Nonparametric estimation of quantiles for a class of stationary processes

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• 作者：Chu Huang ; HanChao Wang ; ZhengYan Lin
• 关键词：quantile estimator ; kernel method ; causal process ; m ; dependent approximation ; asymptotic inference ; 60F05 ; 62G20
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：58
• 期：12
• 页码：2621-2632
• 全文大小：200 KB
• 参考文献：1.Bahadur R R. A note on quantiles in large samples. Ann Math Statist, 1966, 37: 577鈥?80MATH MathSciNet CrossRef
  2.Chen S X, Tang C Y. Nonparametric inference of value-at-risk for dependent financial returns. J Financ Econom, 2005, 3: 227鈥?55CrossRef
  3.Cs枚rg枚 M, Horv谩th L. On the distance between smoothed empirical and quantile processes. Ann Statist, 1995, 23: 113鈥?31MATH MathSciNet CrossRef
  4.Erd枚s P. On a family of symmetric Bernoulli convolutions. Amer J Math, 1939, 61: 974鈥?76MathSciNet CrossRef
  5.Freedman D A. On tail probabilities for martingales. Ann Probab, 1975, 3: 100鈥?18MATH CrossRef
  6.Hesse C H. A Bahadur-type representation for empirical quantiles of a large class of stationary, possibly infinitevariance, linear processes. Ann Statist, 1990, 18: 1188鈥?202MATH MathSciNet CrossRef
  7.Kiefer J. On Bahadur鈥檚 representation of sample quantiles. Ann Math Statist, 1967, 38: 1323鈥?342MATH MathSciNet CrossRef
  8.Kulik R. Bahadur-Kiefer theory for sample quantiles of weakly dependent linear processes. Bernoulli, 2007, 13: 1071鈥?090MATH MathSciNet CrossRef
  9.Liu W D, Lin Z Y. Strong approximation for a class of stationary processes. Stochastic Process Appl, 2009, 119: 249鈥?80MATH MathSciNet CrossRef
  10.Liu W D, Wu W B. Simultaneous nonparametric inference of time series. Ann Statist, 2010, 38: 2388鈥?421MATH MathSciNet CrossRef
  11.Mack Y P. Bahadur鈥檚 representation of sample quantiles based on smoothed estimates of a distribution function. Probab Math statist, 1987, 8: 183鈥?89MATH MathSciNet
  12.Serfling R J. Approximation Theorems of Mathematical Statistics. Hoboken: John Wiley & Sons, 1980MATH CrossRef
  13.Withers C S. Conditions for linear processes to be strongly mixing. Zeitschrift f眉r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1981, 57: 477鈥?80MATH MathSciNet CrossRef
  14.Wu W B. Empirical processes of long-memory sequences. Bernoulli, 2003, 9: 809鈥?31MATH MathSciNet CrossRef
  15.Wu W B. On the Bahadur representation of sample quantiles for dependent sequences. Ann Statist, 2005, 33: 1934鈥?963MATH MathSciNet CrossRef
  16.Wu W B. Nonlinear system theory: Another look at dependence. Proc Natl Acad Sci India Sect A, 2005, 102: 14150鈥?4154MATH CrossRef
  17.Wu W B. Oscillations of empirical distribution functions under dependence. IMS Lecture Notes Monogr Ser, 2006, 51: 53鈥?1CrossRef
  18.Wu W B, Huang Y X, Huang Y B. Kernel estimation for time series: An asymptotic theory. Stochastic Process Appl, 2010, 120: 2412鈥?431MATH MathSciNet CrossRef
  19.Wu W B, Zhou Z. Gaussian approximations for non-stationary multiple time series. Statist Sinica, 2011, 21: 1397鈥?413MATH MathSciNet CrossRef
  
• 作者单位：Chu Huang (1)
  HanChao Wang (2)
  ZhengYan Lin (2)
  
  1. Department of Science, Hangzhou Normal University, Hangzhou, 310036, China
  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Chinese Library of Science
  Applications of Mathematics
  
• 出版者：Science China Press, co-published with Springer
• ISSN：1869-1862

文摘

We study smoothed quantile estimator for a class of stationary processes. We obtain the convergency rates and the Bahadur representation, as well as the asymptotic normality for this estimator by the method of m-dependent approximation. Our results can be used in the study of the estimation of value-at-risk (VaR) and applied to many time series which have important applications in econometrics. Keywords quantile estimator kernel method causal process m-dependent approximation asymptotic inference