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Some Comments on Characteristic Function-Based Estimators

J. L. Bryant and A. S. Paulson
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 41, No. 1/2 (Jul., 1979), pp. 109-116
Stable URL: http://www.jstor.org/stable/25050181
Page Count: 8
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Some Comments on Characteristic Function-Based Estimators
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Abstract

In a recent article, Thornton and Paulson (1977) provide conditions for weak consistency and asymptotic normality of estimators based on sample characteristic functions. One of their conditions for normality is difficult to apply, and in particular has not been verified for the case of estimation of the parameters of the stable laws when none of the four parameters are known, the problem which provided the original motivation for the use of such estimators. We derive an equivalent but somewhat more convenient condition, and show that it is satisfied in the stable estimation problem. We also show that the estimators of Thornton and Paulson are strongly consistent.

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