Data driven estimates for mixtures

Computational Statistics and Data Analysis

Volumn 47, Issue 3, 2004, Pages 583-598

  Mendes, Beatriz Vaz De Melo ^a,b   Lopes, Hedibert Freitas ^a  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b NONE   (Brazil)

Author keywords

Extreme value theory; Mixtures; Robustness; Simulations

Indexed keywords

COMPUTER SIMULATION; DATA REDUCTION; MAXIMUM LIKELIHOOD ESTIMATION; NORMAL DISTRIBUTION; PROBABILITY; RISK ASSESSMENT; ROBUSTNESS (CONTROL SYSTEMS); THEORY;

DATA DISTRIBUTIONS; EXTREME VALUE THEORY; RANDOM VARIABLE;

MIXTURES;

EID: 4944223838     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2003.12.006     Document Type: Article

References (31)

1. Coles, S., 2001. An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statistics. Springer, Berlin.
2. Danielsson, J., de Vries, C.G., 1997. Value-at-risk and extreme returns. Working paper, Department of Economics, University of Iceland.
3. Danielsson, J., de Vries, C.G., 1998. Beyond the sample: extreme quantile and probability estimation. Paper provided by Financial Markets Group and ESRC in its Series FMG Discussion Papers, Number dp0298.
4. Diebolt J., Robert C.P. Estimation of finite mixture distributions by Bayesian sampling. J. Roy. Statist. Soc. B. 56:1994;363-375.
5. Embrechts P., Klüppelberg C., Mikosch T. Modelling Extremal Events for Insurance and Finance. 1997;Springer, Berlin.
6. Engle R.F., González-Rivera G. Semi-parametric estimation of ARCH model. J. Business Econom. Statist. 9(4):1991;345-358.
7. Escobar M.D. Estimating normal means with a Dirichlet process prior. J. Amer. Statist. Assoc. 89:1994;268-277.
8. Escobar M.D., West M. Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90:1995;577-588.
9. Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A. Robust Statistics: The Approach Based on Influence Functions. 1986;Wiley, New York.
10. Harvey, C., Siddique, A., 1999. Autoregressive conditional skewness. Preprint, Duke University. J. Financial Quantitative Anal. 34(4), 465-488.
11. Hoaglin D.C., Mosteller F., Tukey J.W. Understanding Robust and Exploratory Data Analysis. 1983;Wiley, New York.
12. Hosking J., Wallis J. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics. 29:1987;339-349.
13. Hosking J., Wallis J., Wood E. Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics. 27:1985;251-261.
14. Huber P.J. Robust Statistics. 1981;Wiley, New York.
15. Leadbetter M., Lindgren G., Rootzén H. Extremes and Related Properties of Random Sequences and Processes. 1983;Springer, Berlin.
16. McLachlan G.J., Peel D. Finite Mixture Models. 2000;Wiley, New York.
17. McNeil, A.J., 1996. Estimating the Tails of Loss Severity Distributions using Extreme Value Theory, Department Mathematik, ETH Zentrum, Zürich.
18. McNeil, A.J., 1998. Calculating Quantile Risk Measures for Financial Return Series Using Extreme Value Theory, Department Mathematik, ETH Zentrum, Zürich.
19. McNeil, A., Frey, R., 1998. Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: an Extreme Value Approach, Department Mathematik, ETH Zentrum, Zürich.
20. Mendes B.V.M. Computing robust risk measures in emerging equity markets using extreme value theory. Emerging Markets Quart. 4(2):2000;25-41.
21. Pickands J. III. Statistical inference using extreme order statistics. Ann. Statist. 3:1975;119-131.
22. Richardson S., Green P. On Bayesian analysis of mixtures with an unknown number of components. J. Roy. Statist. Soc. Ser. B. 59:1997;731-792.
23. Roeder K., Wasserman L. Practical Bayesian density estimation using mixtures of normals. J. Amer. Statist. Assoc. 92:1997;894-902.
24. Silverman B.W. Density Estimation for Statistics and Data Analysis. 1986;Chapman & Hall, London.
25. Smith R.L. Estimating tails of probability distributions. Ann. Statist. 15:1987;1174-1207.
26. Smith, R.L., 1999. Measuring risk with extreme value theory. Working paper, Department of Statistics, University of North Carolina, Chapel Hill.
27. Susmel R. Switching volatility in Latin American emerging equity markets. Emerging Markets Quart. 2(1):1998;44-56.
28. Titterington, D.M., Smith, A.F.M., Makov, U.E., 1985. Statistical Analysis of Finite Mixture Distributions, Wiley Series in Probability and Mathematical Statistics. Wiley, New York.
29. Tukey J.W. A survey of sampling from contaminated distributions. Olkin I., Ghurye S.G., Hoeffding W., Madow W.G., Mann H.B. Contributions to Probability and Statistics, Essays in Honor of Harold Hotelling. 1960;448-485 Stanford University Press, Stanford, CA.
30. West M. Kernel density estimation and marginalization consistency. Biometrika. 78:1991;421-425.
31. West M. Approximating posterior distributions by mixtures. J. Roy. Statist. Soc. 55:1993;409-422.