Optimal model averaging for partially linear models with missing response variables and error-prone covariates

We consider the problem of optimal model averaging for partially linear models when the responses are missing at random and some covariates are measured with error. A novel weight choice criterion based on the Mallows-type criterion is proposed for the weight vector to be used in the model averaging. The resulting model averaging estimator for the partially linear models is shown to be asymptotically optimal under some regularity conditions in terms of achieving the smallest possible squared loss. In addition, the existence of a local minimizing weight vector and its convergence rate to the risk-based optimal weight vector are established. Simulation studies suggest that the proposed model averaging method generally outperforms existing methods. As an illustration, the proposed method is applied to analyze an HIV-CD4 dataset.

Model averaging for right censored data with measurement error

This paper studies a novel model averaging estimation issue for linear regression models when the responses are right censored and the covariates are measured with error. A novel weighted Mallows-type criterion is proposed for the considered issue by introducing multiple candidate models. The weight vector for model averaging is selected by minimizing the proposed criterion. Under some regularity conditions, the asymptotic optimality of the selected weight vector is established in terms of its ability to achieve the lowest squared loss asymptotically. Simulation results show that the proposed method is superior to the other existing related methods. A real data example is provided to supplement the actual performance.

Analysis of length-biased and partly interval-censored survival data with mismeasured covariates

In this paper, we analyze the length-biased and partly interval-censored data, whose challenges primarily come from biased sampling and interfere induced by interval censoring. Unlike existing methods that focus on low-dimensional data and assume the covariates to be precisely measured, sometimes researchers may encounter high-dimensional data subject to measurement error, which are ubiquitous in applications and make estimation unreliable. To address those challenges, we explore a valid inference method for handling high-dimensional length-biased and interval-censored survival data with measurement error in covariates under the accelerated failure time model. We primarily employ the SIMEX method to correct for measurement error effects and propose the boosting procedure to do variable selection and estimation. The proposed method is able to handle the case that the dimension of covariates is larger than the sample size and enjoys appealing features that the distributions of the covariates are left unspecified.

Estimation of the average treatment effect with variable selection and measurement error simultaneously addressed for potential confounders

In the framework of causal inference, the inverse probability weighting estimation method and its variants have been commonly employed to estimate the average treatment effect. Such methods, however, are challenged by the presence of irrelevant pre-treatment variables and measurement error. Ignoring these features and naively applying the usual inverse probability weighting estimation procedures may typically yield biased inference results. In this article, we develop an inference method for estimating the average treatment effect with those features taken into account. We establish theoretical properties for the resulting estimator and carry out numerical studies to assess the finite sample performance of the proposed estimator.