In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong...In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.展开更多
We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior...We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior of a class of infinite weighted sums of random variableswith heavy-tailed probabilities. And then, the main results are applied tothree important types of time series models:infinite order moving averages, the simple bilinear time series and the solutions of stochasticdifference equations. The explicit formulas are given to describe how the marginaltail probabilities come from the innovation's tail probabilities for these time series.Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.展开更多
Let {Xni, 1 ≤ n,i 〈 ∞} be an an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 〈 an ↑∞ . The limiting behavior of maximum partial sums 1/an max 1≤k≤n｜^k∑i=1 Xni｜ is inv...Let {Xni, 1 ≤ n,i 〈 ∞} be an an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 〈 an ↑∞ . The limiting behavior of maximum partial sums 1/an max 1≤k≤n｜^k∑i=1 Xni｜ is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2].展开更多
We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to c...We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.展开更多
Let {X, X_n; n≥1} be i.i.d.r.v.'s taking values in a separable Banach space (B,||·||)such that EX=0 and Ef^2(X)<+∞, ?∈6B~*, and S_n=X_1+…+X_n for n≥1. The purposeof this paper is to study the rates of...Let {X, X_n; n≥1} be i.i.d.r.v.'s taking values in a separable Banach space (B,||·||)such that EX=0 and Ef^2(X)<+∞, ?∈6B~*, and S_n=X_1+…+X_n for n≥1. The purposeof this paper is to study the rates of convergence to zero of P(inf||Sn/(2nloglogn)^(1/2)-x||≥ε) and P(sup inf||S_k/(2kloglogk)^(1/2)-x||≥ε) (?ε>0) under precisely necessary and sufficientconditions. We also give new necessary and sufficient conditions for X to satisfy the boundand compact law of the iterated logarithm, respectively. Our results improve some resultsof Darling and Robbins (1967) as well as Davis (1968) even in the case B=R.展开更多
In the problem of classification （or pattern recognition）, given a set of n samples, we attempt to construct a classifier gn with a small misclassification error. It is important to study the convergence rates of th...In the problem of classification （or pattern recognition）, given a set of n samples, we attempt to construct a classifier gn with a small misclassification error. It is important to study the convergence rates of the misclassification error as n tends to infinity. It is known that such a rate can＇t exist for the set of all distributions. In this paper we obtain the optimal convergence rates for a class of distributions L^（λ,ω） in multicategory classification and nonstandard binary classification.展开更多
基金the National Natural Science Foundation of China(10671149)
文摘In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.
基金This work was supported by the National Natural Science Foundation of China (Grant No.10071003).
文摘We discuss the relationship between the marginal tail risk probability and the innovation'stail risk probability for some stationary financial time series models.We first give the main results on the tail behavior of a class of infinite weighted sums of random variableswith heavy-tailed probabilities. And then, the main results are applied tothree important types of time series models:infinite order moving averages, the simple bilinear time series and the solutions of stochasticdifference equations. The explicit formulas are given to describe how the marginaltail probabilities come from the innovation's tail probabilities for these time series.Our results can be applied to the tail estimation of time series and are useful for risk analysis in finance.
文摘Let {Xni, 1 ≤ n,i 〈 ∞} be an an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 〈 an ↑∞ . The limiting behavior of maximum partial sums 1/an max 1≤k≤n｜^k∑i=1 Xni｜ is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2].
基金Supported by the National Natural Science Foundation of China (10671149)
文摘We first obtain the Petrov theorem for pairwise NQD（negative quadrant dependent） random variables which may have different distributions.Some well-known results are improved and extended.Next,we give an example to clarify one of the important properties of sequences of pairwise NQD random variables,so that we can point out some mistakes that have appeared in recent published papers.
基金Project supported by the National Natural Science Foundation of China.
文摘Let {X, X_n; n≥1} be i.i.d.r.v.'s taking values in a separable Banach space (B,||·||)such that EX=0 and Ef^2(X)<+∞, ?∈6B~*, and S_n=X_1+…+X_n for n≥1. The purposeof this paper is to study the rates of convergence to zero of P(inf||Sn/(2nloglogn)^(1/2)-x||≥ε) and P(sup inf||S_k/(2kloglogk)^(1/2)-x||≥ε) (?ε>0) under precisely necessary and sufficientconditions. We also give new necessary and sufficient conditions for X to satisfy the boundand compact law of the iterated logarithm, respectively. Our results improve some resultsof Darling and Robbins (1967) as well as Davis (1968) even in the case B=R.
基金Research supported in part by NSF of China under Grants 10571010 and 10171007The work was partially done while the first author was visiting the Institute for Mathematical Sciences, National University of Singapore in 2003The visit was supported by the Institute
文摘In the problem of classification （or pattern recognition）, given a set of n samples, we attempt to construct a classifier gn with a small misclassification error. It is important to study the convergence rates of the misclassification error as n tends to infinity. It is known that such a rate can＇t exist for the set of all distributions. In this paper we obtain the optimal convergence rates for a class of distributions L^（λ,ω） in multicategory classification and nonstandard binary classification.
