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Detecting Difference Between Coefficients in Linear Model Using Jackknife Empirical Likelihood

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Journal of Systems Science & Complexity 2016年第2期29卷 542-556页

作者： WU Xinqi zhang Qingzhao zhang sanguo School of Mathematical Sciences University of Chinese Academy of Sciences Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of Sciences

Empirical likelihood has been found very useful in many different occasions. It usually runs into serious computational difficulties while jackknife empirical likelihood （JEL） is shown to be effective when applied to some complicated statistics. In this paper, to test the difference between coefficients of two linear regression models, the authors apply JEL to construct the confidence regions. Based on the 3EL ratio test, a version of Wilks＇ theorem is developed. Furthermore, to improve the coverage accuracy of confidence regions, a Bartlett correction is applied. Simulation studies are carried out to show the effectiveness of the proposed method in aspects of coverage accuracy. A real data set is analyzed with the proposed method as an example.

关键词： Bartlett correction coverage accuracy Jackknife empirical likelihood linear regression model.

Empirical Likelihood Test for Regression Coefficients in High Dimensional Partially Linear Models

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Journal of Systems Science & Complexity 2021年第3期34卷 1135-1155页

作者： LIU Yan REN Mingyang zhang sanguo School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of SciencesBeijing 100190China

This paper considers tests for regression coefficients in high dimensional partially linear *** authors first use the B-spline method to estimate the unknown smooth function so that it could be linearly ***,the authors propose an empirical likelihood method to test regression *** authors derive the asymptotic chi-squared distribution with two degrees of freedom of the proposed test statistics under the null *** addition,the method is extended to test with nuisance *** show that the proposed method have a good performance in control of type-I error rate and *** proposed method is also employed to analyze a data of Skin Cutaneous Melanoma(SKCM).

关键词： Empirical likelihood test high dimensional analysis partially linear models regression coefficients

SIEVE LEAST SQUARES ESTIMATOR FOR PARTIAL LINEAR MODELS WITH CURRENT STATUS DATA

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Journal of Systems Science & Complexity 2011年第2期24卷 335-346页

作者： Songlin WANG sanguo zhang Hongqi XUE School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Beijing 100049 China. Department of Biostatistics and Computational Biology University of Rochester 601 Elmwood Avenue Box 630 Rochester NY 14642 USA

Current status data often arise in survival analysis and reliability studies, when a continuous response is reduced to an indicator of whether the response is greater or less than an observed random threshold value. This article considers a partial linear model with current status data. A sieve least squares estimator is proposed to estimate both the regression parameters and the nonparametric function. This paper shows, under some mild condition, that the estimators are strong consistent. Moreover, the parameter estimators are normally distributed, while the nonparametric component achieves the optimal convergence rate. Simulation studies are carried out to investigate the performance of the proposed estimates. For illustration purposes, the method is applied to a real dataset from a study of the calcification of the hydrogel intraocular lenses, a complication of cataract treatment.

关键词： Convergence rate current status data partial linear model sieve least squares estimator strong consistent.

On some problems of weak consistency of quasi-maximum likelihood estimates in generalized linear models

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Science China Mathematics 2008年第7期51卷 1287-1296页

作者： zhang sanguo Liao Yuan School of Mathematical Sciences Graduate University of Chinese Academy of SciencesBeijing 100049China

In this paper, we explore some weakly consistent properties of quasi-maximum likelihood estimates (QMLE) concerning the quasi-likelihood equation $ \sum\nolimits_{i = 1}^n {X_i (y_i - \mu (X_i^\prime \beta ))} $ for univariate generalized linear model E(y|X) = μ(X′β). Given uncorrelated residuals {e i = Y i ? μ(X i ′ β0), 1 ? i ? n} and other conditions, we prove that $$ \hat \beta _n - \beta _0 = O_p (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n^{ - 1/2} ) $$ holds, where $ \hat \beta _n $ is a root of the above equation, β 0 is the true value of parameter β and $$ \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{\lambda } _n $$ denotes the smallest eigenvalue of the matrix S n = ∑ i=1 n X i X i ′ . We also show that the convergence rate above is sharp, provided independent non-asymptotically degenerate residual sequence and other conditions. Moreover, paralleling to the elegant result of Drygas (1976) for classical linear regression models, we point out that the necessary condition guaranteeing the weak consistency of QMLE is S n ?1 → 0, as the sample size n → ∞.

关键词： generalized linear models (GLMs) quasi-maximum likelihood estimates (QMLE) weak consistency convergence rate 62E20 62J12

A theoretic study of a distance-based regression model

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Science China Mathematics 2019年第5期62卷 979-998页

作者： Jialu Li Wei zhang sanguo zhang Qizhai Li School of Mathematics and Statistics Beijing Institute of Technology Biostatistics and Bioinformatics Branch National Institute of Child Health and Human Development School of Mathematical Sciences University of Chinese Academy of Sciences Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of Sciences LSC NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences

The distance-based regression model has many applications in analysis of multivariate response regression in various ?elds, such as ecology, genomics, genetics, human microbiomics, and neuroimaging. It yields a pseudo F test statistic that assesses the relation between the distance(dissimilarity) of the subjects and the predictors of interest. Despite its popularity in recent decades, the statistical properties of the pseudo F test statistic have not been revealed to our knowledge. This study derives the asymptotic properties of the pseudo F test statistic using spectral decomposition under the matrix normal assumption, when the utilized dissimilarity measure is the Euclidean or Mahalanobis distance. The pseudo F test statistic with the Euclidean distance has the same distribution as the quotient of two Chi-squared-type mixtures. The denominator and numerator of the quotient are approximated using a random variable of the form ξχ_d^2+ η, and the approximate error bound is given. The pseudo F test statistic with the Mahalanobis distance follows an F *** simulation studies, the approximated distribution well matched the "exact" distribution obtained by the permutation procedure. The obtained distribution was further validated on H1N1 in?uenza data, aging human brain data, and embryonic imprint data.

关键词： distance-based regression Euclidean pseudo F test statistic Mahalanobis

A Model-Embedded Trend Test with Incorporating Hardy-Weinberg Equilibrium Information

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Journal of Systems Science & Complexity 2017年第1期30卷 101-110页

作者： HU Xiaonan DUAN Xiaogang PAN Dongdong zhang sanguo LI Qizhai School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China KeyLaboratory of Big Data Mining and Knowledge Management Chinese Academy of Sciences Beijing 100190China. School of Statistics Beijing Normal University Beijing 100875 China. Department of Statistics Yunnan University Kunming 650091 China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy ofSciences Beijing 100190 China.

The genetic models are greatly important in the analysis of genetic epidemiologic studies and many of the studies are conducted using the trend test under the additive model. However, for many complex diseases and traits, the underlying genetic model for a genetic locus is usually uncertain. So a robust test free of genetic model is appropriate. In this paper, the authors propose a model-embedded trend test by incorporating Hardy-Weinberg equilibrium information and obtain the explicit formula to calculate its statistical significance. Extensive simulation studies show the proposed test is more robust than the existing procedures. Finally, a real application is further analyzed to show the performance of the proposed test.

关键词： Genetic model hardy-weinberg equilibrium power robust trend test.

Linear EV model with replicate observations on independent variables

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Science China Mathematics 2006年第6期49卷 752-769页

作者： LIU Jixue, zhang sanguo & CHEN Xiru Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China Department of Mathematics, Graduate School of Chinese Academy of Sciences, Beijing 100049, China Department of Statistics and Finance University of Science and Technology of China Hefei China Department of Mathematics Graduate School of Chinese Academy of Sciences Beijing China

This paper studies the linear EV model when replicate observations are made only on independent variables. We construct the estimates of regression coefficients and prove the consistency and asymptotic normality under some proper conditions. Results obtained reveal the difference between the case where the independent and dependent variables are observed repeatedly and simultaneously and the case studied in this article.

关键词： linear EV model, consistency, asymptotic normality.

ON ASYMPTOTIC NORMALITY OF PARAMETERS IN LINEAR EV MODEL

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Chinese Annals of Mathematics,Series B 2002年第4期23卷 495-506页

作者： zhang sanguo CHEN XIRUHua Lee-Keng Institue for applied Mathematics and Information Science, Graduate School of ChineseAcademy of Sciences, Beijing 100039, China. Department of Mathematics, Graduate School of Chinese Academy of Sciences, Hua Lee-Keng Institue for applied Mathematics and Information Science Graduate School of Chinese Academy of Sciences Beijing 100039 China Department of Mathematics Graduate School of Chinese Academy of Sciences Beijing 100039 China

This paper studies the parameter estimation of one dimensional linear errors-in-variables(EV) models in the case that replicated observations are available in some experimental *** normality is established under mild conditions, and the parameters entering the asymptotic variance are consistently estimated to render the result useable in construction of large-sample confidence regions.

关键词： Errors-in-Variables model Asymptotic normality Replicated observations

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基于高频夏普比率和稳健相关系数的资产选择

中国科学院大学学报（中英文） 2023年第6期40卷 834-842页

作者：张杉桦张三国中国科学院大学数学科学学院北京100049

高频夏普比率是衡量收益和风险的指标,可以避免估计高维分析中的协方差矩阵,所以在目前的投资组合构建方法中被普遍使用。近年提出的D-SEV方法,通过测量股票收益和高频夏普比率指数之间的相关性,来进一步构建投资组合。然而,D-SEV中用... 详细信息

高频夏普比率是衡量收益和风险的指标,可以避免估计高维分析中的协方差矩阵,所以在目前的投资组合构建方法中被普遍使用。近年提出的D-SEV方法,通过测量股票收益和高频夏普比率指数之间的相关性,来进一步构建投资组合。然而,D-SEV中用来度量股票与高频夏普比率的相关性的方法存在一些问题,如缺乏稳健性和计算速度慢。在本文中,使用由Sourav Chatterjee提出的新的相关系数来代替。新的相关系数保证了稳健性,特别是它可以降低异常值对相关性的影响,比如对资产价格有很大影响的重大事件。同时它的计算速度也非常快。大量的模拟表明,新的相关系数在几个不同的模型中的表现优于D-SEV和其他传统方法。2019年和2020年的上证和深证股市数据也显示,新的相关系数选择的资产组合比D-SEV选择的资产组合的年化收益高出8%,同时也拥有较高的夏普比率。

关键词：资产组合高频夏普比率稳健相关系数