A weak invariance principle for self-normalized products of sums of mixing sequences

Let variables in the {X, Xn, n ≥ 1} be a sequence of strictly stationary φ-mixing positive random domain of attraction of the normal law. Under some suitable conditions the principle for self-normalized products of partial sums is obtained.

A Self-normalized Law of the Iterated Logarithm for the Geometrically Weighted Random Series

Let {X, Xn; n ≥ 0} be a sequence of independent and identically distributed random variables with EX=0, and assume that EX^2I（｜X｜ ≤ x） is slowly varying as x →∞, i.e., X is in the domain of attraction of the normal law. In this paper, a self-normalized law of the iterated logarithm for the geometrically weighted random series Σ~∞（n=0）β~nXn（0 〈 β 〈 1） is obtained, under some minimal conditions.

A LIL and Limit Distributions for Trimmed Sums of Random Vectors Attracted to Operator Semi-stable Laws

Let θ∈^d be a unit vector and let X, X1, X2,…… be a sequence of i.i.d. Xd-valued random vectors attracted to operator semi-stable laws. For each integer n ≥1, let X1,≤……≤ Xn,n denote the order statistics of X1, X2,..., Xn according to priority of index, namely ｜（X1,nθ）｜≥…≥ [（Xn,n,θ）1, where （., .） is an inner product on Rd. For all integers r ≥ 0, define by （r）Sn =∑n-r i=1Xi,n the trimmed sum. In this paper we investigate a law of the iterated logarithm and limit distributions for trimmed sums （r）Sn. Our results give information about the maximal growth rate of sample paths for partial sums of X when r extreme terms are excluded. A stochastically compactness of （r）Sn is obtained.

Empirical Likelihood Statistical Inference for Compound Poisson Vector Processes under Infinite Covariance Matrix

The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.

A strong approximation of self-normalized sums

Let {X,Xn,n1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX2I(|X|≤x) is slowly varying as x→∞,i.e.,X is in the domain of attraction of the normal law.In this paper a Strassen-type strong approximation is established for self-normalized sums of such random variables.

关于Chover重对数律

J.Chover(1966)对分布为特征指数为α(0<α<2)的对称稳定分布的独立同分布随机变量序列部分和建立了一个重对数律,本文将此推广到分布属于特征指数为α(0<α<2)的非退化稳定分布的正则吸引场的独立同分布随机变量序列部分和上。

稳定律吸引场中学生化的Hanson-Russo型增量定理

该文通过建立关于部分和学生化增量的大偏差不等式 ,在稳定律吸引场中证得了学生化的 Hanson- Russo型增量定理 .

方差可能无穷的“中度偏离”单位根过程的复合分位数估计

考虑一类"中度偏离"单位根过程,y_t=q_ny_t-1+u_t,其中qn=1+c/(k_n),k_n=o(n),c为一非零常数,{u_t}为随机扰动项序列.在允许扰动项方差无穷的条件下,构造q_n的复合分位数估计,并得到了该估计的渐近分布.最后通过数值模拟,在扰动项服从t(2)分布下,说明了该估计的稳健和有效性.

Studentized Increments of Partial Sums

Using suitable self-normalization for partial sums of i.i.d.random variables,Griffin and Kuelbs established the law of the iterated logarithm for all distributions in the domain of attraction of a normal law.We obtain the corresponding results for Studentized increments of partial sums under thesame condition.

总体协方差矩阵不存在情形下的经验似然

本文证明当总体分布处于多元正态分布的广义吸引域时,总体均值的对数经验似然比统计量渐近服从卡方分布.