Statisticians are constantly looking for methods of statistical inference that would be both effective and would require meeting as few assumptions as possible. Permutation tests seem to fit here, as using them makes it possible to perform statistical inference in situations where classical...

In this paper, we develop methods of the determination of the rank of random matrix. Using the matrix perturbation theory to construct or find a suitable bases of the kernel (null space) of the matrix and to determine the limiting distribution of the estimator of the smallest singular values. We...

In this paper, we propose methods of the determination of the rank of matrix. We consider a rank test for an unobserved matrix for which an estimate exists having normal asymptotic distribution of order N1/2 where N is the sample size. The test statistic is based on the smallest estimated...

In this paper, we develop methods of the determination of the rank of random matrix. Using the matrix perturbation theory to construct or find a suitable bases of the kernel (null space) of the matrix and to determine the limiting distribution of the estimator of the smallest singular values. We...

We propose an easy to use derivative based two-step estimation procedure for semi-parametric index models. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators. The functionals used provide moment conditions...

We propose an easy to use derivative based two-step estimation procedure for semi-parametric index models. In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators. The functionals used provide moment conditions...

In this paper, we develop methods of the determination of the rank of random matrix. Using the matrix perturbation theory to construct or find a suitable bases of the kernel (null space) of the matrix and to determine the limiting distribution of the estimator of the smallest singular values. We...

This paper presents the likelihood ratio (LR) test for the number of cointegrating and multi-cointegrating relations in the I(2) vector autoregressive model. It is shown that the asymptotic distribution of the LR test for the (multi-) cointegration ranks is identical to the asymptotic...