Asymptotic Properties of Wavelet Estimators in Partially Linear Errors-in-variables Models with Long-memory Errors

While the random errors are a function of Gaussian random variables that are stationary and long dependent, we investigate a partially linear errors-in-variables（EV） model by the wavelet method. Under general conditions, we obtain asymptotic representation of the parametric estimator, and asymptotic distributions and weak convergence rates of the parametric and nonparametric estimators. At last, the validity of the wavelet method is illuminated by a simulation example and a real example.

TESTING SERIAL CORRELATION IN SEMIPARAMETRIC VARYING COEFFICIENT PARTIALLY LINEAR ERRORS-IN-VARIABLES MODEL

The authors propose a V_(N,p) test statistic for testing finite-order serial correlation in asemiparametric varying coefficient partially linear errors-in-variables model.The test statistic is shownto have asymptotic normal distribution under the null hypothesis of no serial correlation.Some MonteCarlo experiments are conducted to examine the finite sample performance of the proposed V_(N,p) teststatistic.Simulation results confirm that the proposed test performs satisfactorily in estimated sizeand power.

Penalized profile least squares-based statistical inference for varying coefficient partially linear errors-in-variables models

The purpose of this paper is two fold. First, we investigate estimation for varying coefficient partially linear models in which covariates in the nonparametric part are measured with errors. As there would be some spurious covariates in the linear part, a penalized profile least squares estimation is suggested with the assistance from smoothly clipped absolute deviation penalty. However, the estimator is often biased due to the existence of measurement errors, a bias correction is proposed such that the estimation consistency with the oracle property is proved. Second, based on the estimator, a test statistic is constructed to check a linear hypothesis of the parameters and its asymptotic properties are studied. We prove that the existence of measurement errors causes intractability of the limiting null distribution that requires a Monte Carlo approximation and the absence of the errors can lead to a chi-square limit. Furthermore, confidence regions of the parameter of interest can also be constructed. Simulation studies and a real data example are conducted to examine the performance of our estimators and test statistic.

Estimation of Parameters of Partially Linear Errors-in-variables Models with Replicated Net Points of Observation

A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that the estimators of the unknown parameters are strongly consistent and their a.s. convergence rates are achieved.

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.

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.

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.

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.

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.

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.

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 ?  ??

Testing Equality of Nonparametric Functions in Two Partially Linear Models

We propose the test statistic to check whether the nonpararnetric functions in two partially linear models are equality or not in this paper. We estimate the nonparametric function both in null hypothesis and the alternative by the local linear method, where we ignore the parametric components, and then estimate the parameters by the two stage method. The test statistic is derived, and it is shown to be asymptotically normal under the null hypothesis.

Empirical Likelihood Inference for Generalized Partially Linear Models with Longitudinal Data

In this article, we propose a generalized empirical likelihood inference for the parametric component in semiparametric generalized partially linear models with longitudinal data. Based on the extended score vector, a generalized empirical likelihood ratios function is defined, which integrates the within-cluster?correlation meanwhile avoids direct estimating the nuisance parameters in the correlation matrix. We show that the proposed statistics are asymptotically?Chi-squared under some suitable conditions, and hence it can be used to construct the confidence region of parameters. In addition, the maximum empirical likelihood estimates of parameters and the corresponding asymptotic normality are obtained. Simulation studies demonstrate the performance of the proposed method.

Function-on-Partially Linear Functional Additive Models

We consider a functional partially linear additive model that predicts a functional response by a scalar predictor and functional predictors. The B-spline and eigenbasis least squares estimator for both the parametric and the nonparametric components proposed. In the final of this paper, as a result, we got the variance decomposition of the model and establish the asymptotic convergence rate for estimator.

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.

Efficient Shrinkage Estimation about the Partially Linear Varying Coefficient Model with Random Effect for Longitudinal Data

In this paper, an efficient shrinkage estimation procedure for the partially linear varying coefficient model (PLVC) with random effect is considered. By selecting the significant variable and estimating the nonzero coefficient, the model structure specification is accomplished by introducing a novel penalized estimating equation. Under some mild conditions, the asymptotic properties for the proposed model selection and estimation results, such as the sparsity and oracle property, are established. Some numerical simulation studies and a real data analysis are presented to examine the finite sample performance of the procedure.

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).

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).

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

Testing Linearity in Functional Partially Linear Models

For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.