Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Rates of convergence in semi-parametric modelling of longitudinal data.
AU - Moyeed, R.
AU - Diggle, Peter J.
PY - 1994
Y1 - 1994
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
IS - 1
ER -