Kernel regression estimation using repeated measurements data. (English) Zbl 0635.62030

Hart, Jeffrey D.; Wehrly, Thomas E.

J. Am. Stat. Assoc. 81, 1080-1088 (1986).

The nonparametric estimation of an average growth curve has been considered. It is supposed that there are observations from several experimental units, each following the regression model \(y(x_ j)=f(x_ j)+\epsilon_ j\) \((j=1,...,n)\), where \(\epsilon_ 1,...,\epsilon_ n\) are correlated zero mean errors and \(0\leq x_ 1<...<x_ n\leq 1\) are fixed constants.
Asymptotic and finite-sample results concerning the mean squared error of the estimator are obtained. The influence of correlation on the bandwidth minimizing mean squared error is discussed. A data-based method for selecting the bandwidth is illustrated in a data analysis.

Reviewer: V.P.Gupta

MSC:

62G05	Nonparametric estimation
62G99	Nonparametric inference
62J99	Linear inference, regression

Keywords:

kernel regression estimation; repeated measurements data; nonparametric regression; correlated data; optimum bandwidth; asymptotic properties; average growth curve; finite-sample results; mean squared error; data- based method