Abstract
In this paper, we focus on heteroscedastic partially linear varying-coefficient errors-in-variables models under right-censored data with censoring indicators missing at random. Based on regression calibration, imputation, and inverse probability weighted methods, we define a class of modified profile least square estimators of the parameter and local linear estimators of the coefficient function, which are applied to constructing estimators of the error variance function. In order to improve the estimation accuracy and take into account the heteroscedastic error, reweighted estimators of the parameter and coefficient function are developed. At the same time, we apply the empirical likelihood method to construct confidence regions and maximum empirical likelihood estimators of the parameter. Under appropriate assumptions, the asymptotic normality of the proposed estimators is studied. The strong uniform convergence rate for the estimators of the error variance function is considered. Also, the asymptotic chi-squared distribution of the empirical log-likelihood ratio statistics is proved. A simulation study is conducted to evaluate the finite sample performance of the proposed estimators. Meanwhile, one real data example is provided to illustrate our methods.
Highlights
In regression analysis, for a long period of time, the flexible and refined statistical regression models are widely applied in theoretical study and practical application. e main results related to parameter regression models and nonparameter regression models are rather mature
We illustrate the methodology via an application to a dataset from a breast cancer clinical trial [25]. is clinical trial was conducted by the Eastern Cooperative Oncology Group, whose target was evaluating tamoxifen as a treatment for stage II breast cancer among elderly women, who are older than 65. ere are 169 elderly women participating in the trial, and we focus on 79 women who died by the end of the trial
We consider the estimation and confidence regions based on modified profile least square (PLS) method and empirical likelihood (EL) inference for partially linear varying-coefficient errorsin-variables (PLVCEV) model with heteroscedastic errors under censoring indicators missing at random (MAR), respectively
Summary
For a long period of time, the flexible and refined statistical regression models are widely applied in theoretical study and practical application. e main results related to parameter regression models and nonparameter regression models are rather mature. Partially linear varying-coefficient errorsin-variables (PLVCEV) model, as a typical example, was introduced by You and Chen [1] and has the following form:. Αq(·))⊤ is an unknown q-dimensional vector of coefficient function, and ε is the random error. Heteroscedastic error models have attracted much attention of many scholars. You et al [8] considered the estimation of parametric and nonparametric parts for partially linear regression models with heteroscedastic errors. Fan et al [9] constructed confidence regions of parameter for heteroscedastic PLVCEV model based on empirical likelihood method. Shen et al [10] discussed estimation and inference for PLVC model with heteroscedastic errors. Xu and Duan [11] extended the results of Shen et al [10] to efficient estimation for PLVCEV model with heteroscedastic errors
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