\(L_{1}\) -Estimation for covariate-adjusted regression

[摘要] We study a covariate-adjusted regression(CAR) model that is proposed for such situations where both predictors and response in a regression model are not directly observable but are distorted by a multiplicative factor that is determined by an unknown function of some observable covariate. By establishing a connection to varying-coefficient models, we present the local linear $L_{1}$-estimation method when the underlying error distribution deviates from a normal distribution. The robust estimators of parameters are proposed in the underlying regression model. The consistency and asymptotic normality of the robust estimators are investigated. Since the limit distribution depends on the unknown components of the errors, an empirical likelihood ratio method based on $L_{1}$ estimator is proposed. The confidence intervals for the regression coefficients are constructed. Simulation results demonstrate the superiority of the proposed estimators over other classical estimators when the underlying errors have heavy tails. Pima Indian diabetes data set is conducted to illustrate the performance of the proposed method, where the response and predictors are potentially contaminated by body mass index.

[学科分类] 电力