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Consistent estimates of the mode of the probability density function in nonparametric deconvolution problems

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  • Rachdi, Mustapha
  • Sabre, Rachid

Abstract

We propose two estimates of the mode of the probability density function for nonparametric deconvolution problems. In fact, we observe Y=X+[xi], where [xi] is a measurement error with a known distribution f[xi], and we are interesting by estimating the mode of fX the unknown probability density function of X, where Y1,...,Yn are n i.i.d given observations of Y. We study the asymptotic properties of these mode estimates and the asymptotic normality of the two mode estimates is also given.

Suggested Citation

  • Rachdi, Mustapha & Sabre, Rachid, 2000. "Consistent estimates of the mode of the probability density function in nonparametric deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 105-114, April.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:2:p:105-114
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    References listed on IDEAS

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    1. Masry, Elias, 1993. "Strong consistency and rates for deconvolution of multivariate densities of stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 47(1), pages 53-74, August.
    2. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    3. Stefanski, Leonard A., 1990. "Rates of convergence of some estimators in a class of deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 229-235, March.
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    1. A. Delaigle & I. Gijbels, 2004. "Bootstrap bandwidth selection in kernel density estimation from a contaminated sample," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(1), pages 19-47, March.
    2. Barbara Wieczorek, 2010. "On optimal estimation of the mode in nonparametric deconvolution problems," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(1), pages 65-80.
    3. Meister, Alexander, 2009. "On testing for local monotonicity in deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 312-319, February.

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