Consider the partial linear model Yi=X[tau]i[beta]+g(Ti)+[var epsilon]i, i=1, ..., n, where [beta] is a p-1 unknown parameter vector, g is an unknown function, Xi's are p-1 observable covariates, Ti's are other observable covariates in [0, 1], and Yi's are the response variables. In...

Consider the nonparametric regression model Yni=g(xni)+[epsilon]ni for i=1,...,n, where g is unknown, xni are fixed design points, and [epsilon]ni are negatively associated random errors. Nonparametric estimator gn(x) of g(x) will be introduced and its asymptotic properties are studied. In...

In this paper we investigate the weighted bootstrap for U-statistics and its properties. Under very general choices of random weights and certain regularity conditions, we show that the weighted bootstrap method with U-statistics provides second-order accurate approximations to the distribution...