广义U—统计量的指数收敛速度

文「１」研究了一样本Ｕ－统计量的指数收敛速度，本文则研究了广义Ｕ－统计量的指数收敛速度。     

U-统计量的指数收敛速度的进一步讨论

在独立未必同分布的情形下，对U－统计量的指数收敛速度进行了讨论，减弱文[2]中的部分条件，给出了类似的结果，同时对Von-Mises统计量也给出了指数收敛速度。     

U-统计量投影残差的指数收敛速度及其应用(英文)

本文研究了一样本U-统计量投影残差的收敛速度,在核函数有界及某种意义下的指数型有界时,本文得到了一些指数收敛速度,最后,利为上述结果的应用,本文还研究了刻度参数的变点问题.     

U—统计计量投影残差的指数收敛速度及其应用

本文研究了一样本Ｕ－统计量投影残差的收敛速度，在核函数有界及某种意义下的指数型有界时，本文得到了一些指数收敛速度，最后，利为上述结果的应用，本文还研究了刻度参数的变点问题。     

关于有界核两样本U统计量余项的指数收敛速度

设Ｕｍｎ是以有界对称函数　（ｘ，ｙ）为核的两样本Ｕ－统计量．本文讨论了Ｕｍｎ与其投影之差的指数收敛速度问题，它有别于Ｈｏｅｆｆｄｉｎｇ关于有界核Ｕ－统计量的指数不等式．是两样本Ｕ－统计量所特有的．     

关于Von－Mises统计量的非一致性收敛速度

本文研究了Ｖｏｎ－Ｍｉｓｅｓ统计量的非一致性收敛速度，得到与Ｕ－统计量类似的收敛速度．     

关于线性秩统计量的渐近正态性及其收敛速度

本文讨论线性秩统计量的渐近正态性的条件及其收敛速度．推广了Hajek关于线性秩统计量收敛于正态分布的条件的重要定理，并得出了一个较易验证的充分条件．对于一般形式的计分函数，在一定条件下得出了相应线性秩统计量收敛于正态分布的速度．     

关于U-统计量和Von-Mises统计量的极限性质

本文在核的r阶矩(r≥1)有限的条件下,获得了U-统计量的r阶矩的数量级.利用这个结果,完全解决了在上述条件下U-统计量的a.e.收敛速度问题.另一方面,在核的上述假定下得出了U-统计量和Von-Mises统计量的联系公式,并解决了Von-Mises统计量的收敛速度问题.特别,在三阶矩有限的条件下建立了Von-Mises统计量的Berry-Esseen界限.     

关于U-统计量的非一致性收敛速度

研究了高阶矩条件下,U-统计量的非一致性收敛速度,给出了一系列平行于独立和的理想结果.     

关于线性秩统计量的渐近下在态性及其收敛速度

本文讨论线性失统计量的渐近正诚性的条件及其收敛速度。     

The positive-divergence and blowing-up properties

A property of ergodic finite-alphabet processes, called the blowing-up property, is shown to imply exponential rates of convergence for frequencies and entropy, which in turn imply a positive-divergence property. Furthermore, processes with the blowing-up property-divergence property. Furthermore, processes with the blowing-up property are finitely determined and the finitely determined property plus exponential rates of convergence for frequencies and for entropy implies blowing-up. It is also shown that finitary codings of i.i.d. processes have the blowing-up property. Partially supported by Hungarian National Foundation for Scientific Research Grant OTKA 1906. Partially supported by NSF grant DMS-9024240.     

On exceedances of record and order statistics

Exact, limiting distributions along with their rates of convergence of exceedance statistics for both order statistics and record statistics are provided when the underlying distribution is arbitrary. The exact distribution of record statistics for arbitrary underlying distributions is obtained as well.

     

On Rates of Uniform Convergence of Lower Extreme Generalized Order Statistics

Under a von Mises-type condition the joint distribution of suitable normalized lower extreme generalized order statistics converges w.r.t. the variational distance to the asymptotic joint distribution of lower extreme order statistics. Rates of uniform convergence are established. It turns out that the rates of uniform convergence known for ordinary extremes carry over to lower generalized extremes. Finally, models of Weibull type are concerned, where uniform rates are used in connection with model approximations in order to simplify statistical inference.AMS 2000 Subject Classification. Primary—60G70     

Exponential Convergence Rates of Markov Chains under a Weaken Minorization Condition

In this paper, we obtain the quantitative bound of the exponential convergence rates of Markov chains under a weaken minorization condition, using the coupling method and the analytic approach. And also, we obtain the convergence rates for continuous time Markov processes.     

Rate of Convergence of Intermediate Order Statistics

Exact rates are derived for the uniform convergence of the density of intermediate order statistics towards the normal or lognormal density under certain smoothness conditions. Our methods also give the exact rate of convergence in the uniform metric and in the total variation metric.     

连续型单参数指数族的经验Bayes检验

本文讨论了连续型单参数指数族的经验Bayes检验问题 .利用核估计方法构造了EB检验函数并获得了它的收敛速度 .     

The Weighted Lebesgue Constant of Lagrange Interpolation for Exponential Weights on [-1, 1]

We establish uniform estimates for the weighted Lebesgue constant of Lagrange interpolation for a large class of exponential weights on [-1, 1]. We deduce theorems on uniform convergence of weighted Lagrange interpolation together with rates of convergence.     

基于纵向数据下连续型单参数指数族参数的经验贝叶斯检验(英文)

本文讨论了在纵向数据下,运用非参数估计方法构造了连续型单参数指数族参数的经验贝叶斯检验函数,证明了所提出的经验贝叶斯检验函数的渐近最优性,并获得了它的收敛速度.     

指数分布危险函数的经验Bayes双侧检验的收敛速度: Ⅱ型截尾情形

本文讨论了Ⅱ型截尾情形下指数分布危险函数的经验Bayes (EB)双侧检验问题. 利用概率密度函数的核估计构造了经验Bayes检验函数, 在适当的条件下获得了它的收敛速度.