We consider nonparametric regression models in which the regression function is a step function, and construct a convolution estimator for the response density that has the same bias as the usual estimators based on the responses, but a smaller asymptotic variance.

We consider a partially linear regression model with multivariate covariates and with responses that are allowed to be missing at random. This covers the usual settings with fully observed data and the nonparametric regression model as special cases. We first develop a test for additivity of the...

Suppose we observe a time series that alternates between different nonlinear autoregressive processes. We give conditions under which the model is locally asymptotically normal, derive a characterization of efficient estimators for differentiable functionals of the model, and use it to construct...

We consider nonparametric regression models with multivariate covariates and estimate the regression curve by an undersmoothed local polynomial smoother. The resulting residual-based empirical distribution function is shown to differ from the error-based empirical distribution function by the...

Suppose we observe an ergodic Markov chain and know that the stationary law of one or two successive observations fulfills a linear constraint. We show how to improve the given estimators exploiting this knowledge, and prove that the best of these estimators is efficient.

Densities of functions of independent and identically distributed random observations can be estimated by using a local U-statistic. Under an appropriate integrability condition, this estimator behaves asymptotically like an empirical estimator. In particular, it converges at the parametric...