A semi-bayesian method for nonparametric density estimation

Computational Statistics and Data Analysis

Volumn 30, Issue 1, 1999, Pages 19-30

  De Bruin, R ^b   Salome D ^a   Schaafsma, W ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

ESTIMATION; POLYNOMIALS; PROBABILITY DENSITY FUNCTION;

BERNSTEIN POLYNOMIALS;

REGRESSION ANALYSIS;

BAYESIAN ANALYSIS; DENSITY; ESTIMATION METHOD;

EID: 0033611819     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(98)00089-9     Document Type: Article

References (20)

1. Aggarwal O.P. Some minimax invariant procedures of estimating a cumulative distribution function. Ann. Math. Statist. 26:1955;450-462.
2. Azzalini A. A note on the estimation of a distribution function and quantiles by a kernel method. Biometrika. 68:1981;326-328.
3. Barron A.R., Sheu C.H. Approximating densities by exponential families. Ann. Statist. 19(3):1991;1347-1369.
4. Chow Y.S., Geman S., Wu I.-D. Consistent cross-validated density estimation. Ann. Statist. 11:1983;25-38.
5. David, H.A., 1981. Order Statistics, 2nd ed. Wiley, New York.
6. Dehling, H.G., Kalma, J.N., Moes, C, Schaafsma, W., 1991. The islamic mean: a peculiar L-statistic. Studia Scientiarum Mathematicarum Hungarica, vol. 26. Akadémiai Kiadó, Budapest, pp. 297-308.
7. Devroye, L., 1987. A course in density estimation, Progress in Probability and Statistics. Birkhäuser, Boston.
8. Devroye L., Gyorfi L. No empirical probability measure can converge in the total variation sense for all distributions. Ann. Statist. 18(3):1990;1496-1499.
9. Ferguson, T., 1967. Mathematical Statistics: a Decision Theoretic Approach. Academic Press, New York.
10. Ferguson T. A Bayesian analysis of some nonparametric problems. Ann. Statist. 1(2):1973;209-230.
11. Hall P. On Kullback-Leibler loss and density estimation. Ann. Statist. 15(4):1987;1491-1519.
12. IMSL, 1987. Stat / Library, Houston.
13. Jones M.C. Estimating densities, quantiles, quantile densities and density quantiles. Ann. Inst. Statist. Math. 44:1992;721-727.
14. Marron J.S. An asymptotically efficient solution to the bandwidth problem of kernel density estimation. Ann. Statist. 13(3):1985;1011-1023.
15. Munoz-Perez, J., Fernandez-Palacini, A., 1987. Estimating the quantile function by Bernstein polynomials. Comput. Statist. Data Anal. 5, 391-397.
16. Rosenblatt M. Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27:1956;832-837.
17. Rosenblatt, M., 1991. Stochastic curve estimation. NSF-CBMS Regional Conf. Ser. in Probability and Statistics, vol. 3. IMS, Hayward, California.
18. Sheather S.J., Marron J.S. Kernel quantile estimators. J. Amer. Statist. Assoc. 85:1990;410-416.
19. Silverman, B.W., 1986. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
20. Vitale, R.A., 1975. A Bernstein polynomial approach to density function estimation. Stoch Proc. and Related Topics, Proc. of Summer Res. Inst. on Statistical Inference for Stochastic Processes, Bloomington, pp. 87-100.