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**Rates of convergence in semi-parametric modelling of longitudinal data.** / Moyeed, R.; Diggle, Peter J.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Moyeed, R & Diggle, PJ 1994, 'Rates of convergence in semi-parametric modelling of longitudinal data.', *Australian Journal of Statistics*, vol. 36, no. 1, pp. 75-93. https://doi.org/10.1111/j.1467-842X.1994.tb00640.x

Moyeed, R., & Diggle, P. J. (1994). Rates of convergence in semi-parametric modelling of longitudinal data. *Australian Journal of Statistics*, *36*(1), 75-93. https://doi.org/10.1111/j.1467-842X.1994.tb00640.x

Moyeed R, Diggle PJ. Rates of convergence in semi-parametric modelling of longitudinal data. Australian Journal of Statistics. 1994;36(1):75-93. doi: 10.1111/j.1467-842X.1994.tb00640.x

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title = "Rates of convergence in semi-parametric modelling of longitudinal data.",

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.",

keywords = "Autocorrelation • cross-validation • kernel regression • longitudinal data • semi-parametric regression • smoothing • time series",

author = "R. Moyeed and Diggle, {Peter J.}",

year = "1994",

doi = "10.1111/j.1467-842X.1994.tb00640.x",

language = "English",

volume = "36",

pages = "75--93",

journal = "Australian Journal of Statistics",

issn = "0004-9581",

publisher = "Statistical Society of Australia",

number = "1",

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T1 - Rates of convergence in semi-parametric modelling of longitudinal data.

AU - Moyeed, R.

AU - Diggle, Peter J.

PY - 1994

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N2 - 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.

AB - 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.

KW - Autocorrelation • cross-validation • kernel regression • longitudinal data • semi-parametric regression • smoothing • time series

U2 - 10.1111/j.1467-842X.1994.tb00640.x

DO - 10.1111/j.1467-842X.1994.tb00640.x

M3 - Journal article

VL - 36

SP - 75

EP - 93

JO - Australian Journal of Statistics

JF - Australian Journal of Statistics

SN - 0004-9581

IS - 1

ER -