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Activity Number:
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369
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Type:
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Contributed
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Date/Time:
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Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Nonparametric Statistics
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Abstract #319014
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View Presentation
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Title:
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Accelerated Nonparametric Maximum Likelihood Density Deconvolution Using Bernstein Polynomial
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Author(s):
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Zhong Guan*
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Companies:
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Indiana University South Bend
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Keywords:
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Measurement Error Models ;
Density Estimation ;
Beta Mixture Model ;
EM Algorithm ;
Deconvolution
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Abstract:
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A new method for deconvoluting density in measurement error models using the Bernstein type polynomial model which is actually a finite mixture of specific beta distributions is proposed and studied. The change-point detection method is used to choose an optimal model degree. Based a contaminated sample of size $n$, the rate of convergence of the mean integrated squared error is proved to be $k^{-1}\mathcal{O}(n^{-1+1/k}\log^3 n)$ if the underlying unknown density $f$ has continuous $2k$-th derivative with $k>1$. In addition if the error distribution is generalized normal with not too high noise level the mean chi-squared distance between the proposed density estimate and $f$ is shown to be possibly $\mathcal{O}(n^{-1}\log^2 n)$.
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Authors who are presenting talks have a * after their name.
