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Revisit of Sheppard corrections in linear regression

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Science China Mathematics 2010年第6期53卷 1435-1451页

作者： LIU TianQing1,ZHANG BaoXue1,HU GuoRong1 & BAI ZhiDong1,2,1Key Laboratory for applied statistics of MOE and School of Mathematics and statistics,Northeast Normal university,Changchun 130024,China 2department of statistics and applied probability,national university of singapore,singapore 117543,singapore Key Laboratory for applied statistics of MOE and School of Mathematics and statistics Northeast Normal University Changchun China department of statistics and applied probability National University of Singapore Singapore Singapore

Dempster and Rubin(D&R) in their JRSSB paper considered the statistical error caused by data rounding in a linear regression model and compared the Sheppard correction,BRB correction and the ordinary LSE by *** asymptotic results when the rounding scale tends to 0 were also *** a previous research,we found that the ordinary sample variance of rounded data from normal populations is always inconsistent while the sample mean of rounded data is consistent if and only if the true mean is a multiple of the half rounding *** the light of these results,in this paper we further investigate the rounding errors in linear *** notice that these results form the basic reasons that the Sheppard corrections perform better than other methods in D&R examples and their conclusion in general cases is *** in which the Sheppard correction works worse than the BRB correction are also ***,we propose a new approach to estimate the parameters,called "two-stage estimator",and establish the consistency and asymptotic normality of the new estimators.

关键词： asymptotic normality consistency linear regression model rounded data two-stage estimates

Computational intelligence:From mathematical point of view

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Chinese Science Bulletin 1999年第10期44卷 865-880页

作者： QIAN Minping and GONG Guangludepartment of probability and statistics, Peking university, Beijing 100871, China department of applied Mathematics, Tsinghua university, Beijing 100084, China Deportment of probability and statistics Peking University Beijing China department of applied Mathematics Tsinghua University Beijing China

A simple but illustrative survey is given on various approaches of computational intelligence with their features, applications and the mathematical tools involved, among which the simulated annealing, neural networks, genetic and evolutionary programming, self-organizing learning and adapting algorithms, hidden Markov models are recommended intensively. The common mathematical features of various computational intelligence algorithms are ***, two common principles of concessive strategies implicated in many computational intelligence algorithms are discussed.

关键词： computational intelligence simulated annealing neural network genetic algorithm evolutionary program-ming self-organizing learning self-adapting algorithm hidden Markov model concession strategy.

On comparison of jump point detection for an exchange rate series

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Science China Mathematics 2004年第1期47卷 52-64页

作者： IP Wai-Cheung, WONG Heung, XIE Zhongjie & LUAN Yihuidepartment of applied Mathematics, Hong Kong Polytechnic university, Hong Kong, China department of probability and statistics, Peking university, Beijing 100871, China department of applied Mathematics Hong Kong Polytechnic University Hong Kong China department of probability and statistics Peking University Beijing China

The main purpose of this paper is to investigate the detection of jump points of a discontinuous function in the presence of a noise by the wavelet approach. A computing algorithm of our method is proposed and then applied to the daily exchange rate of US Dollar against Deutsche Mark. All the points detected by our method reflect very strong economic and political impacts. Other statistical methods to detect jump points have also been applied to the same exchange rate data. Our proposed method has produced more convincing empirical results than others.

关键词： exchange rate, jump points, threshold, wavelets.

THE ASYMPTOTICS OF THE INTEGRATEDSQUARE ERROR FOR THE KERNEL HAZARD RATEESTIMATORS WITH LEFT TRENCATED ANDRIGHT CENSORED DATA

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Systems Science and Mathematical Sciences 1999年第3期12卷 251-262页

作者： SUN Liuquan(Institute of applied Mathematics, Academia Sinica, Beijing 100080, China)ZHENG Zhongguo(department of probability and statistics, Peking university, Beijing 100871, China) 中科院应用数学所北京 100080 北京大学概率统计系北京 100871

A central limit theorem for the integrated square error (ISE) of the kernelhazard rate estimators is obtained based on left truncated and right censored data. Anasymptotic representation of the mean integrated square ... 详细信息

关键词： Left truncation and right censorship kernel hazard rate estimators integrated square error central limit theorem an asymptotic representation

STRONG REPRESENTATIONS OF THE SURVIVAL FUNCTION ESTIMATOR ON INCREASING SETS FOR TRUNCATED AND CENSORED DATA

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Acta Mathematica Scientia 1999年第3期19卷 251-260页

作者：孙六全郑忠国 Institute of applied Mathematics Chinese Academy of Sciences Beijing 100080 China department of probability and statistics Peking University Beijing 100871 China

In this paper, based on random left truncated and right censored data, the authors derive strong representations of the cumulative hazard function estimator and the product-limit estimator of the survival function. which are valid up to a given order statistic of the observations. A precise bound for the errors is obtained which only depends on the index of the last order statistic to be included.

关键词： truncated and censored data cumulative hazard function product-limit estimator strong representations

Uniform estimate for maximum of randomly weighted sums with applications to insurance risk theory

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Science China Mathematics 2005年第10期48卷 1379-1394页

作者： WANG Dingcheng~1 SU Chun~2 & ZENG Yong~1 1. School of Management and School of applied Mathematics,university of Electronic Science and Technology of China,Chengdu 610054,China 2. department of statistics and Finance,university of Science and Technology of China,Hefei 230026,China School of Management and School of applied Mathematics University of Electronic Science and Technology of China Chengdu China department of statistics and Finance University of Science and Technology of China Hefei China

This paper obtains the uniform estimate for maximum of sums of independent and heavy-tailed random variables with nonnegative random weights, which can be arbitrarily dependent of each other. Then the applications to ... 详细信息

关键词： dependent stochastic return, discount factor, heavy-tails, discrete time insurance risk model, maxima of randomly weighted sums, ruin probability, tail probabilities, uniformly asymptotic estimate.

Uniform design over a convex polyhedron

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Chinese Science Bulletin 1999年第2期44卷 112-114页

作者： FANG Kaitai , TIAN Guoliang XIE Minyu Hong Kong Baptist university, Kowloon, Hong Kong, China Institute of applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China Central China Normal university, Wuhan 430070, ChinaCorresponding author: Present address: department of probability and statistics, Peking university, Beijing 100871, China Hong Kong Baptist university Hong Kong China Institute of applied Mathematics Chinese Academy of Sciences Beijing China Central China Normal university Wuhan China

A new method, called the simplex method, is proposed to generate the uniform design over a convex polyhedron in n-dimensional Euclidean

关键词： convex polyhedron experimental design uniform design.

Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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Science China Mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2 1. College of applied Sciences,Beijing university of Technology,Beijing 100022,China 2. department of Mathematics,Hong Kong Baptist university,Hong Kong,China College of applied Sciences Beijing University of Technology Beijing China department of Mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

Convergence of Jamison-Type Weighted Sums of Pairwise Negatively Quadrant Dependent Random Variables

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Acta Mathematicae Applicatae Sinica 2002年第1期18卷 161-168页

作者： Han-ying LIANG, Zhi-jing Chen, Chun SUdepartment of applied Mathematics, Tongji university, Shanghai 200092, Chinadepartment of statistics and Finance, university of Science and Technology of China, Hefei 230026, China department of applied Mathematics Tongji University Shanghai China department of statistics and Finance University of Science and Technology of China Hefei China

Under very general weight function, we discuss the convergence of Jamison-type weighted sums of pairwise negatively quadrant dependent (NQD) r.v.'s. The results on i.i.d. setting of [3] and [1] are extended and genera... 详细信息

关键词： Pairwise NQD sequence weighted sum convergence in probability almost sure convergence