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Large deviations for Glauber dynamics of continuous gas

Science China Mathematics 2008年第5期51卷 973-986页

作者： SONG QiongXia~(1,2) 1 School of Mathematical Sciences,Wuhan University,Wuhan 430072,China 2 Department of Statistics and Probability,Michigan State University,East Lansing,MI48824,USA School of Mathematical Sciences Wuhan University Wuhan China Department of Statistics and Probability Michigan State University East Lansing USA

This paper is devoted to the large deviation principles of the Glauber-type dynamics of finite or infinite volume continuous particle systems. We prove that the level-2 empirical process satisfies the large deviation principles in the weak convergence topology, while it does not satisfy the large deviation principles in the τ-topology.

关键词： Gibbs measures Glauber dynamics empirical processes large deviation principles 60J25 60F10 82B21 82C21

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A simple construction of optimal estimation in multivariate marginal Cox regression

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Science China Mathematics 2012年第9期55卷 1827-1857页

作者： CUI WenQuan YING ZhiLiang ZHAO LinCheng Department of Statistics and Finance University of Science and Technology of China Hefei 230026 China Department of Statistics Columbia University New York NY 10027 USA

The multivariate extension of the Cox model proposed by Wei,Lin and Weissfeld in 1989 has been widely used for analyzing multivariate survival *** the model assumption,failure times from an individual are assumed to marginally follow their respective proportional hazards regression relation,leaving the joint distribution completely *** paper presents a simple approach to efficiency improvement through segmentation of stochastic integrals in the marginal estimating equations and incorporation of the limiting covariance *** is shown that when partition of the time interval is done at a suitable rate,the resulting estimator is consistent and asymptotically *** the reproducing kernel Hilbert space arising from the covariance function of the limiting Gaussian process,it is also shown that the proposed estimator is asymptotically optimal within a reasonable class of estimators under marginal *** are conducted to assess the finite-sample performance of the proposed method.

关键词： multivariate survival data marginal proportional hazards regression WLW method estimatingequations empirical processes martingale reproducing kernel Hilbert spaces limit theorem of reproducingkernels

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PROJECTION-PURSUIT BASED PRINCIPAL COMPONENT ANALYSIS:A LARGE SAMPLE THEORY

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Journal of Systems Science & Complexity 2006年第3期19卷 365-385页

作者： Jian ZHANG Institute of Mathematics,Statistics and Actuarial Science,University of Kent,Canterbury,Kent CT2 7NF,U.K. Institute of Systems Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100080,China Institute of Mathematics Statistics and Actuarial Science University of Kent Canterbury Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences

The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techniques. However, the application of this extended procedure is often hampered by its complexity in computation and by lack of some appropriate theory. In this paper, by use of the empirical processes we established a large sample theory for the robust PP estimators of the principal components and dispersion matrix.

关键词： Dispersion matrices eigenvalues and eigenvectors empirical processes principal component analysis projection pursuit (PP).

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