This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allo...This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.展开更多
ζk is one of the most important constant in the siève methods.Tlus paper gives the relatively accurate lower bound and upper bound on it,that is,3<sup>-1/k</sup>ck,where c=1.22... and k】16.
We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline e...We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline estimators of the functional coefficient and the smooth functions are considered,and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions.Some simulation results and a real data example are presented to illustrate the performance of our estimation method.展开更多
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. T...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.展开更多
基金The talent research fund launched (3004-893325) of Dalian University of Technologythe NNSF (10271049) of China.
文摘This article concerded with a semiparametric generalized partial linear model （GPLM） with the type Ⅱ censored data. A sieve maximum likelihood estimator （MLE） is proposed to estimate the parameter component, allowing exploration of the nonlinear relationship between a certain covariate and the response function. Asymptotic properties of the proposed sieve MLEs are discussed. Under some mild conditions, the estimators are shown to be strongly consistent. Moreover, the estimators of the unknown parameters are asymptotically normal and efficient, and the estimator of the nonparametric function has an optimal convergence rate.
文摘ζk is one of the most important constant in the siève methods.Tlus paper gives the relatively accurate lower bound and upper bound on it,that is,3<sup>-1/k</sup>ck,where c=1.22... and k】16.
基金supported by National Natural Science Foundation of China(Grant Nos.71420107025,11071022,11231010 and 11471223)the Innovation Foundation of Beijing University of Aeronautics and Astronautics for Ph.D.graduates(Grant No.YWF-14-YJSY-027)+2 种基金the National High Technology Research and Development Program of China(863 Program)(Grant No.SS2014AA012303)Beijing Center for Mathematics and Information Interdisciplinary Sciences,Key Project of Beijing Municipal Educational Commission(Grant No.KZ201410028030)Youth Doctor Development Funding Project for"121"Human Resources of Central University of Finance and Economics(Grant No.QBJ1423)
文摘We propose sieve M-estimator for a semi-functional linear model in which the scalar response is explained by a linear operator of functional predictor and smooth functions of some real-valued random variables.Spline estimators of the functional coefficient and the smooth functions are considered,and by selecting appropriate knot numbers the optimal convergence rate and the asymptotic normality can be obtained under some mild conditions.Some simulation results and a real data example are presented to illustrate the performance of our estimation method.
基金This research is supported in part by the National Natural Science Foundation of. China under Grant No. 10801133.
文摘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.
