Generalized empirical likelihood inference in partially linear model for longitudinal data with missing response variables and error-prone covariates |
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Authors: | Juanfang Liu Liugen Xue Ruiqin Tian |
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Institution: | 1. College of Applied Sciences, Beijing University of Technology, Beijing, China;2. College of Mathematics and Information Science, Henan Normal University, Henan, China;3. Department of Statistics, Zhejiang Agriculture and Forestry University, Zhejiang, China |
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Abstract: | In this article, we consider statistical inference for longitudinal partial linear models when the response variable is sometimes missing with missingness probability depending on the covariate that is measured with error. A generalized empirical likelihood (GEL) method is proposed by combining correction attenuation and quadratic inference functions. The method that takes into consideration the correlation within groups is used to estimate the regression coefficients. Furthermore, residual-adjusted empirical likelihood (EL) is employed for estimating the baseline function so that undersmoothing is avoided. The empirical log-likelihood ratios are proven to be asymptotically Chi-squared, and the corresponding confidence regions for the parameters of interest are then constructed. Compared with methods based on NAs, the GEL does not require consistent estimators for the asymptotic variance and bias. The numerical study is conducted to compare the performance of the EL and the normal approximation-based method, and a real example is analysed. |
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Keywords: | Confidence region Generalized empirical likelihood Longitudinal data Measurement error Missing data Partially linear model |
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