Rank-based testing in linear models with stable errors

References

• Andrews , B. , Calder , M. and Davis , R. A. 2009 . Maximum Likelihood Estimation for α-Stable Autoregressive Processes . Annals of Statistics , 37 : 1946 – 1982 .
   Web of Science ®Google Scholar
• Benktus , V. , Bing-Yi , J. , Shao , S. M. and Zhou , W. 2007 . Limiting Distributions of the Non-central t-Statistic and their Applications to the Power of t-Tests Under Non-normality . Bernoulli , 13 ( 2 ) : 346 – 364 .
   Web of Science ®Google Scholar
• Blattberg , R. and Sargent , T. 1971 . Regression with Non-Gaussian Disturbances: Some Sampling Results . Econometrica , 39 : 501 – 510 .
   Web of Science ®Google Scholar
• Borak , Sz. , Härdle , W. and Weron , R. 2005 . “ Stable Distributions ” . In Statistical Tools for Finance and Insurance , Edited by: Cizek , P. , Härdle , W. and Weron , R. 21 – 44 . Berlin : Springer-Verlag .
   Google Scholar
• DuMouchel , W. H. 1973 . On the Asymptotic Normality of the Maximum-likelihood Estimate when Sampling from a Stable Distribution . Annals of Statistics , 1 : 948 – 957 .
   Web of Science ®Google Scholar
• Efron , B. 1969 . Student's t-Test Under Symmetry Conditions . Journal of the American Statistical Association , 64 : 1278 – 1302 .
   Web of Science ®Google Scholar
• El Barmi , H. and Nelson , P. I. Inference from Stable Distributions . Proceedings of the Symposium on Estimating Functions . Vol. 32 , pp. 439 – 456 . IMS Lecture Notes-Monograph Series
   Google Scholar
• Fama , E. 1965a . Behavior of Stock Market Prices . Journal of Business , 38 : 34 – 105 .
   Web of Science ®Google Scholar
• Fama , E. 1965b . Portfolio Analysis in a Stable Paretian Market . Management Science , 11 : 404 – 419 .
   Web of Science ®Google Scholar
• Fama , E. and Roll , R. 1968 . Some Properties of Symmetric Stable Distributions . Journal of the American Statistical Association , 63 ( 323 ) : 817 – 836 .
   Web of Science ®Google Scholar
• Fama , E. and Roll , R. 1971 . Parameter Estimates for Symmetric Stable Distributions . Journal of the American Statistical Association , 66 ( 334 ) : 331 – 338 .
   Web of Science ®Google Scholar
• Feller , W. 1971 . An Introduction to Probability and its Applications , 2 , Vol. 2 , New York : Wiley .
   Google Scholar
• Garcia , R. , Renault , E. and Veredas , D. 2010 . Estimation of Stable Distributions with Indirect Inference . Journal of Econometrics , to appear
   Web of Science ®Google Scholar
• Giné , E. , Götze , F. and Mason , D. 1997 . When is the Student t-Statistic Asymptotically Standard Normal? . Annals of Probability , 25 : 1514 – 1531 .
   Web of Science ®Google Scholar
• Hájek , J. and Šidák , S. 1967 . Theory of Rank Tests , New York : Academic Press .
   Google Scholar
• Hallin , M. and Werker , B. J.M. 2003 . Semiparametric Efficiency, Distribution-freeness, and Invariance . Bernoulli , 9 : 137 – 165 .
   Web of Science ®Google Scholar
• Jensen , D. R. 1979 . Linear Models without Moments . Biometrika , 66 ( 3 ) : 611 – 617 .
   Web of Science ®Google Scholar
• Le Cam , L. 1986 . Asymptotic Methods in Statistical Decision Theory , New York : Springer .
   Google Scholar
• Le Cam , L. and Yang , G. L. 2000 . Asymptotics in Statistics , 2 , New York : Springer .
   Google Scholar
• Lehmann , E. L. and Romano , J. P. 2005 . Testing Statistical Hypotheses , New York : Springer .
   Google Scholar
• Liese , F. and Miescke , K.-J. 2008 . Statistical Decision Theory , New York : Springer .
   Google Scholar
• Logan , B. F. , Mallows , C. L. , Rice , S. O. and Shepp , L. 1973 . Limit Distributions of Self-normalized Sums . Annals of Probability , 1 : 788 – 809 .
   Web of Science ®Google Scholar
• Mandelbrot , B. 1963 . The Variation of Speculative Prices . Journal of Business , 36 : 394 – 419 .
   Web of Science ®Google Scholar
• McCulloch , J. H. 1986 . Simple Consistent Estimators of Stable Distribution Parameters . Communications in Statistics-Simulations , 15 : 1109 – 1136 .
   Google Scholar
• Mittnik , S. , Paolella , M. S. and Rachev , S. T. 2000 . Diagnosis and Treating the Fat Tails in Financial Returns Data . Journal of Empirical Finance , 7 : 389 – 416 .
   Google Scholar
• Mittnik , S. , Rachev , S. T. and Paolella , M. S. 1998 . “ Stable Paretian Modeling in Finance: Some Empirical and Theoretical Aspects ” . In A Practical Guide to Heavy Tails , Edited by: Adler , R. , Feldman , R. and Taqqu , M. S. 79 – 110 . Boston : Birkhäuser .
   Google Scholar
• Nolan , J. P. 1997 . Numerical Calculation of Stable Densities and Distribution Functions . Stochastic Models , 13 : 759 – 774 .
   Google Scholar
• Nolan , J. P. 1999 . An Algorithm for Evaluating Stable Densities in Zolotarev's (M) Parametrization . Mathematical and Computer Modelling , 29 : 229 – 233 .
   Google Scholar
• Nolan , J. P. 2010 . Stable Distributions – Models for Heavy Tailed Data , Boston : Birkhäuser .
   Google Scholar
• Press , S. J. 1972 . ’Estimation in Univariate and Multivariate Stable Distribution . Journal of the American Statistic Association , 67 : 842 – 846 .
   Web of Science ®Google Scholar
• Puri , M. L. and Sen , P. K. 1985 . Nonparametric Methods in General Linear Models , New York : Wiley .
   Google Scholar
• Rimmer , R. H. and Nolan , J. P. 2005 . Stable Distributions in Mathematica . Mathematica Journal , 9 : 776 – 789 .
   Google Scholar
• Samorodnitsky , G. and Taqqu , M. S. 1994 . Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance , New York : Chapman and Hall .
   Google Scholar
• van der Vaart , A. 2000 . Asymptotic Statistics , Cambridge : Cambridge University Press .
   Google Scholar
• Zolotarev , V. M. 1986 . One-dimensional Stable Distributions , 65 Providence, RI: American Mathematical Society Translations of Mathematical Monographs, American Mathematical Society
   Google Scholar
• Zolotarev , V. M. 1995 . On Representation of Densities of Stable Laws by Special Functions . Theory of Probability and its Applications , 39 : 354 – 362 .
   Web of Science ®Google Scholar