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

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.

KEYWORDS:

• Local linear estimator
• longitudinal model
• time-depending autoregressive error process
• two-stage estimator
• within-subject correlation structure.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H12
• Secondary 62G08

Additional information

Funding

Hang’s research has been supported by SHUFE Graduate Innovation and Creativity Funds [grant number 2014110618].