J. Japan Statist. Soc., Vol. 33 (No. 2), pp. 215-229, 2003

Estimation of Moment Parameter in Elliptical Distributions

Yosihito Maruyama and Takashi Seo

Abstract. As a typical non-normal case, we consider a family of elliptically symmetric distributions. Then, the moment parameter and its consistent estimator are presented. Also, the asymptotic expectation and the asymptotic variance of the consistent estimator of the general moment parameter are given. Besides, the numerical results obtained by Monte Carlo simulation for some selected parameters are provided.

Key words and phrases: Asymptotic expansion, consistent estimator, elliptical distribution, kurtosis parameter, moment parameter, Monte Carlo simulation, perturbation method.

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