The Nonparametric Deconvolution Problem with Gaussian Error Distribution

  • Published : 1996.06.01

Abstract

The nonparametric deconvolution problems are studied to recover an unknown density when the data are contaminated with Gaussian error. We propose the estimator which is a linear combination of kernel type estimates of derivertives of the observed density function. We show that this estimator is consistent and also consider the properties of estimator at small sample by simulation.

Keywords

References

  1. Aerosal Science and Technology v.1 A new algorithm for inversion of aerosal size distribution data Crump,J.G.;Seinfeld,J.H.
  2. The Canadian Journal of Statistics v.20 Deconvolution with supersmooth distributions Fan,J.
  3. The Canadian Journal of Statistics v.17 A consistent nonparametric dentisty estimator for the deconvolution problem Liu, M.C.;Taylor, R.L.
  4. The Canadian Journal of Statistics v.20 Gaussian deconvolution via differentiation Masry,E.;Rice,J.A.
  5. The Journal of American Statistical Association v.77 Deconvolution of microfluorometic histograms with B splines Mendelsohn,J.;Rice,J.A.
  6. The Canadian Journal of Statistics v.9 On the inversion of the Gauss Transformation Rooney, P.G.
  7. Statistics v.21 Deconvoluting Kernel Density Estimators Stefanski, L.;Carrol R.J.
  8. IEEE Transactions on Information Theory v.23 The estimation of a probability dentisty function from measurements corrupted by Poission noise Wise, G.L.;Traganttis,A.P.;Thomas,J.B.