Window Subsampling of Estimating Functions with Application to Regression Models

Abstract

We propose a subsampling method for estimating the asymptotic standard error of a statistic β _n that is the solution to an estimating equation 1/n Σⁿ _j=1 U_j(Y _j X_j, β) = 0 where the data Y_j may be temporally or spatially correlated and the estimating function may depend on covariates X_j . A key statistic that we consider in detail is a generalized linear model regression coefficient computed under the assumption of independence. The availability of a consistent variance estimator allows semiparametric regression approaches for clustered and longitudinal data to be used with time series and spatial data. The methods that we develop extend the subsampling ideas of Carlstein, Sherman, and Garcia-Soidan and Hall to estimating functions. Our approach provides an attractive alternative to the jackknife method of Lele, particularly for large datasets, because we do not require parameter reestimation.

Key Words:

• Bootstrap
• Marginal model
• Quasi-likelihood
• Variance estimation.