its density. The asymptotic optimal bandwidth of the d-dimensional kernel...

This paper investigates a new test for normality that is easy for biomedical researchers to understand and easy to implement in all dimensions. In terms of power comparison against a broad range of alternatives, the new test outperforms the best known competitors in the literature as...

Many statistical problems can be reformulated in terms of tests of uniformity. Some strong laws of large numbers and a central limit theorem for the logarithm of transformed spacings are obtained. These theorems provide a characterization of the uniform distribution. A general information-type...

This paper introduces a new characterization of multivariate normality of a random vector based on univariate normality of linear combinations of its components.