Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications

Mengmei Xi, Rui Wang, Zhaoyang Cheng and Xuejun Wang ()
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Mengmei Xi: Anhui University
Rui Wang: Anhui University
Zhaoyang Cheng: Wendian College, Anhui University
Xuejun Wang: Anhui University

Statistical Papers, 2020, vol. 61, issue 4, No 15, 1663-1684

Abstract: Abstract In this paper, we present the $$L_p$$ L p convergence for partial sums $$S_n=\sum _{k=1}^nX_k$$ S n = ∑ k = 1 n X k under the Cesàro uniform integrability condition and the complete convergence for the maximum of $$S_n$$ S n for sequences of widely orthant dependent random variables $$\{X_n,n\ge 1\}.$$ { X n , n ≥ 1 } . Some of the results extend the corresponding ones in reference. As applications, we get the complete consistency and the strong consistency for the estimator in a nonparametric regression model.

Keywords: Widely orthant dependent random variables; Cesàro uniform integrability; Complete convergence; Complete consistency; Nonparametric regression model; 60F15; 62G05; 62G20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-018-0996-y

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