On non-existence of moment estimators of the GED power parameter

• Autorzy: Bartosz Stawiarski
• Języki publikacji: EN

Abstrakty

EN

We reconsider the problem of the power (also called shape) parameter estimation within symmetric, zero-mean, unit-variance one-parameter Generalized Error Distribution family. Focusing on moment estimators for the parameter in question, through extensive Monte Carlo simulations we analyze the probability of non-existence of moment estimators for small and moderate samples, depending on the shape parameter value and the sample size. We consider a nonparametric bootstrap approach and prove its consistency. However, despite its established asymptotics, bootstrap does not substantially improve the statistical inference based on moment estimators once they fall into the non-existence area in case of small and moderate sample sizes.

Słowa kluczowe

EN

Generalized Error Distribution; nonparametric bootstrap; bootstrap consistency; moment estimator; power parameter

Kategorie tematyczne

• 62F40: Bootstrap, jackknife and other resampling methods
• 60F99: None of the above, but in this section
• 62F12: Asymptotic properties of estimators
• 60E05: Distributions: general theory

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2016
• Tom: 36
• Numer: 1-2
• Strony: 5-23

Daty

wydano

2016

otrzymano

2015-10-07

otrzymano

2015-12-10

Twórcy

autor

Bartosz Stawiarski

• Cracow University of Technology, Institute of Mathematics

Bibliografia

• [1] A. Ayebo and T.J. Kozubowski, An asymmetric generalization of Gaussian and laplace laws, J. Probab. Statist. Sci. 1 (2) (2004), 187-210.
• [2] A. Azzalini, Further results on a class of distributions which includes the normal ones, Statistica 46 (1986), 199-208.
• [3] P.J. Bickel and D.A. Freedman, Some asymptotic theory for the bootstrap, Ann. Stat. 9 (6) (1981), 1196-1217.
• [4] G.E. Box and G.C. Tiao, Bayesian Inference in Statistical Analysis (Addison Wesley Ed., 1973).
• [5] Y. Chen and N.C. Beaulieu, Novel low-complexity estimators for the shape parameter of the Generalized Gaussian Distribution, IEEE Transactions on Vehicular Technology 58 (4) (2009), 2067-2071.
• [6] D. Coin, A method to estimate power parameter in exponential power distribution via polynomial regression, Banca D’Italia 834 (2011), working paper.
• [7] C. Fernandez, J. Osiewalski and M.F.J. Steel, Modeling and inference with vdistributions, J. Amer. Statist. Association 90 (432) (1995), 1331-1340.
• [8] G. González-Farías, J.A. Domnguez-Molina and R.M. Rodrguez-Dagnino, Efficiency of the approximated shape parameter estimator in the generalized Gaussian distribution, IEEE Transactions on Vehicular Technology 58 (8) (2009), 4214-4223.
• [9] R. Krupiński and J. Purczyński, Approximated fast estimator for the shape parameter of Generalized Gaussian Distribution, Signal Processing 86 (2006), 205-211.
• [10] G. Lunetta, Di una generalizzazione dello schema della curva normale, Annali della Facolta di Economia e Commercio di Palermo 17 (1963), 237-244.
• [11] S. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern Anal. Machine Intell. 11 (1989), 674-693.
• [12] A.M. Mineo and M. Ruggieri, A software tool for the exponential power distribution: The normalp package, J. Statist. Software 12 (4) (2005), 1-24.
• [13] S. Nadarajah, A generalized normal distribution, J. Appl. Stat. 32 (7) (2005), 685-694.
• [14] J. Purczyński, Simplified method of GED distribution parameters estimation, Folia Oeconomica Stetinensia 10 (2) (2012), 35-49.
• [15] K.-S. Song, A globally convergent and consistent method for estimating the shape parameter of a Generalized Gaussian Distribution, IEEE Transactions on Information Theory 52 (2) (2006), 510-527.
• [16] M.T. Subbotin, On the law of frequency of errors, Matematicheskii Sbornik 31 (1923), 296-301.
• [17] P.R. Tadikamalla, Random sampling from the exponential power distribution, J. Amer. Statist. Association 75 (1980), 683-686.
• [18] Van der Vaart, Asymptotic Statistics (Cambridge University Press, 1998).
• [19] M.K. Varanasi and B. Aazhang, Parametric generalized Gaussian density estimation, J. Acoustical Society of America 86 (4) (1989), 1404-1415.
• [20] D. Zhu and V. Zinde-Walsh, Properties and estimation of asymmetric exponential power distribution, J. Econometrics 148 (2009), 86-99.

Identyfikatory

DOI

10.7151/dmps.1185