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Abstract.In this article, we study the convergence rate of asymptotic normality for the estimator in a non parametric regression model under φ-mixing random variables by using the blockwise technique. With different choices of the parameters, the rates are shown as O(n−1/9) and O(n−1/6). We also carry out some simulation studies and a real data analysis to support the theoretical results established here. [ABSTRACT FROM AUTHOR]

This article is concerned with the uniform strong consistency of histogram density estimator and the convergence rate under φ -mixing samples. By using the Bernstein's type inequality, we give the uniformly strong consistency of the estimator and obtain the corresponding rate under some mild conditions. These results extend or improve the corresponding ones for strong mixing process to umixing samples. Also, the simulation study of the finite samples provided in this article shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we establish some results on strong consistency for the least square estimator in a simple linear errors-in-variables regression models based on widely orthant dependent errors. The results obtained in the paper generalize or improve the corresponding ones for dependent random variables. We also carry out some simulation studies to verify the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the consistency of nonparametric regression model. For the weighted estimator of unknown regression function, the strong consistency, the complete consistency and the convergence rate of the complete consistency are investigated under some mild conditions. These results extend or improve the corresponding ones of Yang et al. (2018) for extended negatively dependent (END, for short) random variables to asymptotically almost negatively associated random variables. Also, the simulation study of the finite samples provided in this paper shows the validity of our results. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the asymptotic normality of wavelet estimators in the heteroscedastic regression model with φ-mixing errors. Under some suitable conditions, the asymptotic normality of the wavelet estimators of g and f in the heteroscedastic regression model with φ-mixing errors are obtained, which generalize or improve the corresponding ones for α-mixing random variables and martingale difference sequence in some sense. Also, the simulation study of the finite samples provided in this paper shows the validity of our results. [ABSTRACT FROM AUTHOR]

This article is concerned with the estimating problem of nonparametric regression model. Under certain regularity conditions, we derive the Berry-Esseen bound for wavelet estimators of the unknown regression function with asymptotically negatively associated assumptions. Also, we present a numerical simulation study to verify the validity of the results established here. [ABSTRACT FROM AUTHOR]

In this paper, we present an inequality of characteristic functions for ψ-mixing random vectors, and derive an upper bound for the supremum of the absolute value of the difference of two multivariate probability density functions based on ψ-mixing random vectors. For its application, we discuss the Berry-Esseen type bounds for conditional value-at-risk estimator based on ψ-mixing sequences, by the suitable choice of some constants, the Berry-Esseen type bounds of the estimator can attain O ( n − 1 / 6 ). [ABSTRACT FROM AUTHOR]

For the heteroscedastic regression model , where , are known to be nonrandom design points, and are defined on the closed interval [0,1]. When is known, we investigate the Berry-Esseen type bounds for wavelet estimators of β and under are identically distributed ϕ-mixing random errors, when is unknown, the Berry-Esseen type bounds for wavelet estimators of β, and established under are independent random errors. [ABSTRACT FROM AUTHOR]