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 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 present a test for the maximal rank of the volatility process in continuous diffusion models observed with noise. Such models are typically applied in mathematical finance, where latent price processes are corrupted by microstructure noise at ultra high frequencies. Using high...

This paper demonstrates that all rank test statistics are functions of implicit null space estimators. The paper proposes a novel theory of null space estimation that allows for standard asymptotics, polynomial regressions, and cointegration asymptotics. The paper proves that the behaviour of...

This paper demonstrates that all rank test statistics are functions of implicit null space estimators. The paper proposes a novel theory of null space estimation that allows for standard asymptotics, polynomial regressions, and cointegration asymptotics. The paper proves that the behaviour of...

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...

This paper proposes a semiparametric estimator for single- and multiple index models. It provides an extension of the average derivative estimator to the multiple index model setting. The estimator uses the average of the outer product of derivatives and is shown to be root-N consistent and...

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...