There has been substantial recent interest in non- and semiparametric methods for longitudinal or clustered data with dependence within clusters. It has been shown rather inexplicably that, when standard kernel smoothing methods are used in a natural way, higher efficiency is obtained by assuming independence than by using the true correlation structure. It is shown here that this result is a natural consequence of how standard kernel methods incorporate the within-subject correlation in the asymptotic setting considered, where the cluster sizes are fixed and the cluster number increases. In this paper, an alternative kernel smoothing method is proposed. Unlike the standard methods, the smallest variance of the new estimator is achieved when the true correlation is assumed. Asymptotically, the variance of the proposed method is uniformly smaller than that of the most efficient working independence approach. A small simulation study shows that significant improvement is obtained for finite samples. Copyright Biometrika Trust 2003, Oxford University Press.
[1]
S. Zeger,et al.
Longitudinal data analysis using generalized linear models
,
1986
.
[2]
K Y Liang,et al.
Longitudinal data analysis for discrete and continuous outcomes.
,
1986,
Biometrics.
[3]
Jianqing Fan,et al.
Generalized Partially Linear Single-Index Models
,
1997
.
[4]
R. Carroll,et al.
Nonparametric Function Estimation for Clustered Data When the Predictor is Measured without/with Error
,
2000
.
[5]
Zhiliang Ying,et al.
Semiparametric and Nonparametric Regression Analysis of Longitudinal Data
,
2001
.
[6]
A note on nonparametric estimation for clustered data
,
2004
.