Goodness-of-Fit Test for Non-Stationary and Strongly Dependent Samples

In this article we improve a goodness-of-fit test, of the Kolmogorov-Smirnov type, for equally distributed- but not stationary-strongly dependent data. The test is based on the asymptotic behavior of the empirical process, which is much more complex than in the classical case. Applications to simulated data and discussion of the obtained results are provided. This is, to the best of our knowledge, the first result providing a general goodness of fit test for non-weakly dependent data.

Asymptotic Extremal Distribution for Non-Stationary, Strongly-Dependent Data

Fisher-Tippet-Gnedenko classical theory shows that the normalized maximum of n iid random variables with distribution F belonging to a very wide class of functions, converges in law to an extremal distribution H, that is determined by the tail of F. Extensions of this theory from the iid case to stationary and weak dependent sequences are well known from the work of Leadbetter, Lindgreen and Rootzén. In this paper, we present a very simple class of random processes that runs from iid sequences to non-stationary and strongly dependent processes, and we study the asymptotic behavior of its normalized maximum. More interesting, we show that when the process is strongly dependent, the asymptotic distribution is no longer an extremal one, but a mixture of extremal distributions. We present very simple theoretical and simulated examples of this result. This provides a simple framework to asymptotic approximations of extremes values not covered by classical extremal theory and its well-known extensions.

Estimating the Components of a Mixture of Extremal Distributions under Strong Dependence

In this paper, we provide a method based on quantiles to estimate the parameters of a finite mixture of Fréchet distributions, for a large sample of strongly dependent data. This is a situation that appears when dealing with environmental data and there was a real need of such method. We validate our approach by means of estimation and goodness-of-fit testing over simulated data, showing an accurate performance.

The maxima and sums of multivariate non-stationary Gaussian sequences

Let {Xkl,…, Xkp, k≥ 1} be a p-dimensional standard （zero-means, unit-variances）non-stationary Gaussian vector sequence. In this work, the joint limit distribution of the maximaof {Xkl,…, Xkp, k 〉 1}, the incomplete maxima of those sequences subject to random failureand the partial sums of those sequences are obtained.

Hájek-Rényi-type Inequality for a Class of Random Variable Sequences and Its Applications

In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

A New Procedure to Test for Fractional Integration

It is now widely recognized that the statistical property of long memory may be due to reasons other than the data generating process being fractionally integrated. We propose a new procedure aimed at distinguishing between a null hypothesis of unifractal fractionally integrated processes and an alternative hypothesis of other processes which display the long memory property. The procedure is based on a pair of empirical, but consistently defined, statistics namely the number of breaks reported by Atheoretical Regression Trees (ART) and the range of the Empirical Fluctuation Process (EFP) in the CUSUM test. The new procedure establishes through simulation the bivariate distribution of the number of breaks reported by ART with the CUSUM range for simulated fractionally integrated series. This bivariate distribution is then used to empirically construct a test which rejects the null hypothesis for a candidate series if its pair of statistics lies on the periphery of the bivariate distribution determined from simulation under the null. We apply these methods to the realized volatility series of 16 stocks in the Dow Jones Industrial Average and show that the rejection rate of the null is higher than if either statistic was used as a univariate test.

Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications

Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.

A CENTRAL LIMIT THEOREM FOR STRONG NEAR-EPOCH DEPENDENT RANDOM VARIABLES

In this paper, a central limit theorem for strong near-epoch dependent sequences of random variables introduced in [9] is showed. Under the same moments condition,the authors essentially weaken the "size" requirement mentioned in other papers about near epoch dependence.

The invariance principle for fractionally integrated processes with strong near-epoch dependent innovations

In this paper, we show the invariance principle for the partial sum processes of fractionally integrated processes, otherwise known as I(d + m) processes, where |d| < 1/2 and m is a nonnegative integer, with strong near-epoch dependent innovations. The results are applied to the test of unit root. The conditions given improve previous results in the literature concerning fractionally integrated processes.

THE STRONG LAW OF LARGE NUMBERS FOR PAIRWISE NQD RANDOM VARIABLES

In this paper, the almost sure convergence for pairwise negatively quadrant dependent random variables is studied. The strong law of large numbers for pairwise negatively quadrant dependent random variables is obtained. Our results generalize and improve those on almost sure convergence theorems previously obtained by Marcinkiewicz （1937）, Jamison （1965）, Matula （1992） and Wu （2001） from the independent identically distributed （i.i.d.） case to pairwise NQD sequences.

Rapid transition of the hole Rashba effect from strong field dependence to saturation in semiconductor nanowires

With the support by the National Natural Science Foundation of China,a study by the research group led by Prof.Luo Junwei(骆军委)from the Institute of Semiconductors,Chinese Academy of Sciences discovered a rapid transition of the hole Rashba effect from strong field dependence to saturation