Nonparametric Function Estimation for Clustered Data When the Predictor is Measured without/with Error

Abstract

We consider local polynomial kernel regression with a single covariate for clustered data using estimating equations. We assume that at most m < ∞ observations are available on each cluster. In the case of random regressors, with no measurement error in the predictor, we show that it is generally the best strategy to ignore entirely the correlation structure within each cluster and instead pretend that all observations are independent. In the further special case of longitudinal data on individuals with fixed common observation times, we show that equivalent to the pooled data approach is the strategy of fitting separate nonparametric regressions at each observation time and constructing an optimal weighted average. We also consider what happens when the predictor is measured with error. Using the SIMEX approach to correct for measurement error, we construct an asymptotic theory for both the pooled and the weighted average estimators. Surprisingly, for the same amount of smoothing, the weighted average estimators typically have smaller variances than the pooling strategy. We apply the proposed methods to analysis of the AIDS Costs and Services Utilization Survey.