LOCAL ESTIMATING EQUATIONS

Estimating equations have found wide popularity recently in parametric problems, yielding consistent estimators with asymptotically valid in ferences obtained via the sandwich formula. Motivated by a problem in nutritional epidemiology, we use estimating equations to derive nonpar ametric estimators of a ''parameter'' depending on a predictor. The no nparametric component is estimated via local polynomials with loess or kernel weighting; asymptotic theory is derived for the latter, in kee ping with the estimating equation paradigm. variances of the nonparame tric function estimate are estimated using the sandwich method, in an automatic fashion, without the need (typical in the literature) to der ive asymptotic formulas and plug-in an estimate of a density function. The same philosophy is used in estimating the bias of the nonparametr ic function; that is, an empirical method is used without deriving asy mptotic theory on a case-by-case basis. The methods are applied to a s eries of examples, The application to nutrition is called ''nonparamet ric calibration'' after the term used for studies in that field. Other applications include local polynomial regression for generalized line ar models, robust local regression, and local transformations in a lat ent variable model. Extensions to partially parametric models are disc ussed.