Journal of Guangxi Normal University(Natural Science Edition) ›› 2012, Vol. 30 ›› Issue (3): 22-29.

Previous Articles     Next Articles

Empirical Likelihood for Marginal Joint Probability Density Functions of a Negatively Associated Sample

QIN Yong-song, YANG Cui-lian   

  1. College of Mathematical Sciences,Guangxi Normal University,Guilin Guangxi 541004,China
  • Received:2012-05-19 Online:2012-09-20 Published:2018-12-04

Abstract: This paper studies the construction of confidenceintervals for the marginal joint probability density functions of a negatively associated (NA) sample by are studied using the blockwise technique.It is shows that the blockwise empiricallikelihood (EL) ratio statistic is asymptotically χ2-type distributed,which is used to obtain EL-based confidence interval for the probability densityfunctions.

Key words: marginal probability density function, blockwise empirical likelihood, negatively associated sample, confidence interval

CLC Number: 

  • O212.7
[1] ROSENBLATT M.Remarks on some nonparametric estimates of a density function[J].Ann Math Statist,1956,27:832-837.
[2] PARZEN E.On estimation of a probability density function and mode[J].Ann Math Statist,1962,33:1065-1076.
[3] NADARAJA E.On non-parameter estimates of density functions and regression curves[J].Theory Probab Appl,1965,10:186-190.
[4] SINGH R S.Improvement of some known nonparametric uniformly consistent estimators of derivatives of a density[J].Ann Statist,1977,5:394-399.
[5] SILVERMAN B W.Density Estimation for Statistics and Data Analysis[M].New York:Chapman and Hall,1986.
[6] ROBINSON P M.Nonparametric estimators for time series[J].J Time Ser Anal,1983,4:185-197.
[7] LU Zu-di.Asymptotic normality of kernel density estimators underdependence[J].Ann Inst Statist Math,2001,53:447-468.
[8] LIN Zhing-yan.On the kernel estimation of a density for dependent sample[J].Science Bull,1983,28:709-713.
[9] ROUSSAS G G.Asymptotic normality of the kernel estimate of a probabilitydensity function under association[J].Statist Probab Lett,2000,50:1-12.
[10] MASRY E.Multivariate probability density estimation for associated processes:strong con-sistency and rates[J].Statist Probab Lett,2002,58:205-219.
[11] BLOCK H W,SAVITS T H,SHARKED M.Some concepts of negative dependence[J].Ann Probab,1982,10:765-772.
[12] JOAG-DEV K,PROSCHAN F.Negative association of random variables with applica-tions[J].Ann Statist,1983,11:286-295.
[13] SU Chun,ZHAO Lin-cheng,WANG Yue-bao.Moment inequalities and week convergence for negatively associated sequences[J].Sci in China (Ser A),1997,40:172-182.
[14] HUANG Wen-tao,XU Bing.Some maximal inequalities and complete convergence of negatively associated random sequences[J].Statist Probab Lett,2002,57:183-191.
[15] MATULA P.A note on the almost sure convergence of sums of negatively dependent random variables[J].Statist Probab Lett,1992,15:209-213.
[16] LIANG Han-ying,SU Chun.Complete convergence for weighted sums ofNA sequences[J].Statist Probab Lett,1999,45:85-95.
[17] SHAO Qi-man.A comparison theorem on moment inequalities betweennegatively associated and independent random variables[J].J Theoret Probab,2000,13:343-356.
[18] ZHANG Li-xing.The weak convergence for functions of negatively associated random vari-ables[J].J Multivariate Anal,2001,78:272-298.
[19] LI Ying-xin,ZHANG Li-xing.Complete moment convergence of moving-average processes under dependence assumptions[J].Statist Probab Lett,2004,70:191-197.
[20] OWEN A B.Empirical likelihood ratio confidence intervals for a single functional[J].Biometrika,1988,75:237-249.
[21] OWEN A B.Empirical likelihood ratio confidence regions[J].Ann Statist,1990,18:90-120.
[22] CHEN Song-xi.Empirical likelihood confidence intervals for nonparametric density estimation[J].Biometrika,1996,83:329-341.
[23] KITAMURA Y.Empirical likelihood methods with weakly dependent processes[J].Ann Statist,1997,25:2084-2102.
[24] CHEN Song-xi,WONG Chiu-min.Smoothed block empirical likelihoodfor quantiles of weakly dependent processes[J].Statistica Sinica,2009,19:71-81.
[25] QIN Yong-song,LI Ying-hua,LEI Qing-zhu.Empirical likelihood for probability density functionsunder negatively associated samples[J].J Statist Plann Infer,2011,141:373-381.
[26] CAI Zong-wu,ROUSSAS G G.Berry-esseen bounds for smooth estimator of a distribution function under association[J].J Nonparametric Statist,1999,11:79-106.
[1] LU Wei-xue YANG Shi-juan LI Ying-hua. The Joint Asymptotic Distribution of Distribution Function in a Finite Number of Points under ø-Mixing Samples [J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(2): 67-74.
[2] CUI Yong-jun, YANG Shan-chao, LIANG Dan. Consistency of Nearest Neighbor Estimation of Density Function for Linearly Negative Quadrant Dependent Samples [J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(2): 59-65.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!