Inference for heavy tailed distributions

Athreya, K. B. ; Lahiri, S. N. ; Wu, Wei (1998) Inference for heavy tailed distributions Journal of Statistical Planning and Inference, 66 (1). pp. 61-75. ISSN 0378-3758

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Let X1, X2, ... be a sequence of independent and identically distributed random variables in the domain of attraction of a stable law of order a and asymmetry parameter β. This paper develops some large sample inference procedures for the population mean μ and parameters α and β. Three different approaches to the construction of confidence intervals for μ are proposed, two of them involving bootstrap. For the parameters α and β estimators are proposed that are straightforward, computationally simple and statistically intuitive. The consistency and asymptotically normality of these estimators are also established. It is shown that in addition to these estimators being simple their accuracy is comparable to that of more complicated estimators available in the current literature.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Stable Laws; Heavytailed Distributions; Bootstrap
ID Code:1120
Deposited On:05 Oct 2010 12:54
Last Modified:12 May 2011 09:52

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