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Rates of convergence in semi-parametric modelling of longitudinal data.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>1994
<mark>Journal</mark>Australian Journal of Statistics
Issue number1
Number of pages19
Pages (from-to)75-93
Publication StatusPublished
<mark>Original language</mark>English


We consider the problem of semi-parametric regression modelling when the data consist of a collection of short time series for which measurements within series are correlated. The objective is to estimate a regression function of the form E[Y(t) | x] =x'ß+μ(t), where μ(.) is an arbitrary, smooth function of time t, and x is a vector of explanatory variables which may or may not vary with t. For the non-parametric part of the estimation we use a kernel estimator with fixed bandwidth h. When h is chosen without reference to the data we give exact expressions for the bias and variance of the estimators for β and μ(t) and an asymptotic analysis of the case in which the number of series tends to infinity whilst the number of measurements per series is held fixed. We also report the results of a small-scale simulation study to indicate the extent to which the theoretical results continue to hold when h is chosen by a data-based cross-validation method.