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Local Dependence Test Between Random Vectors Based on the Robust Conditional Spearman's ρ and Kendall's τ

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Acta Mathematicae Applicatae Sinica 2023年第3期39卷 491-510页

作者： Ling-yue ZHANG heng-jian cui School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

This paper introduces two local conditional dependence matrices based on Spearman'sρand Kendall'sτgiven the condition that the underlying random variables belong to the intervals determined by their quantiles.The robustness is studied by means of the influence functions of conditional Spearman'sρand Kendall'sτ.Using the two matrices,we construct the corresponding test statistics of local conditional dependence and derive their limit behavior including consistency,null and alternative asymptotic distributions.Simulation studies illustrate a superior power performance of the proposed Kendall-based test.Real data analysis with proposed methods provides a precise description and explanation of some financial phenomena in terms of mathematical statistics.

关键词： local dependence influence function rank correlation U-statistic

Variance Variation Criterion and Consistency in Estimating the Number of Significant Signals of High-dimensional PCA

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Acta Mathematicae Applicatae Sinica 2022年第3期38卷 513-531页

作者： Guan-peng WANG heng-jian cui School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

In this paper,we propose a criterion based on the variance variation of the sample eigenvalues to correctly estimate the number of significant components in high-dimensional principal component analysis(PCA),and it corresponds to the number of significant eigenvalues of the covariance matrix for p-dimensional variables.Using the random matrix theory,we derive that the consistent properties of the proposed criterion for the situations that the significant eigenvalues tend to infinity,as well as that the bounded significant population eigenvalues.Numerical simulation shows that the probability of estimator is correct by our variance variation criterion converges to 1 is faster than that by criterion of Passemier and Yao[Estimation of the number of spikes,possibly equal,in the high-dimensional case.J.Multivariate Anal.,(2014)](PYC),AIC and BIC under the finite fourth moment condition as the dominant population eigenvalues tend to infinity.Moreover,in the case of the maximum eigenvalue bounded,once the gap condition is satisfied,the rate of convergence to 1 is faster than that of PYC and AIC,especially the effect is better than AIC when the sample size is small.It is worth noting that the variance variation criterion significantly improves the accuracy of model selection compared with PYC and AIC when the random variable is a heavy-tailed distribution or finite fourth moment not exists.

关键词： consistency variance variation criterion significant eigenvalues high dimension spiked model

Efficient Estimation of a Varying-coefficient Partially Linear Binary Regression Model

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Acta Mathematica Sinica,English Series 2010年第11期26卷 2179-2190页

作者： TaoHU heng jian cui School of Mathematical Sciences Capital Normal University Beijing 100048 P. R. China School of Mathematical Sciences Beijing Normal University Beijing 100875 P. R. China

This article considers a semiparametric varying-coefficient partially linear binary regression model. The semiparametric varying-coefficient partially linear regression binary model which is a generalization of binary regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable. A Sieve maximum likelihood estimation method is proposed and the asymptotic properties of the proposed estimators are discussed. One of our main objects is to estimate nonparametric component and the unknowen parameters simultaneously. It is easier to compute, and the required computation burden is much less than that of the existing two-stage estimation method. Under some mild conditions, the estimators are shown to be strongly consistent. The convergence rate of the estimator for the unknown smooth function is obtained, and the estimator for the unknown parameter is shown to be asymptotically efficient and normally distributed. Simulation studies are carried out to investigate the performance of the proposed method.

关键词： Partially linear model varying-coefficient binary regression asymptotically efficient estimator sieve MLE

Hypothesis Test for the Parameters of Linear Part in the Partial Linear EV Model

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Acta Mathematicae Applicatae Sinica 2015年第4期31卷 1153-1166页

作者： Juan ZHANG heng-jian cui Capital University of Economics and Business Capital Normal University

Hypothesis testing for the parametric component in the partial linear errors-in-variables （EV） regression models is discussed in this paper. Based on the corrected profile least square estimator, five test statistics are proposed and the asymptotic null distributions of them are deduced. Simulations have been done to show the performance of these test statistics under null and alternative hypothesis.

关键词： partial linear model measurement error bandwidth selection hypothesis testing

Efficient Distributed Estimation of High-dimensional Sparse Precision Matrix for Transelliptical Graphical Models

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Acta Mathematica Sinica,English Series 2021年第5期37卷 689-706页

作者： Guan Peng WANG heng jian cui School of Mathematical Sciences Capital Normal UniversityBeijing 100048P.R.China

In this paper,distributed estimation of high-dimensional sparse precision matrix is proposed based on the debiased D-trace loss penalized lasso and the hard threshold method when samples are distributed into different machines for transelliptical graphical models.At a certain level of sparseness,this method not only achieves the correct selection of non-zero elements of sparse precision matrix,but the error rate can be comparable to the estimator in a non-distributed setting.The numerical results further prove that the proposed distributed method is more effective than the usual average method.

关键词： Distributed estimator sparse precision matrix high-dimensional hard threshold efficient communication

Robust Nonparametric Function Estimation for Errors-in-variables Models

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Acta Mathematicae Applicatae Sinica 2020年第2期36卷 314-331页

作者： Chao-xia YUAN heng-jian cui School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

This paper discusses robust nonparametric estimators of location regression function for errorsin-variables model with de-convolution kernel.The local constant smoother is used for the estimation of the nonparametric function,and the local linear smoother is proposed to deal with the boundary problem,as well as to improve the local constant smoother.We establish the asymptotic properties of the estimator,the influence function of the statistical functional and the breakdown point.A simulation study is carried out to demonstrate robust performance of the proposed estimator.The motorcycle data is presented to illustrate the application of the robust estimator further.

关键词： errors-in-variables de-convolution kernel robust local linear

Empirical Likelihood Inference for a Partially Linear Errors-in-variables Model with Covariate Data Missing at Random

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 305-318页

作者： Shan-shan WANG heng-jian cui School of Economics and Management Beihang UniversityBeijing 100191China Beijing Key Laboratory of Emergency Support Simulation Technologies for City Operations Beijing 100191China School of Mathematical Sciences&:BCMIIS Capital Normal UniversityBeijing 100048China

The authors study the empirical likelihood method for partially linear errors-in-variables model with covariate data missing at random. Empirical likelihood ratios for the regression coeffidents and the baseline function are investigated, and the corresponding empirical log-likelihood ratios are proved to be asymptotically standard chi-squared, which can be used to construct confidence regions. The finite sample behavior of the proposed methods is evaluated by a simulation study which indicates that the proposed methods are comparable in terms of coverage probabilities and average length of confidence intervals. Finally, the Earthquake Magnitude dataset is used to illustrate our proposed method.

关键词： chi-square distribution confidence region coverage probability empirical likelihood partiallylinear model

Trimmed and Winsorized Transformed Means Based on a Scaled Deviation

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Acta Mathematicae Applicatae Sinica 2015年第2期31卷 475-492页

作者： Si-yang WANG heng-jian cui School of Statistics and Mathematics Central University of Finance and Economics Department Statistics School of Mathematical Sciences Capital Normal University

This paper introduces the Tukey trimmed and Winsorized means for the transformed data based on a scaled deviation. The trimmed and Winsorized means and scale based on a scaled deviation are as special cases. Meanwhile, the trimmed and Winsorized skewness and kurtosis based on a scaled deviation are given.Furthermore, some of their robust properties（influence function, breakdown points） and asymptotic properties（asymptotic representation and limiting distribution） are also obtained.

关键词： trimmed and Winsorized transformed means influence function skewness kurtosis

Partial Penalized Empirical Likelihood Ratio Test Under Sparse Case

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 327-344页

作者： Shan-shan WANG heng-jian cui School of Economics and Management Beihang University School of Mathematical Sciences & BCMIIS Capital Normal University

A consistent test via the partial penalized empirical likelihood approach for the parametric hy- pothesis testing under the sparse case, called the partial penalized empirical likelihood ratio （PPELR） test, is proposed in this paper. Our results are demonstrated for the mean vector in multivariate analysis and regression coefficients in linear models, respectively. And we establish its asymptotic distributions under the null hypoth- esis and the local alternatives of order n-1/2 under regularity conditions. Meanwhile, the oracle property of the partial penalized empirical likelihood estimator also holds. The proposed PPELR test statistic performs as well as the ordinary empirical likelihood ratio test statistic and outperforms the full penalized empirical like- lihood ratio test statistic in term of size and power when the null parameter is zero. Moreover, the proposed method obtains the variable selection as well as the p-values of testing. Numerical simulations and an analysis of Prostate Cancer data confirm our theoretical findings and demonstrate the promising performance of the proposed method in hypothesis testing and variable selection.

关键词： Chi-squared distribution empirical likelihood partial penalized empirical likelihood SCAD sparse