114
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Confidence intervals for nonparametric regression functions under negatively associated errors

, , &
Pages 645-659 | Received 16 Feb 2010, Accepted 22 Feb 2011, Published online: 03 May 2011

References

  • Benedetti , J. K. 1977 . On the Nonparametric Estimation of Regression Functions . Journal of the Royal Statistical Society. Series B , 39 : 248 – 253 .
  • Block , H. W. , Savits , T. H. and Sharked , M. 1982 . Some Concepts of Negative Dependence . The Annals of Probability , 10 : 765 – 772 .
  • Carlstein , E. 1986 . The Use of Subseries Methods for Estimating the Variance of a General Statistic from a Stationary Time Series . The Annals of Statistics , 14 : 1171 – 1179 .
  • Chen , S. X. and Qin , Y. S. 2000 . Empirical Likelihood Confidence Intervals for Local Linear Smoothers . Biometrika , 87 : 946 – 953 .
  • Gasser , T. and Müller , H. G. 1979 . “ Kernel Estimation of Regression Functions ” . In Smoothing Techniques for Curve Estimation-Lecture Notes in Mathematics , Edited by: Gasser , T. and Rosenblatt , M. Vol. 757 , 23 – 68 . New York : Springer .
  • Georgiev , A. A. and Greblicki , W. 1986 . Nonparametric Function Recovering from Noisy Observations . Journal of Statistical Planning and Inference , 13 : 1 – 14 .
  • Hall , P. 1985 . Resampling a Coverage Pattern . Stochastic Processes and their Applications , 20 : 231 – 246 .
  • Hall , P. 1992 . The Bootstrap and Edgeworth Expansion , New York : Springer .
  • Hall , P. and La Scala , B. 1990 . Methodology and Algorithms Of Empirical Likelihood . The International Statistical Review , 58 : 109 – 127 .
  • Huang , W. T. and Xu , B. 2002 . Some Maximal Inequalities and Complete Convergence of Negatively Associated Random Sequences . Statistics & Probability Letters , 57 : 183 – 191 .
  • Joag-Dev , K. and Proschan , F. 1983 . Negative Association of Random Variables With Applications . The Annals of Statistics , 11 : 286 – 295 .
  • Kitamura , Y. 1997 . Empirical Likelihood Methods with Weakly Dependent Processes . The Annals of Statistics , 25 : 2084 – 2102 .
  • Künsch , H. R. 1989 . The Jackknife and the Bootstrap for General Stationary Observations . The Annals of Statistics , 17 : 1217 – 1261 .
  • Lahiri , S. 2003 . Resampling Methods for Dependent Data , New York : Springer .
  • Li , Y. X. and Zhang , L. X. 2004 . Complete Moment Convergence of Moving-Average Processes Under Dependence Assumptions . Statistics & Probability Letters , 70 : 191 – 197 .
  • Liang , H. Y. and Su , C. 1999 . Complete Convergence for Weighted Sums of NA Sequences . Statistics & Probability Letters , 45 : 85 – 95 .
  • Matula , P. 1992 . A Note on the Almost Sure Convergence of Sums of Negatively Dependent Random Variables . Statistics & Probability Letters , 15 : 209 – 213 .
  • Owen , A. B. 1988 . Empirical Likelihood Ratio Confidence Intervals for a Single Functional . Biometrika , 75 : 237 – 249 .
  • Owen , A. B. 1990 . Empirical Likelihood Ratio Confidence Regions . The Annals of Statistics , 18 : 90 – 120 .
  • Politis , D. and Romano , J. P. 1994 . The Stationary Bootstrap . Journal of the American Statistical Association , 89 : 1303 – 1313 .
  • Priestley , M. B. and Chao , M. T. 1972 . Non-Parametric Function Fitting . Journal of the Royal Statistical Society. Series B , 34 : 385 – 392 .
  • Qin , Y. S. 1999 . Empirical Likelihood Ratio Confidence Regions in a Partially Linear Model . Chinese Journal of Applied Probability and Statistics , 15 : 363 – 369 .
  • Shao , Q. M. 2000 . A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables . Journal of Theoretical Probability , 13 : 343 – 356 .
  • Shi , X. Q. 1986 . Bootstrap Estimation for the Mean of a m-Dependent Sample . Chinese Science Bulletin , 6 : 404 – 407 .
  • Su , C. , Zhao , L. C. and Wang , Y. B. 1997 . Moment Inequalities and Week Convergence for Negatively Associated Sequences . Science in China. Series A , 40 : 72 – 182 .
  • Yang , S. C. 2003 . Uniformly Asymptotic Normality of the Regression Weighted Estimator for Negatively Associated Samples . Statistics & Probability Letters , 62 : 101 – 110 .
  • Zhang , L. X. 2001 . The Weak Convergence for Functions of Negatively Associated Random Variables . Journal of Multivariate Analysis , 78 : 272 – 298 .
  • Zhang , J. J. 2006 . Empirical Likelihood for NA Series . Statistics & Probability Letters , 76 : 153 – 160 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.