Summary
When |X|k has a gamma distribution with parametersb −k andk −1,Jakuszenkow [1979] has, for the loss function\((\hat \theta - \theta )^2 \theta ^{ - 2} \), considered the best multiple of ΣX 2 i as an estimator ofb 2 and shown that it is Lehmann unbiased. In this paper, the best multiple of (Σ|X i |k)2/k is shown to be Lehmann unbiased, admissible and better than Jakuszenkow's estimator.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Farrell, R.H.: Estimators of a location parameter in the absolutely continuous case. Ann. Math. Statist.35, 1964, 949–998.
Jakuszenkow, H.: Estimation of the variance in the generalized Laplace distribution with quadratic loss function. Demonstratio Mathematica13, 1979, 581–591.
Lehmann, E.L.: Testing Statistical Hypotheses. New York 1959.
Portnoy, St.: Formal Bayes estimation with application to a random effects model. Ann. Math. Statist42, 1971, 1379–1402.
Sharma, D.: Some admissible estimators of scale parameter and the natural parameter in an exponential family. Sankhyã Series A35, 1973, 85–88.
Stein, C.: The admissibility of Pitman's estimator for a single location parameter. Ann. Math. Statist.30, 1959, 970–979.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sharma, D. On estimating the variance of a generalized Laplace distribution. Metrika 31, 85–88 (1984). https://doi.org/10.1007/BF01915188
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01915188