k-NN METHOD IN PARTIAL LINEAR MODEL UNDER RANDOM CENSORSHIP

Consider the regression model Y=Xβ+ g(T) + e. Here g is an unknown smoothing function on [0, 1], β is a l-dimensional parameter to be estimated, and e is an unobserved error. When data are randomly censored, the estimators βn* and gn*forβ and g are obtained by using class K and the least square methods. It is shown that βn* is asymptotically normal and gn* achieves the convergent rate O(n-1/3).

Sieve MLE for Generalized Partial Linear Models with Type Ⅱ Interval-censored Data

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.

Partial Linear Model Averaging Prediction for Longitudinal Data

Prediction plays an important role in data analysis.Model averaging method generally provides better prediction than using any of its components.Even though model averaging has been extensively investigated under independent errors,few authors have considered model averaging for semiparametric models with correlated errors.In this paper,the authors offer an optimal model averaging method to improve the prediction in partially linear model for longitudinal data.The model averaging weights are obtained by minimizing criterion,which is an unbiased estimator of the expected in-sample squared error loss plus a constant.Asymptotic properties,including asymptotic optimality and consistency of averaging weights,are established under two scenarios:(i)All candidate models are misspecified;(ii)Correct models are available in the candidate set.Simulation studies and an empirical example show that the promise of the proposed procedure over other competitive methods.

ESTIMATORS AND SOME BEHAVIORS FORA PARTIALLY LINEAR MODEL WITH CENSORED DATA

This paper considers the local linear regression estimators for partially linear model with censored data. Which have some nice large-sample behaviors and are easy to implement. By many simulation runs, the author also found that the estimators show remarkable in the small sample case yet.

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

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).

Asymptotics of Huber-Dutter Estimators for Partial Linear Model with Nonstochastic Designs

For partial linear model Y = X~τβ_0 + g_0(T) + ε with unknown β_0 ∈ R^dand an unknown smooth function g_0, this paper considers the Huber-Dutter estimators of β_0, scaleσ for the errors and the function g_0 respectively, in which the smoothing B-spline function isused. Under some regular conditions, it is shown that the Huber-Dutter estimators of β_0 and σ areasymptotically normal with convergence rate n^(-1/2) and the B-spline Huber-Dutter estimator of g_0achieves the optimal convergence rate in nonparametric regression. A simulation study demonstratesthat the Huber-Dutter estimator of β_0 is competitive with its M-estimator without scale parameterand the ordinary least square estimator. An example is presented after the simulation study.

ROBUST ESTIMATION IN PARTIAL LINEAR MIXED MODEL FOR LONGITUDINAL DATA

In this article, robust generalized estimating equation for the analysis of partial linear mixed model for longitudinal data is used. The authors approximate the nonparametric function by a regression spline. Under some regular conditions, the asymptotic properties of the estimators are obtained. To avoid the computation of high-dimensional integral, a robust Monte Carlo Newton-Raphson algorithm is used. Some simulations are carried out to study the performance of the proposed robust estimators. In addition, the authors also study the robustness and the efficiency of the proposed estimators by simulation. Finally, two real longitudinal data sets are analyzed.

Edgeworth Expansion in Partial Linear Models

In this paper, under some fairly general conditions, a first-order Edgeworth expansion for the standardized statistic of βin partial linear models is given, then a non-residual type of consistent estimation for the error variance is constructed, and finally an Edgeworth expansion for the corresponding studentized version is presented.

PARAMETRIC TEST IN PARTIAL LINEAR REGRESSION MODELS

Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.

ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA

In this article, a partially linear single-index model /or longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data.

Consistency and normality of Huber-Dutter estimators for partial linear model

For partial linear model Y = Xτβ0 + g0(T) + with unknown β0 ∈ Rd and an unknown smooth function g0, this paper considers the Huber-Dutter estimators of β0, scale σ for the errors and the function g0 approximated by the smoothing B-spline functions, respectively. Under some regularity conditions, the Huber-Dutter estimators of β0 and σ are shown to be asymptotically normal with the rate of convergence n-1/2 and the B-spline Huber-Dutter estimator of g0 achieves the optimal rate of convergence in nonparametric regression. A simulation study and two examples demonstrate that the Huber-Dutter estimator of β0 is competitive with its M-estimator without scale parameter and the ordinary least square estimator.

STRONG CONVERGENCE RATES OF SEVERAL ESTIMATORS IN SEMIPARAMETRIC VARYING-COEFFICIENT PARTIALLY LINEAR MODELS

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.

Some Asymptotic Properties for Multivariate Partially Linear Models

纸在独立错误下面认为 multivariate 是部分线性的模型，并且为参量的部件和 nonparametric 部件 F 调查 asymptotic 偏爱和变化协变性(洠 ?  ??

TWO-STEP ESTIMATORS IN PARTIAL LINEAR MODELS WITH MISSING RESPONSE VARIABLES AND ERROR-PRONE COVARIATES

有失踪的反应变量和错误容易的 covariates 的一个部分线性模型被考虑。归罪途径被开发估计回归系数和 nonparametric 功能。建议参量的评估者被显示 asymptotically 正常，并且为 nonparametric 部分的评估者被证明以最佳的率收敛。到为回归系数和 nonparametric 功能的构造信心区域，分别地，作者也建议 empirical-likelihood-based 统计并且调查实验可能性的比率的限制分布。模拟学习被进行为建议评估者比较有限样品行为。到爱滋病数据集的一个应用程序被说明。

Variable Selection of Partially Linear Single-index Models

In this article, we study the variable selection of partially linear single-index model(PLSIM). Based on the minimized average variance estimation, the variable selection of PLSIM is done by minimizing average variance with adaptive l1 penalty. Implementation algorithm is given. Under some regular conditions, we demonstrate the oracle properties of aLASSO procedure for PLSIM. Simulations are used to investigate the effectiveness of the proposed method for variable selection of PLSIM.

Testing Linearity of Nonparametric Component in Partially Linear Model

In this paper, we propose the test statistic to check whether the nonparametric function in partially linear models is linear or not. We estimate the nonparametric function in alternative by using the local linear method, and then estimate the parameters by the two stage method. The test statistic under the null hypothesis is calculated, and it is shown to be asymptotically normal.

Double-Penalized Quantile Regression in Partially Linear Models

In this paper, we propose the double-penalized quantile regression estimators in partially linear models. An iterative algorithm is proposed for solving the proposed optimization problem. Some numerical examples illustrate that the finite sample performances of proposed method perform better than the least squares based method with regard to the non-causal selection rate (NSR) and the median of model error (MME) when the error distribution is heavy-tail. Finally, we apply the proposed methodology to analyze the ragweed pollen level dataset.

Asymptotics of the goodness-of-fit test for a partial linear model with randomly censored data

In this paper, we discuss the problem of testing the hypothesis that the underlying regression isa partial linear model. A test statistic, which is based on the quadratic form of a cusum process of residuals,is proposed. The asymptotic distributions of the test statistic under null hypothesis and the local alternativehypothesis are given. The number simulation shows that the test is available.

The Application and Property of Elastic Net Procedure for Partially Linear Models

Variable selection plays an important role in high-dimensional data analysis.But the high-dimensional data often induces the strongly correlated variables problem,which should be properly handled.In this paper,we propose Elastic Net procedure for partially linear models and prove the group effect of its estimate.A simulation study shows that the Elastic Net procedure deals with the strongly correlated variables problem better than the Lasso,ALasso and the Ridge do.Based on the real world data study,we can get that the Elastic Net procedure is particularly useful when the number of predictors pffis much bigger than the sample size n.

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

当前的地位数据经常在幸存分析和可靠性研究产生，当连续回答被归结为反应是否更大的指示物时或不到观察随机的阀值价值。这篇文章与当前的地位数据考虑一个部分线性模型。筛最不摆平评估者被建议估计回归参数和 nonparametric 函数。这份报纸出现，在一些温和状况下面，评估者是强壮的一致。而且，参数评估者通常被散布，当 nonparametric 部件完成最佳的集中时，评价。模拟研究被执行调查建议估计的表演。为说明目的，方法从 hydrogel intraocular 透镜的石灰化的研究被用于真实数据集，奔流处理的复杂并发症。