The analysis of diffusion process in financial models is crucially dependent on the form of the drift and diffusion coefficient functions. A methodology is proposed for estimating and testing coefficient functions for ergodic diffusions that are not directly observable. It is based on...

The analysis of diffusion processes in financial models is crucially dependent on the form of the drift and diffusion coefficient functions. A methodology is proposed for estimating and testing coefficient functions for ergodic diffusions that are not directly observable. It is based on...

Summary A nonparametric probability density estimation problem is studied for the Bahadur-type risk under the sup-norm losses. The risk is minimax over the Hölder classes of densities. The large sample limiting performance of this risk is found, and the links to asymptotic equivalent...

A binary image model is studied with a Lipschitz edge function. The indicator function of the image is observed in random noise at n design points that can be chosen sequentially. The asymptotically minimax rate as n--[infinity] is found in estimating the edge function, and an asymptotically...

Let G be that portion of the unit square which lies below the graph of a smooth function. Assume that observations of the indicator function of G are available at any points X1,...,Xn in the plane. If each consecutive point Xi can be chosen sequentially, on the basis of all the preceding data,...

We develop inference tools in a semiparametric regression model with missing response data. A semiparametric regression imputation estimator, a marginal average estimator and a (marginal) propensity score weighted estimator are defined. All the estimators are proved to be asymptotically normal,...

In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of...

In semiparametric models it is a common approach to under-smooth the nonparametric functions in order that estimators of the finite dimensional parameters can achieve root-n consistency. The requirement of under-smoothing may result as we show from inefficient estimation methods or technical...