This article provides a new test for sphericity of the covariance matrix of a d-dimensional multinormal population X Nd. This test is applicable if the sample size, n + 1, and d both go to infinity while d/n ! y 2 (0,1), provided that the limits of tr(k)/d, k = 1, . . . , 8, are finite. The main...

This article provides a new test for sphericity of the covariance matrix of a d-dimensional multinormal population X ∼ Nd(µ,Σ). This test is applicable if the sample size, n + 1, and d both go to infinity while d/n → y ∈ (0,∞), provided that the limits of tr(Σk)/d, k = 1,...,8, are...

This paper analyzes the spectral properties of Tyler’s M-estimator for scatter Tn,d. It is shown that if a multivariate sample stems from a generalized spherically distributed population and the sample size n and the dimension d both go to infinity while d/n→0, then the empirical spectral...

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett’s...

This article proposes a class of goodness-of-fit tests for the autocorrelation function of a time series process, including those exhibiting long-range dependence. Test statistics for composite hypotheses are functionals of a (approximated) martingale transformation of the Bartlett's Tp-process...

We consider testing normality in a general class of models that admits nonlinear conditional mean and conditional variance functions. We derive the asymptotic distribution of the skewness and kurtosis coefficients of the model’s standardized residuals and propose an asymptotic x2 test of...

The Jarque-Bera normality test verifies if the residues of the regression hyper-plane are normal random variables.In this paper we present some numerical and Monte Carlo methods to obtain normal residues if the Jarque-Bera test fails. We consider the case when we know the pdf, the cdf and the...