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Activity Number:
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277
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Type:
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Topic Contributed
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Date/Time:
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Tuesday, August 8, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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| Abstract - #307510 |
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Title:
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Penalized Likelihood Ratio Method for the Spiking Problem in Nonincreasing Density Estimation
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Author(s):
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Jayanta Pal*+
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Companies:
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University of Michigan
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Address:
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1929 Plymouth Road, Ann Arbor, MI, 48105,
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Keywords:
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likelihood ; monotone ; density ; penalization ; Brownian
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Abstract:
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The maximum likelihood estimation of a decreasing density, f, on the positive real line creates inconsistent estimate of f(0+). This is known as the spiking problem. Woodroofe and Sun (1993) considered a penalized likelihood and achieved consistent estimates. In this article, we characterize the restricted MLE under the null hypothesis H_0 : f(0+) =c. The target is to find out the (asymptotic) distribution of the (penalized) likelihood ratio under the null distribution. It will be useful to construct asymptotic level-alpha confidence interval for the endpoint. The limit distribution of the likelihood ratio with a chosen penalization is shown to be universal, and the quantiles can be numerically tabulated. This problem has applications in renewal theory and astronomical examples.
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- The address information is for the authors that have a + after their name.
- Authors who are presenting talks have a * after their name.
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