In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically indepen...In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.展开更多
Let Mn denote the partial maximum of a strictly stationary sequence （Xn）. Suppose some of the random variables of （Xn） can be observed and let Mn stand for the maximum of observed random variables from the set {X1...Let Mn denote the partial maximum of a strictly stationary sequence （Xn）. Suppose some of the random variables of （Xn） can be observed and let Mn stand for the maximum of observed random variables from the set {X1,..., Xn}. In this paper, the almost sure limit theorems related to random vector （Mn, Mn） are considered in terms of i.i.d, case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.展开更多
Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is...Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is a bivariate spherical random vector. For the distribution function of radius√S12 ＋ S22 belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of p~ to 1 is given. In this paper, under the refinement of the rate of convergence of p~ to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.11171275)the Program for Excellent Talents in Chongqing Higher Education Institutions(Grant No.120060-20600204)supported by the Swiss National Science Foundation Project(Grant No.200021-134785)
文摘In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence （centered at the sample mean） converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions.
基金Supported by National Natural Science Foundation of China （Grant No. 70371061） and the Program for Excellent Talents in Chongqing Higher Education Institutions （Grant No. 120060-20600204）Acknowledgements The authors would like to express their deep thanks to the referees for carefully reading the paper and for their comments which greatly improve the paper.
文摘Let Mn denote the partial maximum of a strictly stationary sequence （Xn）. Suppose some of the random variables of （Xn） can be observed and let Mn stand for the maximum of observed random variables from the set {X1,..., Xn}. In this paper, the almost sure limit theorems related to random vector （Mn, Mn） are considered in terms of i.i.d, case. The related results are also extended to weakly dependent stationary Gaussian sequence as its covariance function satisfies some regular conditions.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11501113,11601330 and 11701469)the Key Project of Fujian Education Committee(Grant No.JA15045)the Funding Program for Junior Faculties of College and Universities of Shanghai Education Committee(Grant No.ZZslg16020)
文摘Let {（ξni, ηni）, 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as （S1,ρnS1 ＋ √1- ρ2nS2）, ρn ∈（0, 1）, where （S1,S2） is a bivariate spherical random vector. For the distribution function of radius√S12 ＋ S22 belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of p~ to 1 is given. In this paper, under the refinement of the rate of convergence of p~ to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.
