JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 69-74.doi: 10.6040/j.issn.1671-9352.0.2018.076

Previous Articles     Next Articles

Consistency of estimator of nonparametric regression function for arrays of rowwise NSD

LI Yong-ming1,3, NIE Cai-ling2, LIU Chao1, GUO Jian-hua1   

  1. 1. School of Mathematics and Computer Science, Shangrao Normal University, Shangrao 334001, Jiangxi, China;
    2. College of Sciences, Nanchang University, Nangchang 330000, Jiangxi, China;
    3. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China
  • Online:2018-12-20 Published:2018-12-18

PDF (PC)

710

Abstract: With the random error of arrays of rowwise NSD, the estimation of the unknown regression function in the nonparametric regression model is considered. Under certain conditions, the strong consistency of the weighted estimator of the unknown regression function is obtained.

Key words: nonparmetric regression function, NSD sequences, weighted function estimator, strong consistency

CLC Number: 

  • O211.67
[1] HU Taizhong. Negatively superadditive dependence of random variables with application[J]. Chinese Journal of Applied Probability and Statistics, 2000, 16(2):133-144.
[2] CHRISTOFIDES T C, VAGGELATOU E. A connection between supermodular ordering and positive/negative association[J]. Journal of Multivariate Analysis, 2014, 88:138-151.
[3] EGHBAL N, AMINI M, BOZORGNIA A. Some maximal inequalities for quadratic forms of negative superadditive dependence random variables[J]. Statistics and Probability Letters, 2010, 80:587-591.
[4] EGHBAL N, AMINI M, BOZORGNIA A. On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variabes[J]. Statistics and Probability Letters, 2011, 81:1112-1120.
[5] WU Yi, WANG Xuejun, HU Shuhe. Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications[J]. Applied Mathematics: A Journal of Chinese Universities, 2016, 48(4):834-850.
[6] WANG Xuejun, SHEN Aiting, CHEN Zhiyong, et al. Complete convergence for weighted sums of NSD random variables and its application in the EV regression model[J]. TEST, 2015, 24(1):166-184.
[7] 杨善朝. 基于鞅序列非参数回归权函数的估计[J]. 系统科学与数学, 1999, 19(1):79-85. YANG Shanchao. The estimation of nonparametric regression function based on martingale sequence[J]. Journal of Systems Science and Mathematical Sciences, 1999, 19(1):79-85.
[8] TRAN L T, IOANNIDES D A, ROUSSAS G G. Fixed design regression for time series: asymptotic normality[M]. Salt Lake City: Academic Press, Inc, 1992.
[9] YANG Shanchao. Uniformly asymptotic normality of the regression weighted estimator for negatively associated samples[J]. Statistics and Probability Letters, 2003, 62(2):101-110.
[10] FAN Y. Consistent nonparametric multiple regression for dependent heterogeneous processes: the fixed design case[J]. Journal of Multivariate Analysis, 2008, 33(1):72-88.
[11] SHEN Aiting, ZHANG Y, VOLODIN A. Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables[J]. Metrika, 2015, 78:295-311.
[12] 吴群英. 混合序列的概率极限理论[M]. 北京: 科学出版社, 2006. WU Qunying. Probability limit theory of mixed sequence[M]. Beijing: Science Press, 2006.
[13] ROUSSAS G G. Consistent regression estimation with fixed design points under dependence conditions[J]. Statistics and Probability Letters, 1989, 8(1):41-50.
[1] HU Xue-ping, ZHANG Hong-mei. Convergence properties of the kernel-type density estimator under WOD dependent samples [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 21-25.
[2] LI Yong-ming, DENG Shao-jian, JIANG Wei-hong. Consistencies of recursive estimator of a probability density for extended negatively dependent samples [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 54-59.
[3] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors [J]. J4, 2013, 48(1): 83-88.
[4] YE Cai-yuan, WU Qun-ying*, WU Xin-ye. Consistency NA samples kernel density estimation for censored data [J]. J4, 2013, 48(09): 40-45.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] YANG Jun. Characterization and structural control of metalbased nanomaterials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 1 -22 .
[2] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[3] YANG Lun, XU Zheng-gang, WANG Hui*, CHEN Qi-mei, CHEN Wei, HU Yan-xia, SHI Yuan, ZHU Hong-lei, ZENG Yong-qing*. Silence of PID1 gene expression using RNA interference in C2C12 cell line[J]. J4, 2013, 48(1): 36 -42 .
[4] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[5] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[6] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63 -67 .
[7] ZHAO Tong-xin1, LIU Lin-de1*, ZHANG Li1, PAN Cheng-chen2, JIA Xing-jun1. Pollinators and pollen polymorphism of  Wisteria sinensis (Sims) Sweet[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 1 -5 .
[8] TANG Xiao-hong1, HU Wen-xiao2*, WEI Yan-feng2, JIANG Xi-long2, ZHANG Jing-ying2, SHAO Xue-dong3. Screening and biological characteristics studies of wide wine-making yeasts[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 12 -17 .
[9] WANG Bi-yu, CAO Xiao-hong*. The perturbation for the Browder’s theorem of operator matrix#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 90 -95 .
[10] YU Xiu-qing. (σ,τ)-expansion model of P-sets and its properties#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 90 -94 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd