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Limit distribution theory for maximum li...
Balabdaoui, Fadoua...

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Limit distribution theory for maximum likelihood estimation of a log-concave density by Balabdaoui, Fadoua ( Author )
Lemonjar Open Access
N.A
24-08-2007
We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form f0=expφ0 where φ0 is a concave function on R. The pointwise limiting distributions depend on the second and third derivatives at 0 of Hk, the "lower invelope" of an integrated Brownian motion process minus a drift term depending on the number of vanishing derivatives of φ0=logf0 at the point of interest. We also establish the limiting distribution of the resulting estimator of the mode M(f0) and establish a new local asymptotic minimax lower bound which shows the optimality of our mode estimator in terms of both rate of convergence and dependence of constants on population values.
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Article
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36.88 KB
English
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MYR 0.00
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https://arxiv.org/abs/0708.3400
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