Empirical Likelihood Inference for Longitudinal Data with Missing Response Variables and Error-Prone Covariates

Abstract We consider statistical inference for longitudinal partially linear models when the response variable is sometimes missing with missingness probability depending on the covariate that is measured with error. The block empirical likelihood procedure is used to estimate the regression coefficients and residual adjusted block empirical likelihood is employed for the baseline function. This leads us to prove a nonparametric version of Wilk's theorem. Compared with methods based on normal approximations, our proposed method does not require a consistent estimators for the asymptotic variance and bias. An application to a longitudinal study is used to illustrate the procedure developed here. A simulation study is also reported. Keywords: Baseline functionConfidence regionEmpirical likelihoodLongitudinal dataMeasurement errorNot missing at randomMathematics Subject Classification: Primary 62G05Secondary 62G20