Non parametric regression analysis for longitudinal data with time-depending autoregressive error process |
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Authors: | Yin Hang Shu Liu |
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Affiliation: | 1. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, P.R. Chinahangyin1986@163.com;3. School of Statistics and Information, Shanghai Universi of International Business and Economics, Shanghai, P. R. China |
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Abstract: | This paper considers a non parametric longitudinal model, where the within-subject correlation structure is represented by a time-depending autoregressive error process. An initial estimator without taking into account the within-subject correlation is obtained to fit the time-depending autoregressive error process. With the initial estimator, we construct a two-stage local linear estimator of the mean function. According to the asymptotic normality of the initial and two-stage estimators, it is discovered that the two-stage estimator has a smaller asymptotic variance. The simulation results show us that the two-stage estimation has some good properties. The analysis of a data set demonstrates its application. |
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Keywords: | Local linear estimator longitudinal model time-depending autoregressive error process two-stage estimator within-subject correlation structure. |
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