For time series nonparametric regression models with discontinuities, we propose to use polynomial splines to estimate locations and sizes of jumps in the mean function. Under reasonable conditions, test statistics for the existence of jumps are given and their limiting distributions are derived...

Under weak conditions of smoothness and mixing, we propose spline-backfitted spline (SBS) estimators of the component functions for a nonlinear additive autoregression model that is both computationally expedient for analyzing high dimensional large time series data, and theoretically reliable...

In this paper, we consider the harmonic measure on the unit sphere Sn−1 on Rn (n≥2) and offer a two-sided estimate of precise order on the Sobolev constant with exponent p∈(1,2). As special cases for p=1 and p tending to 2, our estimates recover those in Barthe et al. (2104) for n≥3...

For stochastic differential equations with jumps, we prove that W1H transportation inequalities hold for their invariant probability measures and for their process-level laws on the right-continuous path space w.r.t. the L1-metric and uniform metric, under dissipative conditions, via Malliavin...

Let (Xn)n=1 be a sequence of i.i.d.r.v.'s with values in a Polish space of law [mu]. Consider the empirical measures . Our purpose is to generalize Sanov's theorem about the large deviation principle of Ln from the weak convergence topology to the stronger Wasserstein metric Wp. We show that Ln...

The large deviation principle is established for the distributions of a class of generalized stochastic porous media equations for both small noise and short time.

A classical damping Hamiltonian system perturbed by a random force is considered. The locally uniform large deviation principle of Donsker and Varadhan is established for its occupation empirical measures for large time, under the condition, roughly speaking, that the force driven by the...

In this paper, we consider a uniformly ergodic Markov process (Xn)n[greater-or-equal, slanted]0 valued in a measurable subset E of Rd with the unique invariant measure , where the density f is unknown. We establish the large deviation estimations for the nonparametric kernel density estimator in...

In this paper, we prove the large deviation principle (LDP) for the occupation measures of not necessarily irreducible random dynamical systems driven by Markov processes. The LDP for not necessarily irreducible dynamical systems driven by i.i.d. sequence is derived. As a further application we...