Bayesian inference for α-stable distributions: A random walk MCMC approach

Computational Statistics and Data Analysis

Volumn 51, Issue 5, 2007, Pages 2688-2700

  Lombardi, Marco J ^a  

^a JOINT RESEARCH CENTRE   (Italy)

Author keywords

Stable distributions; Infinite variance; MCMC

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; FAST FOURIER TRANSFORMS; FUNCTIONS; PARAMETER ESTIMATION; RANDOM PROCESSES;

ALPHA-STABLE DISTRIBUTIONS; INFINITE VARIANCE; MCMC;

PROBABILISTIC LOGICS;

EID: 33751011015     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.01.009     Document Type: Article

References (13)

1. Bergstrøm H. On some expansions of stable distribution functions. Ark. Math. 2 (1952) 375-378
2. Buckle D.J. Bayesian inference for stable distributions. J. Amer. Statist. Assoc. 90 (1995) 605-613
3. DuMouchel W.H. On the asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution. Ann. Statist. 1 (1973) 948-957
4. Gnedenko B.V., and Kolmogorov A.N. Limit Distributions for Sums of Independent Random Variables (1954), Addison-Wesley, Reading, MA
5. Lachmann R. Musik des Orients (1929), Athenaion, Potsdam
6. Lombardi, M.J., Godsill, S.J., 2006. On-line Bayesian estimation of signals in symmetric α-stable noise. IEEE Transactions on Signal Processing, vol. 54, 775-779.
7. McCulloch J.H. Simple consistent estimators of stable distribution parameters. Comm. Statist.-Simulation Computation 15 (1986) 1109-1136
8. Menn, C., Rachev, S.T., 2006. Calibrated FFT-based density approximations for α-stable distributions. Comput. Statist. Data Anal. 52, in press, doi:10.1016/j.csda.2005.03.004.
9. Mittnik S., Rachev S.T., Doganoglu T., and Chenyao D. Maximum likelihood estimation of stable paretian models. Math. Comput. Model. 29 (1999) 275-293
10. Nolan J.P. Numerical computation of stable densities and distribution functions. Comm. Statist.-Stochastic Models 13 (1997) 759-774
11. Robert C.P., and Casella G. Monte Carlo Statistical Methods (1999), Springer, New York
12. Tsionas E.G. Monte Carlo inference in econometric models with symmetric stable distributions. J. Econometrics 88 (1999) 365-401
13. Zolotarev V.M. One-dimensional Stable Distributions (1986), American Mathematical Society, Providence, RI