scholarly journals Precise Rates in Complete Moment Convergence for Negatively Associated Sequences

2009 ◽  
Vol 16 (5) ◽  
pp. 841-849
Author(s):  
Dae-Hee Ryu
Keyword(s):  
Complete Moment Convergence ◽  
Negatively Associated ◽  
Moment Convergence ◽  
Associated Sequences

COMPLETE MOMENT CONVERGENCE FOR ARRAYS OF ROWWISE NEGATIVELY ASSOCIATED RANDOM VARIABLES AND ITS APPLICATION IN NON-PARAMETRIC REGRESSION MODEL

2017 ◽  
Vol 32 (1) ◽  
pp. 37-57 ◽  
Author(s):  
Yi Wu ◽  
Xuejun Wang ◽  
Soo Hak Sung
Keyword(s):  
Numerical Simulation ◽  
Regression Model ◽  
Random Variables ◽  
Complete Moment Convergence ◽  
Parametric Regression ◽  
Associated Random Variables ◽  
Negatively Associated ◽  
Complete Consistency ◽  
Moment Convergence ◽  
Non Parametric

In this paper, some results on the complete moment convergence for arrays of rowwise negatively associated (NA, for short) random variables are established. The results obtained in this paper correct the corresponding one obtained in Ko [13] and also improve and generalize the corresponding ones of Kuczmaszewska [14] and Ko [13]. As an application of the main results, we present a result on complete consistency for the estimator in a non-parametric regression model based on NA errors. Finally, we provide a numerical simulation to verify the validity of our result.

scholarly journals Convergence Theorems for m -Coordinatewise Negatively Associated Random Vectors in Hilbert Spaces

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Lyurong Shi
Keyword(s):  
Hilbert Spaces ◽  
Law Of Large Numbers ◽  
Linear Process ◽  
Random Coefficients ◽  
Complete Moment Convergence ◽  
Random Vectors ◽  
Strong Law ◽  
Negatively Associated ◽  
Moment Convergence ◽  
Large Numbers

In this study, some new results on convergence properties for m -coordinatewise negatively associated random vectors in Hilbert space are investigated. The weak law of large numbers, strong law of large numbers, complete convergence, and complete moment convergence for linear process of H-valued m -coordinatewise negatively associated random vectors with random coefficients are established. These results improve and generalise some corresponding ones in the literature.

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