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The abscissa of convergence of the Laplace transform
- Part of
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- Journal:
- Journal of Applied Probability / Volume 29 / Issue 2 / June 1992
- Published online by Cambridge University Press:
- 14 July 2016, pp. 353-362
- Print publication:
- June 1992
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- Article
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Assume that we want to estimate – σ, the abscissa of convergence of the Laplace transform. We show that no non-parametric estimator of σ can converge at a faster rate than (log n)–1, where n is the sample size. An optimal convergence rate is achieved by an estimator of the form
where xn = O(log n) and 
is the mean of the sample values overshooting xn. Under further parametric restrictions this (log n)–1 phenomenon is also illustrated by a weak convergence result.
where 
is the mean of the sample values overshooting 