A simple resampling method by perturbing the minimand

Suppose that under a semiparametric setting an estimator of a vector of parameters of interest is obtained by optimising an objective function which has a U-process structure. The covariance matrix of the estimator is generally a function of the underlying density function, which may be difficult to estimate well by conventional methods. In this paper, we present a simple resampling method by perturbing the objective function repeatedly. Inferences of the parameters can then be made based on a large collection of the resulting optimisers. We illustrate our proposal by three examples with a heteroscedastic regression model.