Title :
Consistency of estimators under nonparametric regression model for ANA sequences
Author :
Xili Tan ; Hui Zhang
Author_Institution :
Inst. of Math., Beihua Univ., Jilin, China
Abstract :
Consider the moment consistency and strong consistency of the weighted kernel estimator of unknown function under regression model. By the moment inequality, Cr inequality, Borel-Cantelli lemma, we get new moment consistency and strong consistency theorems of weighted kernel estimators of nonparametric regression functions for ANA sequences errors under some suitable conditions. The results obtained extend and improve the corresponding theorem for independent identically distributed random variables sequence.
Keywords :
estimation theory; random sequences; regression analysis; ANA sequences; Borel-Cantelli lemma; Cr inequality; distributed random variables sequence; estimator consistency; moment consistency theorem; moment inequality; nonparametric regression model; strong consistency theorem; weighted kernel estimator; Convergence; Educational institutions; Kernel; Markov processes; Mathematical model; Random variables; Silicon compounds; ANA sequences error; moment consistency; nonparametric regression models; strong consistency; weighted kernel estimators;
Conference_Titel :
Mechatronic Science, Electric Engineering and Computer (MEC), 2011 International Conference on
Conference_Location :
Jilin
Print_ISBN :
978-1-61284-719-1
DOI :
10.1109/MEC.2011.6025679
