Nonparametric function estimation of the relationship between two repeatedly measured variables
Nonparametric function estimation of the relationship between two repeatedly measured variables
We describe methods for estimating the regression function nonparametrically, and for estimating the variance components in a simple variance component model which is sometimes used for repeated measures data or data with a simple clustered structure. We consider a number of different ways of estimating the regression function. The main results are that the simple pooled estimator which treats the data as independent performs very well asymptotically, but that we can construct estimators which perform better asymptotically in some circumstances. The local linear version of the quasi-likelihood estimator is supposed to exploit the covariance structure of the model but does not in fact do so, asymptotically performing worse than the simple pooled estimator.
local linear regression, local quasi-likelihood estimator, semiparametric estimation, smoothing, variance components
51-71
Ruckstuhl, A.F.
8405a5e0-ba61-4ff4-b288-96c8acb35ba3
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
Carroll, R.J.
a496429c-12d6-4417-a2f1-a82d73aafc2a
2000
Ruckstuhl, A.F.
8405a5e0-ba61-4ff4-b288-96c8acb35ba3
Welsh, A.H.
27640871-afff-4d45-a191-8a72abee4c1a
Carroll, R.J.
a496429c-12d6-4417-a2f1-a82d73aafc2a
Ruckstuhl, A.F., Welsh, A.H. and Carroll, R.J.
(2000)
Nonparametric function estimation of the relationship between two repeatedly measured variables.
Statistica Sinica, 10 (1), .
Abstract
We describe methods for estimating the regression function nonparametrically, and for estimating the variance components in a simple variance component model which is sometimes used for repeated measures data or data with a simple clustered structure. We consider a number of different ways of estimating the regression function. The main results are that the simple pooled estimator which treats the data as independent performs very well asymptotically, but that we can construct estimators which perform better asymptotically in some circumstances. The local linear version of the quasi-likelihood estimator is supposed to exploit the covariance structure of the model but does not in fact do so, asymptotically performing worse than the simple pooled estimator.
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Published date: 2000
Keywords:
local linear regression, local quasi-likelihood estimator, semiparametric estimation, smoothing, variance components
Organisations:
Statistics
Identifiers
Local EPrints ID: 29927
URI: http://eprints.soton.ac.uk/id/eprint/29927
ISSN: 1017-0405
PURE UUID: 6edee95f-d939-466e-becc-f979e998a4b8
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Date deposited: 20 Jul 2006
Last modified: 08 Jan 2022 03:51
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Contributors
Author:
A.F. Ruckstuhl
Author:
A.H. Welsh
Author:
R.J. Carroll
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