Modified Local Linear Estimators in Partially Linear Additive Models with Right-Censored Data Based on Different Censorship Solution Techniques

This paper introduces a modified local linear estimator (LLR) for partially linear additive models (PLAM) when the response variable is subject to random right-censoring. In the case of modeling right-censored data, PLAM offers a more flexible and realistic approach to the estimation procedure by involving multiple parametric and nonparametric components. This differs from the widely used partially linear models that feature a univariate nonparametric function. The LLR method is employed to estimate unknown smooth functions using a modified backfitting algorithm, delivering a non-iterative solution for the right-censored PLAM. To address the censorship issue, three approaches are employed: synthetic data transformation (ST), Kaplan-Meier weights (KMW), and the kNN imputation technique (kNNI). Asymptotic properties of the modified backfitting estimators are detailed for both ST and KMW solutions. The advantages and disadvantages of these methods are discussed both theoretically and practically. Comprehensive simulation studies and real-world data examples are conducted to assess the performance of the introduced estimators. The results indicate that LLR performs well with both KMW and kNNI in the majority of scenarios, along with a real data example.

Nonparametric Estimation of Population Average Dose-Response Curves using Entropy Balancing Weights for Continuous Exposures

Weighted estimators are commonly used for estimating exposure effects in observational settings to establish causal relations. These estimators have a long history of development when the exposure of interest is binary and where the weights are typically functions of an estimated propensity score. Recent developments in optimization-based estimators for constructing weights in binary exposure settings, such as those based on entropy balancing, have shown more promise in estimating treatment effects than those methods that focus on the direct estimation of the propensity score using likelihood-based methods. This paper explores recent developments of entropy balancing methods to continuous exposure settings and the estimation of population dose-response curves using nonparametric estimation combined with entropy balancing weights, focusing on factors that would be important to applied researchers in medical or health services research. The methods developed here are applied to data from a study assessing the effect of non-randomized components of an evidence-based substance use treatment program on emotional and substance use clinical outcomes.

Shrinkage estimation applied to a semi-nonparametric regression model

Stein-type shrinkage techniques are applied to the parametric components of a semi-nonparametric regression model recently proposed by (Ma et al. 2015: 285-303). On the basis of an uncertain prior information (restrictions) about the parameters of interest, shrinkage techniques are shown to improve the accuracy of the model. The effectiveness of the proposed estimators are corroborated by a simulation study.

Efficient Semiparametric Regression for Longitudinal Data with Regularized Estimation of Error Covariance Function

Improving estimation efficiency for regression coefficients is an important issue in the analysis of longitudinal data, which involves estimating the covariance matrix of errors. But challenges arise in estimating the covariance matrix of longitudinal data collected at irregular or unbalanced time points. In this paper, we develop a regularization method for estimating the covariance function and a stepwise procedure for estimating the parametric components efficiently in the varying-coefficient partially linear model. This procedure is also applicable to the varying-coefficient temporal mixed effects model. Our method utilizes the structure of the covariance function and thus has faster rates of convergence in estimating the covariance functions and outperforms the existing approaches in simulation studies. This procedure is easy to implement and its numerical performance is investigated using both simulated and real data.

A semivarying joint model for longitudinal binary and continuous outcomes

Semivarying models extend varying coefficient models by allowing some regression coefficients to be constant with respect to the underlying covariate(s). In this paper we develop a semivarying joint modelling framework for estimating the time-varying association between two intensively measured longitudinal response: a continuous one and a binary one. To overcome the major challenge of jointly modelling these responses, namely, the lack of a natural multivariate distribution, we introduce a Gaussian latent variable underlying the binary response. Then we decompose the model into two components: a marginal model for the continuous response, and a conditional model for the binary response given the continuous response. We develop a two-stage estimation procedure and discuss the asymptotic normality of the resulting estimators. We assess the finite-sample performance of our procedure using a simulation study, and we illustrate our method by analyzing binary and continuous responses from the Women's Interagency HIV Study.

Empirical-Likelihood-Based Inferences for Generalized Partially Linear Models

This paper considers generalized partially linear models. We propose empirical likelihood based statistics to construct confidence regions for the parametric and nonparametric componenets. The resulting statistics are shown to be asymptotically chi-squared distributed. Finite sample performance of the proposed statistics is assessed by simulation experiments. The proposed methods are applied to a dataset from an AIDS clinical trial.

Local Linear Regression for Data with AR Errors

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.

Empirical Likelihood based Inference for Additive Partial Linear Measurement Error Models

This paper considers statistical inference for additive partial linear models when the linear covariate is measured with error. To improve the accuracy of the normal approximation based confidence intervals, we develop an empirical likelihood based statistic, which is shown to be asymptotically chi-square distributed. We emphasize the finite-sample performance of the proposed method by conducting simulation experiments. The method is used to analyze the relationship between semen quality and phthalate exposure from an environment study.

Variable Selection in Semiparametric Regression Modeling

In this paper, we are concerned with how to select significant variables in semiparametric modeling. Variable selection for semiparametric regression models consists of two components: model selection for nonparametric components and select significant variables for parametric portion. Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures including stepwise regression and the best subset selection require model selection to nonparametric components for each submodel. This leads to very heavy computational burden. In this paper, we propose a class of variable selection procedures for semiparametric regression models using nonconcave penalized likelihood. The newly proposed procedures are distinguished from the traditional ones in that they delete insignificant variables and estimate the coefficients of significant variables simultaneously. This allows us to establish the sampling properties of the resulting estimate. We first establish the rate of convergence of the resulting estimate. With proper choices of penalty functions and regularization parameters, we then establish the asymptotic normality of the resulting estimate, and further demonstrate that the proposed procedures perform as well as an oracle procedure. Semiparametric generalized likelihood ratio test is proposed to select significant variables in the nonparametric component. We investigate the asymptotic behavior of the proposed test and demonstrate its limiting null distribution follows a chi-squared distribution, which is independent of the nuisance parameters. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed variable selection procedures.