585
Views
4
CrossRef citations to date
0
Altmetric
Theory and Methods

Parametrically Assisted Nonparametric Estimation of a Density in the Deconvolution Problem

Pages 717-729 | Received 01 Oct 2012, Published online: 13 Jun 2014

REFERENCES

  • Burman, P., and Chaudhuri, P. (2011), “On a Hybrid Approach to Parametric and Nonparametric Regression,” in Nonparametric Statistical Methods and Related Topics : A Festschrift in Honor of Professor P K Bhattacharya on the Occasion of his 80th Birthday, eds. J. Jiang, G. G. Roussas, and F. J. Samaniego, Singapore: World Scientific.
  • Cao, R., Cuevas, A., Fraiman, R. (1995), Minimum Distance Density-Based Estimation, Computational Statistics & Data Analysis, 20, 611–631.
  • Carroll, R.J., Delaigle, A., Hall, P. (2011), Testing and Estimating Shape-Constrained Nonparametric Density and Regression in the Presence of Measurement Error, Journal of the American Statistical Association, 106, 191–202.
  • Carroll, R.J., Hall, P. (1988), Optimal Rates of Convergence for Deconvoluting a Density, Journal of the American Statistical Association, 83, 1184–1186.
  • Carroll, R. J., Ruppert, D., Stefanski, L.A., andCrainiceanu, C. (2006), “Measurement Error in Nonlinear Models(2nd ed.), New York: Chapman & Hall.
  • Delaigle, A., Fan, J., Carroll, R.J. (2009), A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem, Journal of the American Statistical Association, 104, 348–359.
  • Delaigle, A., Gijbels, I. (2002), Estimation of Integrated Squared Density Derivatives From a Contaminated Sample, Journal of the Royal Statistical Society, Series B, 64, 869–886.
  • Delaigle, A., Gijbels, I. (2004), Practical Bandwidth Selection in Deconvolution Kernel Density Estimation, Computational Statistics & Data Analysis, 45, 249–267.
  • Delaigle, A., Hall, P. (2008), Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems, Journal of the American Statistical Association, 103, 280–287.
  • Delaigle, A., Meister, A. (2008), Density Estimation With Heteroscedastic Error, Bernoulli, 14, 562–579.
  • Diggle, P.J., Hall, P. (1993), Fourier Approach to Nonparametric Deconvolution of a Density Estimate, Journal of the Royal Statistical Society, Series B, 55, 523–531.
  • Eguchi, S., Copas, J. (1998), A Class of Local Likelihood Methods and Near-Parametric Asymptotics, Journal of the Royal Statistical Society, Series B, 60, 709–724.
  • Fan, J. (1991a), On the Optimal Rates of Convergence for Nonparametric Deconvolution Problem, The Annals of Statistics, 19, 1257–1272.
  • Fan, J. (1991b), Global Behaviour of Deconvolution Kernel Estimates, Statistica Sinica, 1, 541–551.
  • Fan, J. (1993), “Adaptively Local One-Dimensional Subproblems With Application to a Deconvolution Problem, The Annals of Statistics, 21, 600–610.
  • Fan, J., Wu, Y., Feng, Y. (2009), Local Quasi-Likelihood With a Parametric Guide, The Annals of Statistics, 37, 4153–4183.
  • Fan, Y., Ullah, A. (1999), Asymptotic Normality of a Combined Regression Estimator, Journal of Multivariate Analysis, 71, 191–240.
  • Hall, P., Simar, L. (2002), Estimating a Changepoint, Boundary, or Frontier in the Presence of Observation Error, Journal of the American Statistical Association, 97, 523–534.
  • Hazelton, M.L., Turlach, B.A. (2010), Semiparametric Density Deconvolution, Scandinavian Journal of Statistics, 37, 91–108.
  • Hjort, N.L., Glad, I.K. (1995), Nonparametric Density Estimation With a Parametric Start, The Annals of Statistics, 23, 882–904.
  • Hjort, N.L., Jones, M.C. (1996), Locally Parametric Nonparametric Density Estimation, The Annals of Statistics, 24, 1619–1647.
  • Jones, M.C., Linton, O., Nielsen, J.P. (1995), A Simple Effective Bias Reduction Method for Density and Regression Estimation, Biometrika, 82, 327–338.
  • Liu, M.C., Taylor, R.L. (1989), A Consistent Nonparametric Density Estimator for the Deconvolution Problem, Canadian Journal of Statistics, 17, 427–438.
  • Masry, E. (1993), Asymptotic Normality for Deconvolution Estimators of Multivariate Densities of Stationary Processes, Journal of Multivariate Analysis, 44, 47–68.
  • Naito, K. (2004), Semiparametric Density Estimation by Local L2-Fitting, The Annals of Statistics, 32, 1162–1191.
  • Olkin, I., Spiegelman, C.H. (1987), A Semiparametric Approach to Density Estimation, Journal of the American Statistical Association, 82, 858–865.
  • Staudenmayer, J., Ruppert, D. (2004), Local Polynomial Regression and Simulation extrapolation, Journal of the Royal Statistical Society, Series B, 66, 17–30.
  • Staudenmayer, J., Ruppert, D., Buonaccorsi, J. (2008), Density Estimation in the Presence of Heteroscedastic Measurement Error, Journal of the American Statistical Association, 103, 726–736.
  • Stefanski, L., Carroll, R.J. (1990), Deconvoluting Kernel Density Estimators, Statistics, 21, 169–184.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.