Moyeed, R. and Diggle, Peter J. (1994) *Rates of convergence in semi-parametric modelling of longitudinal data.* Australian Journal of Statistics, 36 (1). pp. 75-93.

## Abstract

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.

Item Type: | Article |
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Journal or Publication Title: | Australian Journal of Statistics |

Uncontrolled Keywords: | Autocorrelation • cross-validation • kernel regression • longitudinal data • semi-parametric regression • smoothing • time series |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics Faculty of Health and Medicine > Medicine VC's Office |

ID Code: | 19611 |

Deposited By: | ep_ss_importer |

Deposited On: | 12 Nov 2008 15:19 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 26 Jul 2012 15:33 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/19611 |

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