Almost sure and complete consistency of the estimator in nonparametric regression model for negatively orthant dependent random variables
Bull. Korean Math. Soc. 2020 Vol. 57, No. 1, 51-68
Published online January 31, 2020
Liwang Ding
Guangxi University of Finance and Economics
Abstract : In this paper, the author considers the nonparametric regression model with negatively orthant dependent random variables. The wavelet procedures are developed to estimate the regression function. For the wavelet estimator of unknown function $g(\cdot)$, the almost sure consistency is derived and the complete consistency is established under the mild conditions. Our results generalize and improve some known ones for independent random variables and dependent random variables.
Keywords : Negatively orthant dependent random variables, wavelet estimator, almost sure consistency, complete consistency
MSC numbers : 60E05, 60F15, 62G05
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