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Liu, Ming Chung; Taylor, Robert L.

A consistent nonparametric density estimator for the deconvolution problem. (English) Zbl 0694.62017

Can. J. Stat. 17, No. 4, 427-438 (1989).
Summary: The problem of nonparametric estimation of a probability density function when the sample observations are contaminated with random noise is studied. A particular estimator \(\hat f_ n(x)\) is proposed which uses kernel-density and deconvolution techniques. The estimator \(\hat f_ n(x)\) is shown to be uniformly consistent, and its appearance and properties are affected by constants \(M_ n\) and \(h_ n\) which the user may choose. The optimal choices of \(M_ n\) and \(h_ n\) depend on the sample size n, the noise distribution, and the true distribution which is being estimated. Particular selections for \(M_ n\) and \(h_ n\) which minimize upper-bound functions of the mean squared error for \(\hat f_ n(x)\) are recommended.

Cited in 55 Documents

MSC:

62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics
65C05 Monte Carlo methods

Keywords:

uniform consistency; kernel-density estimators; random noise; deconvolution techniques; mean squared error
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\textit{M. C. Liu} and \textit{R. L. Taylor}, Can. J. Stat. 17, No. 4, 427--438 (1989; Zbl 0694.62017)
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References:

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