On the convergence rates of kernel estimator and hazard estimator for widely dependent samples
In this paper, we establish a Bernstein-type inequality for widely orthant dependent random variables, and obtain the rates of strong convergence for kernel estimators of density and hazard functions, under some suitable conditions.
Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models
We present the Bernstein-type inequality for widely dependent random variables. By using the Bernstein-type inequality and the truncated method, we further study the strong consistency of estimator of fixed design regression model under widely dependent random variables, which generalizes the corresponding one of independent random variables. As an application, the strong consistency for the nearest neighbor estimator is obtained.
Meromorphic function sharing a small function with a homogeneous differential polynomial
Abstract In this paper, we consider a Brück-type result for a homogeneous differential polynomial generated by a meromorphic function.