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Asymptotic theory for the MLE from randomly censored exponential samples

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Chinese Science Bulletin 1998年第13期43卷 1071-1076页

作者： WANG Qihua department of probability and statistics, peking university, beijing 100871, china department of probability and statistics Peking University Beijing China

The MLE of the parameter of the exponential population from the censored observations is considered. The Edgeworth expansions for the Studentized MLE are established by representing the relevant statistic as a U\|statistic plus a remainder. A semiparametric bootstrap method is introduced to the random censored model and the accuracy of bootstrap approximation of the MLE is investigated. Furthermore, it is shown that the MLE is asymptotically minimax efficient.

关键词： maximum likelihood estimate Edgeworth expansion bootstrap approximation asymptotic minimax efficiency law of iterated logarithm.

The LIL Convergence for Stationary Linear Random Field

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Acta Mathematica Sinica,English Series 1996年第4期12卷 385-397页

作者： He Shuyuan department of probability and statistics peking university beijing, 100871 china department of probability and statistics Peking University Beijing China

Let Y={Y_n;n∈N^2} be a stationary linear random field generated by a two- dimensional martingale difference. Where N^2 denotes the two dimensional integer lattice. The main purpose of this paper is to obtain the LIL ... 详细信息

关键词： Stationary linear random field 1/4 Martingale difference LIL convergency.

Random Weighting T-statistics in Linear Regression Models

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Acta Mathematica Sinica,English Series 1995年第2期11卷 188-199页

作者： Shi Jian Zheng Zhongguo department of probability and statistics peking university beijing, 100871 china department of probability and statistics Peking University Beijing People's Republic of China

In this paper, we have constructed a random weighting statistic to approximate the distribution of studentized least square estimator in a linear regression model with ideal accuracy o(n-1/2). Thus, we have provided a... 详细信息

关键词： Random Weighting T-statistics in Linear Regression Models

ON THE ONE-SIDED LOGARITHMIC LAW FOR ARRAYS

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Systems Science and Mathematical Sciences 1999年第2期12卷 123-132页

作者： QI Yongcheng(department of probability and statistics, peking university, beijing 100871, china) 北京大学概率统计系北京

This paper studies the one-sided logarithmic law for arrays of independent random variables and derives the necessary and sufficient condition for it in the case where the random variables are lid.

关键词： Logarithmic law array of random variables.

A　SIMPLE　ESTIMATOR　FOR　AN　EXPONENTIAL　TAIL　COEFFICIENT

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Systems Science and Mathematical Sciences 1996年第2期9卷 151-156页

作者： QI Yongcheng(department of probability and statistics, peking university, beijing 100871, china) 北京大学概率统计系北京

ＡＳＩＭＰＬＥＥＳＴＩＭＡＴＯＲＦＯＲＡＮＥＸＰＯＮＥＮＴＩＡＬＴＡＩＬＣＯＥＦＦＩＣＩＥＮＴＱＩＹｏｎｇｃｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒ... 详细信息

ＡＳＩＭＰＬＥＥＳＴＩＭＡＴＯＲＦＯＲＡＮＥＸＰＯＮＥＮＴＩＡＬＴＡＩＬＣＯＥＦＦＩＣＩＥＮＴＱＩＹｏｎｇｃｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１００８７...

关键词： Exponential tail regular variation estimator.

THE WEAK LAW OF LARGE NUMBERS WHEN EXTREME TERMS ARE EXCLUDED FROM SUMS

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Systems Science and Mathematical Sciences 1996年第1期9卷 83-92页

作者： QI Yongcheng(department of probability and statistics, peking university,beijing 100871,china) 北京大学概率统计系北京

ＴＨＥＷＥＡＫＬＡＷＯＦＬＡＲＧＥＮＵＭＢＥＲＳＷＨＥＮＥＸＴＲＥＭＥＴＥＲＭＳＡＲＥＥＸＣＬＵＤＥＤＦＲＯＭＳＵＭＳ￥ＱＩＹｏｎｇｃｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ... 详细信息

ＴＨＥＷＥＡＫＬＡＷＯＦＬＡＲＧＥＮＵＭＢＥＲＳＷＨＥＮＥＸＴＲＥＭＥＴＥＲＭＳＡＲＥＥＸＣＬＵＤＥＤＦＲＯＭＳＵＭＳ￥ＱＩＹｏｎｇｃｈｅｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ...

关键词： Weak law of large numbers trimmed sums order statistics.

INFLUENCE ANALYSIS IN CATEGORICAL DATA

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Systems Science and Mathematical Sciences 1999年第3期12卷 273-280页

作者： JIANG Jiancheng(department of probability and statistics, peking university, beijing 100871, china) 北京大学概率统计系北京 100871

This paper gives the local influence diagnostics for parametric multinomialdistribution, especially contingency tables. Basing on the iterative weighted least squaresprocedure, we obtain the M.L.E. of the parameters and the modified Cook’s distance. Byperturbing the cell probabilities, we obtain Cook’s curvature under the restrictive conditionfor our model. Example is given to demonstrate the power of our methods.

关键词： Contingency tables Cook’s distance curvature parametric multinomial distribution

CONVERGENCY OF THE MAXIMUM OF PERIODOGRAM

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Systems Science and Mathematical Sciences 1995年第3期8卷 260-269页

作者： HE Shuyuan(department of probability and statistics, peking university, beijing 100871,china) 北京大学概率统计系北京

ＣＯＮＶＥＲＧＥＮＣＹＯＦＴＨＥＭＡＸＩＭＵＭＯＦＰＥＲＩＯＤＯＧＲＡＭ￥ＨＥＳｈｕｙｕａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ... 详细信息

ＣＯＮＶＥＲＧＥＮＣＹＯＦＴＨＥＭＡＸＩＭＵＭＯＦＰＥＲＩＯＤＯＧＲＡＭ￥ＨＥＳｈｕｙｕａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１００８７１，Ｃｈｉｎａ）Ａｂｓｔ...

关键词： Stationary sequence periodogram trigonometric polynomial strong convergence.

STRONG APPROXIMATION FOR PERTURBED EMPIRICAL PROCESSES

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Systems Science and Mathematical Sciences 1996年第4期9卷 345-353页

作者： ZHOU Yong(department of probability and statistics, peking university, beijing 100871, china) 北京大学概率统计系北京

ＳＴＲＯＮＧＡＰＰＲＯＸＩＭＡＴＩＯＮＦＯＲＰＥＲＴＵＲＢＥＤＥＭＰＩＲＩＣＡＬＰＲＯＣＥＳＳＥＳ￥ＺＨＯＵＹｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒ... 详细信息

ＳＴＲＯＮＧＡＰＰＲＯＸＩＭＡＴＩＯＮＦＯＲＰＥＲＴＵＲＢＥＤＥＭＰＩＲＩＣＡＬＰＲＯＣＥＳＳＥＳ￥ＺＨＯＵＹｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＰｒｏｂａｂｉｌｉｔｙａｎｄＳｔａｔｉｓｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１００８７...

关键词： Strong approximation empirical process Brownian bridge Kiefer process KerneLsin’oothing.