In this paper, we mainly investigate the nonparametric regression model based on widely orthant dependent samples. The weak consistency, strong consistency, complete consistency, and the rates of strong consistency and complete consistency for the wavelet estimator are established under some mild conditions, which generalize and improve the corresponding ones for other dependent cases. Some numerical simulations are presented to verify the validity of the theoretical results based on finite samples.
In this paper, we study complete f-moment convergence, complete sth moment convergence and complete convergence for m-widely orthant dependent linear processes with random coefficients under some general conditions. The results presented extend and improve some known results. As an application, we present conclusions on complete f-moment consistency and complete consistency for a weighted estimator in a nonparametric regression model based on widely orthant dependent errors. Moreover, we perform a numerical simulation to verify the validity of the theoretical results. 2020 Mathematics Subject Classification: Primary 60F15; Secondary 62G20.
This paper establishes an exponential inequality for a sequence of widely orthant dependent (WOD) random variables. Leveraging this result, we prove the strong consistency of a non-parametric regression estimator under a general moment condition. We further derive the convergence rate of this estimator, highlighting its alignment with classical results under specific parameter choices. As an application, we examine the nearest neighbor estimator and support our theoretical findings with a numerical study.
In the paper we consider estimation of the regression coefficients in a linear regression model Y = X3 + & varepsilon;, where 3 is assumed to lie in a given ellipsoid Theta. The estimation is performed using a weighted squared error loss function. Under specific conditions, we find an explicit formula for an estimator 3bM of 3, which is minimax in the class D of all decision rules, not limited to linear estimators. We generalize the results of Wilczynski (2007), who found a minimax decision rule 3bM under considerably more restrictive conditions.
