Statistica Sinica 11(2001), 121-134

BOOTSTRAP CONFIDENCE INTERVALS FOR

LOCAL LIKELIHOOD, LOCAL ESTIMATING EQUATIONS

AND VARYING COEFFICIENT MODELS

Christian D. Galindo, Hua Liang, Goran Kauermann and Raymond J. Carrol

Texas A & M University and University of Glasgow

Abstract: Four powerful generalizations of the usual local polynomial nonparametric regression methodology are (a) local polynomial methods in generalized linear models; (b) varying coefficient generalized linear models, where the possibly multivariate coefficients in a generalized linear model are estimated nonparametrically; (c) local likelihood methods; and (d) local estimating equations, which generalize nonparametric regression to the estimating equation context. We construct bootstrap confidence intervals for the nonparametrically estimated functions in all four contexts.

Key words and phrases: Bootstrap, estimating equations, local estimating equations, local likelihood, local polynomial regression, nonparametric regression, robust covariance matrix, sandwich estimator.