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Marginal longitudinal nonparametric regression: locality and efficiency of spline and kernel methods

Marginal longitudinal nonparametric regression: locality and efficiency of spline and kernel methods
Marginal longitudinal nonparametric regression: locality and efficiency of spline and kernel methods
We consider nonparametric regression in a longitudinal marginal model of generalized estimating equation (GEE) type with a time-varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large. In such models, the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations. Two methods of estimating the nonparametric function can be considered: kernel methods and spline methods. Recently, surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature, it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent, that is, working independence in the GEE jargon. As seen through equivalent kernel results, in univariate independent data problems splines and kernels have similar behavior; smoothing splines are equivalent to kernel regression with a specific higher-order kernel, and hence smoothing splines are local. This equivalence suggests that in our marginal model, working independence might be preferable for spline methods. Our results suggest the opposite; via theoretical and numerical calculations, we provide evidence suggesting that for our marginal model, marginal smoothing and penalized regression splines are not local in their behavior. In contrast to the kernel results, our evidence suggests that when using spline methods, it is worthwhile to account for the correlation structure. Our results also suggest that spline methods appear to be more efficient than the previously proposed kernel methods for our marginal model.
0162-1459
482-493
Welsh, Alan H.
71e0487b-c019-4405-ae36-59344e063ff5
Lin, Xihong
8a0c9bf3-f529-4d60-9f9a-ed8d75d12e7d
Carroll, Raymond J.
770bcbd4-711b-4d28-9e6a-653f1f3e371f
Welsh, Alan H.
71e0487b-c019-4405-ae36-59344e063ff5
Lin, Xihong
8a0c9bf3-f529-4d60-9f9a-ed8d75d12e7d
Carroll, Raymond J.
770bcbd4-711b-4d28-9e6a-653f1f3e371f

Welsh, Alan H., Lin, Xihong and Carroll, Raymond J. (2002) Marginal longitudinal nonparametric regression: locality and efficiency of spline and kernel methods. Journal of the American Statistical Association, 97 (458), 482-493.

Record type: Article

Abstract

We consider nonparametric regression in a longitudinal marginal model of generalized estimating equation (GEE) type with a time-varying covariate in the situation where the number of observations per subject is finite and the number of subjects is large. In such models, the basic shape of the regression function is affected only by the covariate values and not otherwise by the ordering of the observations. Two methods of estimating the nonparametric function can be considered: kernel methods and spline methods. Recently, surprising evidence has emerged suggesting that for kernel methods previously proposed in the literature, it is generally asymptotically preferable to ignore the correlation structure in our marginal model and instead assume that the data are independent, that is, working independence in the GEE jargon. As seen through equivalent kernel results, in univariate independent data problems splines and kernels have similar behavior; smoothing splines are equivalent to kernel regression with a specific higher-order kernel, and hence smoothing splines are local. This equivalence suggests that in our marginal model, working independence might be preferable for spline methods. Our results suggest the opposite; via theoretical and numerical calculations, we provide evidence suggesting that for our marginal model, marginal smoothing and penalized regression splines are not local in their behavior. In contrast to the kernel results, our evidence suggests that when using spline methods, it is worthwhile to account for the correlation structure. Our results also suggest that spline methods appear to be more efficient than the previously proposed kernel methods for our marginal model.

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More information

Published date: 2002
Organisations: Statistics

Identifiers

Local EPrints ID: 29943
URI: http://eprints.soton.ac.uk/id/eprint/29943
ISSN: 0162-1459
PURE UUID: e2530b96-1d80-447b-8fc8-db981f81621b

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Date deposited: 10 May 2006
Last modified: 08 Jan 2022 15:53

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Contributors

Author: Alan H. Welsh
Author: Xihong Lin
Author: Raymond J. Carroll

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