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## Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data

#### Juanfang Liu [1] , Liugen Xue [2] , Ruiqin Tian [3]

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This article is concerned with estimations for longitudinal partial linear models with covariate that is measured with error. We propose a generalized empirical likelihood method by combining correction attenuation and quadratic inference functions. The method takes into account
the within-subject correlation without involving direct estimation of nuisance parameters in the correlation matrix. We define a generalized empirical likelihood-based statistic for the regression coefficients and residual adjusted empirical likelihood for the baseline function. The empirical log-likelihood ratios are proven to be asymptotically chi-squared, and the corresponding confidence regions are then constructed.
Compared with methods based on normal approximations, the generalized empirical likelihood does not require consistent estimators for
the asymptotic variance and bias. Furthermore, a simulation study is conducted to evaluate the performance of the proposed method.
Longitudinal Data, Generalized Empirical Likelihood, Confidence Region, Measurement Error, Partially Linear Model
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Primary Language en Mathematics Statistics Author: Juanfang Liu (Primary Author) Author: Liugen Xue Author: Ruiqin Tian Publication Date: August 1, 2018
 Bibtex @research article { hujms453616, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {Hacettepe University}, year = {2018}, volume = {47}, pages = {983 - 1001}, doi = {}, title = {Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data}, key = {cite}, author = {Liu, Juanfang and Xue, Liugen and Tian, Ruiqin} } APA Liu, J , Xue, L , Tian, R . (2018). Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data. Hacettepe Journal of Mathematics and Statistics, 47 (4), 983-1001. Retrieved from http://dergipark.org.tr/hujms/issue/38872/453616 MLA Liu, J , Xue, L , Tian, R . "Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data". Hacettepe Journal of Mathematics and Statistics 47 (2018): 983-1001 Chicago Liu, J , Xue, L , Tian, R . "Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data". Hacettepe Journal of Mathematics and Statistics 47 (2018): 983-1001 RIS TY - JOUR T1 - Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data AU - Juanfang Liu , Liugen Xue , Ruiqin Tian Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 983 EP - 1001 VL - 47 IS - 4 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2016 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data %A Juanfang Liu , Liugen Xue , Ruiqin Tian %T Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 4 %R %U ISNAD Liu, Juanfang , Xue, Liugen , Tian, Ruiqin . "Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data". Hacettepe Journal of Mathematics and Statistics 47 / 4 (August 2018): 983-1001. AMA Liu J , Xue L , Tian R . Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data. Hacettepe Journal of Mathematics and Statistics. 2018; 47(4): 983-1001. Vancouver Liu J , Xue L , Tian R . Generalized empirical likelihood inference in partially linear errors-in-variables models with longitudinal data. Hacettepe Journal of Mathematics and Statistics. 2018; 47(4): 1001-983.