Non parametric regression analysis for longitudinal data with time-depending autoregressive error process

• Published in: Communications in statistics. Theory and methods Vol. 47; no. 18; pp. 4503 - 4533
• Main Authors: Hang, Yin, Liu, Shu
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 17.09.2018; Taylor & Francis Ltd
• Subjects: Autoregressive processes; Computer simulation; Data analysis; Economic models; Local linear estimator; longitudinal model; Nonparametric statistics; Normality; Primary 62H12; Regression analysis; Secondary 62G08; time-depending autoregressive error process; two-stage estimator; within-subject correlation structure
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2017.1377251

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.