In [13], Schaubel et al. proposed a semiparametric partially linear rate model for the statistical analysis of recurrent event data. But they only considered the model with time-independent covariate effects. In this ...In [13], Schaubel et al. proposed a semiparametric partially linear rate model for the statistical analysis of recurrent event data. But they only considered the model with time-independent covariate effects. In this paper, rate function of the recurrent event is modeled by a semipaxametric partially linear function which can include the time-varying effects. We propose the method of generalized estimating equations to make inferences about both the time-varying effects and time-independent effects. The large sample properties are established, while extensive simulation studies are carried out to examine the proposed procedures. At last, we apply the procedures to the well-known bladder cancer study.展开更多
This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） prop...This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.展开更多
In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard n...In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.展开更多
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
Most soft materials behave as if they were hardened when subjected to an impact force. The strain rate dependence of viscosity resistance is the reason for this behavior. The authors carried out drop impact tests on s...Most soft materials behave as if they were hardened when subjected to an impact force. The strain rate dependence of viscosity resistance is the reason for this behavior. The authors carried out drop impact tests on several types of soft materials under the condition of a flat frontal impact. The impact force waveform of soft materials was found to consist of a thorn-shaped waveform and a succeeding mountain-shaped waveform. Based on our experimental observations, we believe that a large viscosity resistance is rapidly changed to a small resistance in the course of the impact. In the present study, the cause of this distinct waveform is discussed based on a dynamics model. The study applies a standard linear solid (SLS) model in which the viscosity transient phenomenon is considered is applied. Three types of impact force waveforms of actual soft materials are simulated using the SLS model. Some features of the impact force waveform of soft materials can be explained using the SLS model.展开更多
Purpose: To formulate and demonstrate methods for regression modeling of probabilities and dispersions for individual-patient longitudinal outcomes taking on discrete numeric values. Methods: Three alternatives for mo...Purpose: To formulate and demonstrate methods for regression modeling of probabilities and dispersions for individual-patient longitudinal outcomes taking on discrete numeric values. Methods: Three alternatives for modeling of outcome probabilities are considered. Multinomial probabilities are based on different intercepts and slopes for probabilities of different outcome values. Ordinal probabilities are based on different intercepts and the same slope for probabilities of different outcome values. Censored Poisson probabilities are based on the same intercept and slope for probabilities of different outcome values. Parameters are estimated with extended linear mixed modeling maximizing a likelihood-like function based on the multivariate normal density that accounts for within-patient correlation. Formulas are provided for gradient vectors and Hessian matrices for estimating model parameters. The likelihood-like function is also used to compute cross-validation scores for alternative models and to control an adaptive modeling process for identifying possibly nonlinear functional relationships in predictors for probabilities and dispersions. Example analyses are provided of daily pain ratings for a cancer patient over a period of 97 days. Results: The censored Poisson approach is preferable for modeling these data, and presumably other data sets of this kind, because it generates a competitive model with fewer parameters in less time than the other two approaches. The generated probabilities for this model are distinctly nonlinear in time while the dispersions are distinctly nonconstant over time, demonstrating the need for adaptive modeling of such data. The analyses also address the dependence of these daily pain ratings on time and the daily numbers of pain flares. Probabilities and dispersions change differently over time for different numbers of pain flares. Conclusions: Adaptive modeling of daily pain ratings for individual cancer patients is an effective way to identify nonlinear relationships in time as well as in other predictors such as the number of pain flares.展开更多
基金Supported by the National Natural Science Foundation of China(No.11326184)the Fundamental Research Funds for the Central Universities(No.14CX02146A)
文摘In [13], Schaubel et al. proposed a semiparametric partially linear rate model for the statistical analysis of recurrent event data. But they only considered the model with time-independent covariate effects. In this paper, rate function of the recurrent event is modeled by a semipaxametric partially linear function which can include the time-varying effects. We propose the method of generalized estimating equations to make inferences about both the time-varying effects and time-independent effects. The large sample properties are established, while extensive simulation studies are carried out to examine the proposed procedures. At last, we apply the procedures to the well-known bladder cancer study.
基金supported by the National Natural Science Funds for Distinguished Young Scholar (70825004)National Natural Science Foundation of China (NSFC) (10731010 and 10628104)+3 种基金the National Basic Research Program (2007CB814902)Creative Research Groups of China (10721101)Leading Academic Discipline Program, the 10th five year plan of 211 Project for Shanghai University of Finance and Economics211 Project for Shanghai University of Financeand Economics (the 3rd phase)
文摘This article is concerned with the estimating problem of semiparametric varyingcoefficient partially linear regression models. By combining the local polynomial and least squares procedures Fan and Huang （2005） proposed a profile least squares estimator for the parametric component and established its asymptotic normality. We further show that the profile least squares estimator can achieve the law of iterated logarithm. Moreover, we study the estimators of the functions characterizing the non-linear part as well as the error variance. The strong convergence rate and the law of iterated logarithm are derived for them, respectively.
文摘In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.
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Most soft materials behave as if they were hardened when subjected to an impact force. The strain rate dependence of viscosity resistance is the reason for this behavior. The authors carried out drop impact tests on several types of soft materials under the condition of a flat frontal impact. The impact force waveform of soft materials was found to consist of a thorn-shaped waveform and a succeeding mountain-shaped waveform. Based on our experimental observations, we believe that a large viscosity resistance is rapidly changed to a small resistance in the course of the impact. In the present study, the cause of this distinct waveform is discussed based on a dynamics model. The study applies a standard linear solid (SLS) model in which the viscosity transient phenomenon is considered is applied. Three types of impact force waveforms of actual soft materials are simulated using the SLS model. Some features of the impact force waveform of soft materials can be explained using the SLS model.
文摘Purpose: To formulate and demonstrate methods for regression modeling of probabilities and dispersions for individual-patient longitudinal outcomes taking on discrete numeric values. Methods: Three alternatives for modeling of outcome probabilities are considered. Multinomial probabilities are based on different intercepts and slopes for probabilities of different outcome values. Ordinal probabilities are based on different intercepts and the same slope for probabilities of different outcome values. Censored Poisson probabilities are based on the same intercept and slope for probabilities of different outcome values. Parameters are estimated with extended linear mixed modeling maximizing a likelihood-like function based on the multivariate normal density that accounts for within-patient correlation. Formulas are provided for gradient vectors and Hessian matrices for estimating model parameters. The likelihood-like function is also used to compute cross-validation scores for alternative models and to control an adaptive modeling process for identifying possibly nonlinear functional relationships in predictors for probabilities and dispersions. Example analyses are provided of daily pain ratings for a cancer patient over a period of 97 days. Results: The censored Poisson approach is preferable for modeling these data, and presumably other data sets of this kind, because it generates a competitive model with fewer parameters in less time than the other two approaches. The generated probabilities for this model are distinctly nonlinear in time while the dispersions are distinctly nonconstant over time, demonstrating the need for adaptive modeling of such data. The analyses also address the dependence of these daily pain ratings on time and the daily numbers of pain flares. Probabilities and dispersions change differently over time for different numbers of pain flares. Conclusions: Adaptive modeling of daily pain ratings for individual cancer patients is an effective way to identify nonlinear relationships in time as well as in other predictors such as the number of pain flares.
