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Comparison Study of Parameter Estimation Methods for Some Extreme Value Distributions (Focused on the Regression Method)
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 Title & Authors
Comparison Study of Parameter Estimation Methods for Some Extreme Value Distributions (Focused on the Regression Method)
Woo, Ji-Yong; Kim, Myung-Suk;
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Parameter estimation methods such as maximum likelihood estimation method, probability weighted moments method, regression method have been popularly applied to various extreme value models in numerous literature. Among three methods above, the performance of regression method has not been rigorously investigated yet. In this paper the regression method is compared with the other methods via Monte Carlo simulation studies for estimation of parameters of the Generalized Extreme Value(GEV) distribution and the Generalized Pareto(GP) distribution. Our simulation results indicate that the regression method tends to outperform other methods under small samples by providing smaller biases and root mean square errors for estimation of location parameter of the GEV model. For the scale parameter estimation of the GP model under small samples, the regression method tends to report smaller biases than the other methods. The regression method tends to be superior to other methods for the shape parameter estimation of the GEV model and GP model when the shape parameter is -0.4 under small and moderately large samples.
Generalized extreme value distribution;generalized Pareto distribution, maximum likelihood estimation method;Monte Carlo simulation;probability weighted moments method;regression method;
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Bali, T. G. (2003). An extreme value approach to estimating volatility and value at risk, Journal of Business, 76, 83-108 crossref(new window)

Davison, A. C. (1984). Modelling excesses over high thresholds, with an application, In Statistical Ex-tremes and Applications, 461-482, Springer, Vimeiro

Gettinby, G. D., Sinclair, C. D., Power, D. M. and Brown, R. A. (2006). An analysis of the distribution of extremes in indices of share returns in the US, UK and Japan from 1963 to 2000, International Journal of Finance and Economics, 11, 97-113 crossref(new window)

Gnedenko, B. V. (1943). Sur la distribution limite du terme maximum d'une serie aleatoire, Annals of Mathematics, 44, 423-453 crossref(new window)

Greenwood, J. A., Landwehr, J. M., Matalas, N. C. and Wallis, J. R. (1979). Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form, Water Re-sources Research, 15, 1049-1054 crossref(new window)

Gumbel, E. J. (1958). Statistics of Extremes, Columbia University Press, New Yor

Haktanir, T. and Bozduman, A. (1995). A study of sensitivity of the probability-weighted moments method on the choice of the plotting position formula, Journal of Hydrology, 168, 265-281 crossref(new window)

Hosking, J. R. M., Wallis, J. R. and Wood, E. F. (1985). Estimation of the generalised extreme value distribution by the method of probability weighted moments, Technometrics, 27, 251-261 crossref(new window)

Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics, Journal of the Royal Statistical Society, Series B, 52, 105-124

Hosking, J. R. M. and Wallis, J. R. (1987). Parameter and quantile estimation for the generalized Pareto distribution, Technometrics, 29, 339-349 crossref(new window)

Jenkinson, A. F. (1955). The frequency distribution of the annual maximum (or minimum) values of me-teorological elements, Quarterly Journal of the Royal Meteorological Society, 81, 158-171 crossref(new window)

Jenkinson, A. F. (1969). Statistics of extremes of maximum floods. WMO Technical Note, 98. World Meteorological Organization, Geneva, 183-228

Kim, M. S. (2007). On the effects of plotting positions to the probability weighted moments method for the generalized logistic distribution, The Korean Communications in Statistics, 14, 561-576 crossref(new window)

Landwehr, J. M., Matalas, N. C. and Wallis, J. R. (1979a). Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles, Water Resources Research, 15, 1055-1064 crossref(new window)

Landwehr, J. M., Matalas, N. C. and Wallis, J. R. (1979b). Estimation of parameters and quantiles of Wakeby distributions, Water Resources Research, 15, 1361-1379 crossref(new window)

Longin, F. M. (1996). The asymptotic distribution of extreme stock market returns, Journal of Business, 69, 383-408 crossref(new window)

Login, F. M. (2000). From value a risk to stress testing: The extreme value approach, Journal of Banking and Finance, 24, 1097-1130 crossref(new window)

Pickands, J. (1975). Statistical inference using extreme order statistics, The Annals of Statistics, 3, 119-131 crossref(new window)

Prescott, P. and Walden, A. T. (1980). Maximum likelihood estimation of the parameters of the generalized extreme-value distribution, Biometriika, 67, 723-724 crossref(new window)

Singh, V. P. and Ahmad, M. (2004). A comparative evaluation of the estimators of the three parameter generalized Pareto distribution, Journal of Statistical Computation & Simulation, 74, 91-106 crossref(new window)

Smith, R. L. (1985). Maximum likelihood estimation in a class of nonregular cases, Biometrika, 72, 67-90 crossref(new window)