Density Estimation for the Case of Supersmooth Measurement Error

Journal of the American Statistical Association

Volumn 92, Issue 438, 1997, Pages 526-535

  Efromovich, Sam ^a  

^a UNIVERSITY OF NEW MEXICO   (United States)

Author keywords

Acute pancreatitis; Adaptation; Characteristic function; Circular data; Deconvolution; Monte Carlo; Pointwise and global losses; Sharp optimality; Small samples

Indexed keywords

EID: 0031533944     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1997.10474005     Document Type: Article

References (27)

1. Ash, R. (1972), Real Analysis and Probability, New York: Academic Press.
2. Carroll, R. J., and Hall, P. (1988), "Optimal Rates of Convergence for Deconvolving a Density," Journal of the American Statistical Association, 83, 1184-1186.
3. Clavien, P.-A., Robert, J., Meyer, P., Borst, E, Hauser, H., Herrmann, E, Dunand, v., and Rohner, A. (1989), "Acute Pancreatitis and.Normoamylasemia," The Annals of Surgery, 210, 614-620.
4. Devroy, L., and Gyorfi, L. (1985), The Nonparametric Density Estimation. L 1 View, New York: Wiley.
5. Donoho, D. L., and Johnstone, I. M. (1995), "Adapting to Unknown Smoothness via Wavelet Shrinkage," Journal ofthe American Statistical Association, 90, 1200-1222.
6. Donoho, D. L., and Low, M. G. (1992), "Renormalization Exponents and Optimal Pointwise Rates of Convergence," The Annals of Statistics, 20, 944-970.
7. Fan, J. (1991), "On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems," The Annals of Statistics, 19, 1257-1272.
8. Fan, J (1993), "Adaptively Local One-Dimensional Subproblems With Application to a Deconvolution Problem," The Annals of Statistics, 21, 600-610.
9. Fisher, N. 1. (1993), Statistical Analysis ofCircular Data, New York: Cambridge University Press.
10. Efromovich, S. (1985), "Nonparametric Estimation of a Density With Unknown Smoothness," Theory of Probability and Its Applications, 30, 557-568.
11. Efromovich, S. (1989), "Sequential Nonparametric Estimation of a Density," Theory of Probability and Its Applications, 34, 228-239.
12. Efromovich, S. (1994), "Nonparametric Curve Estimation From Indirect Data," Computing Science and Statistics, 26, 196--200.
13. Efromovich, S. (1996), "Adaptive Orthogonal Series Density Estimation for Small Samples," Computational Statistics and Data Analysis, 22, 559-617.
14. Hengartner, N. W. (1997), "Adaptive Demixing in Poisson Mixture Models," The Annals of Statistics, in press.
15. Korostelev, A., and Tsybakov, A. (1993), Minimax Theory of Image Re-535 construction, New York: Springer-Verlag.
16. Lehmann, E. L. (1983), Theory of Point Estimation, Pacific Grove, CA: Wadsworth and Brooks.
17. Mardia, K. V. (1972), Statistics of Directional Data, New York: Academic Press.
18. Nikolskii, S. M. (1946), "Approximation of Functions in the Mean by Trigonometric Polynomials," Bulletin De L'Academie Des Sciences des L' URSS, 10, 207-255.
19. Silverman, B. (1986), Density Estimation, New York: Chapman and Hall.
20. Serfling, R. J. (1980), Approximation Theorems ofMathematical Statistics, New York: Wiley.
21. Stefanski, L., and Carroll, R. J. (1990), "Deconvoluting Kernel Density Estimators," Statistics, 2, 169-184.
22. Tandberg, D., Deely, J. J., and O'Malley, A. J. (1995), "Generalized Likelihood Ratios for Quantitative Diagnostic Test Scores," Technical Report, University of New Mexico School of Medicine, Dept. of Emergency Medicine.
23. Tarter, M. E., and Lock, M. D. (1994), Model-Free Curve Estimation, New York: Chapman and Hall.
24. Timan, A. F. (1963), Theory ofApproximation ofFunctions of a Real Variable, New York: Pergamon Press.
25. Watson, G. S. (1983), Statistics on Spheres, New York: Wiley.
26. Zhang, C.-H. (1990), "Fourier Methods for Estimating Mixing Densities and Distributions," The Annals of Statistics, 18, 806--831.
27. Zhang, C.-H (1995), "On Estimating Mixing Densities in Exponential Family Models for Discrete Variables;' The Annals of Statistics, 23, 929-945.