Wild Bootstrap of the Sample Mean in the Infinite Variance Case

REFERENCES

• Abadir , K. , Magnus , J. ( 2003 ). The central limit theorem for Student's distribution . Econometric Theory 19 : 1195 – 1195 ; Solution in Econometric Theory 20:1261–1264 .
   Google Scholar
• Andrews , D. W. K. , Buchinsky , M. ( 2000 ). A three-step method for choosing the number of bootstrap repetitions . Econometrica 68 : 23 – 51 .
   Web of Science ®Google Scholar
• Arcones , M. A. , Giné , E. ( 1989 ). The bootstrap of the mean with arbitrary bootstrap sample size . Annales Institut Henri Poincare Probabilites et Statistiques B 25 : 457 – 481 .
   Web of Science ®Google Scholar
• Arcones , M. A. , Giné , E. ( 1991 ). Additions and corrections to “The bootstrap of the mean with arbitrary bootstrap sample size.” Annales Institut Henri Poincare Probabilites et Statistiques B 27 : 583 – 585 .
   Web of Science ®Google Scholar
• Athreya , K. B. ( 1987 ). Bootstrap of the mean in the infinite variance case . Annals of Statistics 15 : 724 – 731 .
   Web of Science ®Google Scholar
• Bertail , P. , Politis , D. N. , Romano , J. P. ( 1999 ). On subsampling estimators with unknown rate of convergence . Journal of the American Statistical Association 94 : 569 – 579 .
   Web of Science ®Google Scholar
• Chambers , J. M. , Mallows , C. L. , Stuck , B. W. ( 1976 ). A method for simulating stable random variables . Journal of the American Statistical Association 71 : 340 – 344 .
   Web of Science ®Google Scholar
• Chan , N. H. , Tran , L. T. ( 1989 ). On the first-order autoregressive process with infinite variance . Econometric Theory 5 : 354 – 362 .
   Web of Science ®Google Scholar
• Cornea , A. , Davidson , R. (2009). A refined bootstrap for heavy tailed distributions. Mimeo. Available at http://russell-davidson.arts.mcgill.ca/articles/
   Google Scholar
• Daley , D. J. , Vere-Jones , D. ( 2008 ). An Introduction to the Theory of Point Processes . New York : Springer .
   Google Scholar
• Feller , W. ( 1971 ). An Introduction to Probability Theory and Its Applications . Vol. 2 . , 2nd ed. New York : Wiley .
   Google Scholar
• Hall , P. ( 1992 ). Asymptotic properties of the bootstrap for heavy-tailed distributions . Annals of Probability 18 : 1342 – 1360 .
   Web of Science ®Google Scholar
• Hall , P. , Yao , Q. ( 2003 ). Inference in ARCH and GARCH models with heavy-tailed errors . Econometrica 71 : 285 – 317 .
   Web of Science ®Google Scholar
• Hansen , B. E. ( 1996 ). Inference when a nuisance parameter is not identified under the null hypothesis . Econometrica 64 : 413 – 430 .
   Web of Science ®Google Scholar
• Knight , K. ( 1989 ). On the bootstrap of the mean in the infinite variance case . Annals of Statistics 17 : 1168 – 1175 .
   Web of Science ®Google Scholar
• Lehmann , E. L. , Romano , J. P. ( 2005 ). Testing Statistical Hypotheses. , 3rd ed. New York : Springer .
   Google Scholar
• LePage , R. , Woodroofe , M. , Zinn , J. ( 1981 ). Convergence to a stable distribution via order statistics . Annals of Probability 9 : 624 – 632 .
   Web of Science ®Google Scholar
• Lévy , P. ( 1931 ). Sur les séries dont les termes sont des variables ventuelles indépendanes . Studia Math. 3 : 119 – 155 .
   Google Scholar
• Liu , R. Y. ( 1988 ). Bootstrap procedures under some non iid models . Annals of Statistics 16 : 1696 – 1708 .
   Web of Science ®Google Scholar
• Mammen , E. ( 1993 ). Bootstrap and wild bootstrap for high dimensional linear models . Annals of Statistics 21 : 255 – 285 .
   Web of Science ®Google Scholar
• Politis , D. N. , Romano , J. P. ( 1994 ). Large sample confidence regions based on subsamples under minimal assumptions . Annals of Statistics 22 : 2031 – 2050 .
   Web of Science ®Google Scholar
• Politis , D. N. , Romano , J. P. , Wolf , M. ( 1999 ). Subsampling . New York : Springer-Verlag .
   Google Scholar
• Resnick , S. ( 1997 ). Heavy tailed modeling and teletraffic data . Annals of Statistics 25 : 1805 – 1869 .
   Web of Science ®Google Scholar
• Romano , J. P. , Wolf , M. ( 1999 ). Subsampling inference for the mean in the heavy-tailed case . Metrika 50 : 55 – 69 .
   Web of Science ®Google Scholar
• Shao , X. ( 2010 ). The dependent wild bootstrap . Journal of the American Statistical Association 105 : 218 – 235 .
   Web of Science ®Google Scholar
• Wu , C. F. J. ( 1986 ). Jackknife, bootstrap, and other resampling methods . Annals of Statistics 14 : 1261 – 1295 .
   Web of Science ®Google Scholar