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A Note on Estimation for Gamma and Stable Processes

I. V. Basawa and P. J. Brockwell
Biometrika
Vol. 67, No. 1 (Apr., 1980), pp. 234-236
Published by: Oxford University Press on behalf of Biometrika Trust
DOI: 10.2307/2335341
Stable URL: http://www.jstor.org/stable/2335341
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Note on Estimation for Gamma and Stable Processes
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Abstract

Maximum likelihood estimators of the parameters of nondecreasing pure-jump gamma and stable processes based on the jumps of size greater than or equal to ε were studied in a previous paper (Basawa & Brockwell, 1978). In particular, for a single realization X(u), 0 ⩽ u ⩽ t, the estimators for the stable process are consistent as $\varepsilon \downarrow 0$, but this is not so for the gamma process. In the present note we derive asymptotic distributions as $\varepsilon \downarrow 0$ for these estimators, centred and scaled as appropriate.

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