Premium
RATES OF CONVERGENCE IN SEMI‐PARAMETRIC MODELLING OF LONGITUDINAL DATA
Author(s) -
MOYEED R.A.,
DIGGLE P.J.
Publication year - 1994
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1994.tb00640.x
Subject(s) - estimator , series (stratigraphy) , mathematics , parametric statistics , regression function , regression analysis , convergence (economics) , statistics , kernel regression , kernel (algebra) , semiparametric regression , combinatorics , paleontology , economics , biology , economic growth
Summary 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.