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Activity Number:
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400
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Type:
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Contributed
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Date/Time:
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Wednesday, August 6, 2008 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #301052 |
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Title:
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Asymptotic Properties of Hill's Estimator for Shot Noise Sequence
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Author(s):
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Chenhua Zhang*+
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Companies:
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Colorado State University
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Address:
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Department of Statistics, Fort Collins, CO, 80523,
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Keywords:
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shot noise ; heavy tail ; regular variation ; tail index ; Hill's estimator
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Abstract:
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We study a shot noise sequence of the form $X_j=\sum_{i \leq j} h(\tau_j-\tau_i)A_i$, where the distribution of $A_i$ has regularly varying tail with index $-\alpha$. Under a mild integration condition on $h$ the distribution of $X_i$ also has regularly varying tail with index $-\alpha$ and the Hill's estimator is a weakly consistent estimator of $1/\alpha$. If the tail distribution of $X_i$ is normalized and second order regularly varying the Hill's estimator is asymptotically normal for a large class of functions $h$.
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