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Using Local Correlation in Kernel‐Based Smoothers for Dependent Data
Author(s) -
Peterson Derick R.,
Zhao Hongwei,
Eapen Sara
Publication year - 2003
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2003.00113.x
Subject(s) - estimator , smoothing , mathematics , kernel smoother , nonparametric regression , kernel (algebra) , bounded function , nonparametric statistics , conditional independence , independence (probability theory) , polynomial , simple (philosophy) , correlation , variance function , polynomial regression , statistics , kernel method , regression analysis , computer science , discrete mathematics , mathematical analysis , artificial intelligence , geometry , epistemology , radial basis function kernel , support vector machine , philosophy
Summary . We consider the general problem of smoothing correlated data to estimate the nonparametric mean function when a random, but bounded, number of measurements is available for each independent subject. We propose a simple extension to the local polynomial regression smoother that retains the asymptotic properties of the working independence estimator, while typically reducing both the conditional bias and variance for practical sample sizes, as demonstrated by exact calculations for some particular models. We illustrate our method by smoothing longitudinal functional decline data for 100 patients with Huntington's disease. The class of local polynomial kernel‐based estimating equations previously considered in the literature is shown to use the global correlation structure in an apparently detrimental way, which explains why some previous attempts to incorporate correlation were found to be asymptotically inferior to the working independence estimator.