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ESTIMATION FOR THE AYMPTOTIC VARIANCE OF PARAMETRIC ESTIMATES IN PARTIAL LINEAR MODEL WITH CENSORED DATA

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Acta Mathematica Scientia 1996年第2期16卷 192-208页

作者：秦更生蔡雷 Dept. of Math. Sichuan University Chengdu 610064 China

Consider tile partial linear model Y=Xβ+ g(T) + e. Wilers Y is at risk of being censored from the right, g is an unknown smoothing function on [0,1], β is a 1-dimensional parameter to be estimated and e is an unobserved error. In Ref[1,2], it wes proved that the estimator for the asymptotic variance of βn(βn) is consistent. In this paper, we establish the limit distribution and the law of the iterated logarithm for,En, and obtain the convergest rates for En and the strong uniform convergent rates for gn(gn).

关键词： Partial linear model Censored data Kernel method asymptotic normality Thc law of the iterated logarithm.

Testing for Random Effects in Linear Mixed Models for Longitudinal Data under Moment Conditions

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Acta Mathematica Sinica,English Series 2010年第3期26卷 497-514页

作者： Zai King LI Li Xing ZHU Ping WU Jian Hong WU Wang Li XU Department of Mathematics China University of Mining & Technology Beijing 100083 P. R. China Department of Mathematics Hong Kong Baptist University Hong Kong P. R. China School of Finance and Statistics East China Normal University Shanghai 200241 P. R. China College of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 P. R. China School of Statistics Renmin University of China Beijing 100872 P. R. China

In this paper, we consider whether the random effect exists in linear mixed models （LMMs） when only moment conditions are assumed. Based on the estimators of parameters and their asymptotic properties, a Wald-type test is constructed. It is consistent against global alternatives and is sensitive to the local alternatives converging to the null hypothesis at parametric rates, a fastest possibly rate for goodness-of-fit testing. Moreover, a simulation study shows the performance of the test is good. The procedure also applies to a real data.

关键词： consistent estimators asymptotic normality LMMs random effects

A scalar dynamic conditional correlation model:Structure and estimation

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Science China Mathematics 2018年第10期61卷 1881-1906页

作者： Hui Wang Jiazhu Pan School of Finance Central University of Finance and Economics Department of Mathematics and Statistics University of Strathclyde

The dynamic conditional correlation(DCC) model has been widely used for modeling the conditional correlation of multivariate time series by Engle(2002). However, the stationarity conditions have been established only recently and the asymptotic theory of parameter estimation for the DCC model has not yet to be fully discussed. In this paper, we propose an alternative model, namely the scalar dynamic conditional correlation(SDCC) model. Sufficient and easily-checked conditions for stationarity, geometric ergodicity, andβ-mixing with exponential-decay rates are provided. We then show the strong consistency and asymptotic normality of the quasi-maximum-likelihood estimator(QMLE) of the model parameters under regular *** asymptotic results are illustrated by Monte Carlo experiments. As a real-data example, the proposed SDCC model is applied to analyzing the daily returns of the FSTE(financial times and stock exchange) 100 index and FSTE 100 futures. Our model improves the performance of the DCC model in the sense that the Li-Mc Leod statistic of the SDCC model is much smaller and the hedging efficiency is higher.

关键词： dynamic conditional correlation stationarity ergodicity QMLE consistency asymptotic normality

M-estimation for Periodic GARCH Model with High-frequency Data

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Acta Mathematicae Applicatae Sinica 2017年第3期33卷 717-730页

作者： Peng-ying FAN Si-xin WU Zi-long ZHAO Min CHEN School of Economics Beijing Technology and Business University Academy of Mathematics and Systems Science Chinese Academy of Sciences

This paper studies an M-estimator of a proxy periodic GARCH （p, q） scaling model and establishes its consistency and asymptotic normality. Simulation studies are carried out to assess the performance of the estimator. The numerical results show that our M-estimator is more efficient and robust than other estimators without the use of high-frequency data.

关键词： asymptotic normality consistency high-frequency data PGARCH model M-estimator

LARGE SAMPLE PROPERTIES OF THE SIR IN CDMA WITH MATCHED FILTER RECEIVERS

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Chinese Annals of Mathematics,Series B 2005年第3期26卷 401-412页

作者： PANGUANGMING MIAOBAIQI ZHUCHUNHUA DepartmentofStatisticsandFinance UniversityofScienceandTechnologyofChinaHefei230026China DepartmentofStatisticsandFinance UniversityofScienceandTechnologyofChinaHefei230026China DepartmentofMathematics AnhuiUniversityHefei230026China

The output signal-to-interference (SIR) of conventional matched filter receiver in random environment is considered. When the number of users and the spreading factors tend to infinity with their ratio fixed, the convergence of SIR is showed to be with probability one under finite *** of the spreading sequences. The asymptotic distribution of the SIR is also obtained.

关键词： Strong convergence asymptotic normality Empirical distribution Martingale

asymptotic Theory for Relative-Risk Models with Missing Time-Dependent Covariates

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Acta Mathematicae Applicatae Sinica 2018年第4期34卷 669-692页

作者： Zai-ying ZHOU Peng-cheng ZHANG Ying YANG Department of Mathematical Sciences Tsinghua University Beijing 100084 China Center for Statistical Science of Tsinghua University Beijing 100084 China

Relative-risk models are often used to characterize the relationship between survival time and time-dependent covariates. When the covariates are observed, the estimation and asymptotic theory for parameters of interest are available; challenges remain when missingness occurs. A popular approach at hand is to jointly model survival data and longitudinal data. This seems efficient, in making use of more information, but the rigorous theoretical studies have long been ignored. For both additive risk models and relative-risk models, we consider the missing data nonignorable. Under general regularity conditions, we prove asymptotic normality for the nonparametric maximum likelihood estimators.

关键词： relative-risk model missing time-dependent covariate nonparametric maximum likelihood esti-mation asymptotic normality

ESTIMATING EXTREME-VALUE INDEX FROM RECORDS

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Chinese Annals of Mathematics,Series B 1998年第4期19卷 499-510页

作者： QI YONGCHENG (Department of Probability & Statistics, Peking University, Beijing 100871, China.) 北京大学概率统计系北京

This paper constructs from the record values an estimator of the extreme-value index. It is proved that the estimator is consistent in the domain of attraction of extremesvalue distributions, and that under very mild ... 详细信息

关键词： Record Extreme value distribution Estimator Consistency asymptotic normality

Generalized Profile LSE in Varying-Coefficient Partially Linear Models with Measurement Errors

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Acta Mathematicae Applicatae Sinica 2013年第3期29卷 477-490页

作者： Yun-bei MA Jin-hong YOU Yong ZHOU School of Statistics Southwestern University of Finance and Economics School of Statistics and Management Shanghai University of Finance and Economics Academy of Mathematics and System Sciences Chinese Academy of Sciences

This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Yi=Xτiβ＋Zτiα（Ui）＋εi , Wi=Xi＋ξi,i=1, · · · , n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.

关键词： Semiparametric modeling varying-coefficient measurement error local polynomial profile least squares asymptotic normality

A　KERNEL　ESTIMATOR　OF　A　DENSITY　FUNCTION　IN　MULTIVARIATE　CASE　FROM　RANDOMLY　CENSORED　DATA

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Acta Mathematica Scientia 1996年第2期16卷 170-180页

作者：周勇 Probability laboratory in Inst. of Appl. Math. Academia Sinica Beijing 100080 China

A kernel density estimator is proposed when tile data are subject to censorship in multivariate case. The asymptotic normality, strong convergence and asymptotic optimal bandwidth which minimize the mean square error ... 详细信息

关键词： Kernel density estimator asymptotic normality product-limit estimator,mean square error and censored data.