No abstract

We study the problem of multivariate estimation in the nonparametric regression model with random design. We assume that the regression function to be estimated possesses partially linear structure, where parametric and nonparametric components are both unknown. Based on Goldenshulger and Lepski methodology, we propose estimation procedure that adapts to the smoothness of the nonparametric component, by selecting from a family of specific kernel estimators. We establish a global oracle inequality (under the Lp-norm, 1≤p＜1) and examine its performance over the anisotropic H¨older space.

We study a minimum distance estimation in L 2 -norm for a stochastic equation with additive fractional Brownian sheet. The consistency and asymptotic normality of this estimator are established in the asymptotic of small noise.

We are interested in bounds on the large deviations probability and Berry–Esseen type inequalities for maximum likelihood estimator and Bayes estimator of the parameter appearing linearly in the drift of nonhomogeneous stochastic differential equation driven by fractional Brownian motion.