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A note on deconvolution density estimation

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  • Patil, Prakash

Abstract

We consider the problem of estimating the unknown common density f of unobservable independent random variables Xi from observable independent random variables Yij, where conditional density of Yij given Xi, is of the form gYijXi(y) = g(y - Xi; = 1,...,n and J = 1,...,m. It is shown that if E[Y2ijXi] is finite and m grows sufficiently fast then mean square error of the kernel estimator of f converges to zero with usual rate of nonparametric density estimators based on a random sample from a density that is to be estimated. This is in contrast to the case of fixed m.

Suggested Citation

  • Patil, Prakash, 1996. "A note on deconvolution density estimation," Statistics & Probability Letters, Elsevier, vol. 29(1), pages 79-84, August.
    • Handle: RePEc:eee:stapro:v:29:y:1996:i:1:p:79-84
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    References listed on IDEAS

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    1. Mack, Y. P. & Matloff, Norman S., 1990. "Estimating a mixing distribution in a multiple observation setting," Statistics & Probability Letters, Elsevier, vol. 10(5), pages 369-376, October.
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    Cited by:

    1. Julie McIntyre & Leonard Stefanski, 2011. "Density Estimation with Replicate Heteroscedastic Measurements," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 81-99, February.

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