A combined adaptive-mixtures/plug-in estimator of multivariate probability densities

Computational Statistics and Data Analysis

Volumn 26, Issue 2, 1997, Pages 199-218

  Cwik J ^a   Koronacki, J ^a  

^a INSTITUTE OF COMPUTER SCIENCE   (Poland)

Author keywords

Gaussian clustering algorithm; Nonparametric density estimation; Plug in kernel estimation; Recursive EM algorithm

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; ESTIMATION; MATRIX ALGEBRA;

GAUSSIAN CLUSTERING ALGORITHM; MULTIVARIATE PROBABILITY DENSITIES; NONPARAMETRIC DENSITY ESTIMATION; PLUG IN KERNEL ESTIMATION;

PROBABILITY DENSITY FUNCTION;

EID: 0031553354     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(97)00032-7     Document Type: Article

References (30)

1. Cao, R., Cuevas, A., Gonzales-Manteiga, W., 1994. A comparative study of several smoothing methods in density estimation. Comp. Statist. Data Anal. 17, 153-176.
2. Ciesielski, Z., 1990. Asymptotic nonparametric spline density estimation in several variables. In: International Studies of Numerical Mathematics, vol. 94. Birkhauser, pp. 25-53.
3. Ciesielski, Z., 1991. Asymptotic nonparametric spline density estimation. Probab. Math. Statist. 12, 1-24.
4. Ćwik, J., Koronacki, J., 1996a. Probability density estimation using a Gaussian clustering algorithm. Neural Comput. Appl. 4, 149-160.
5. Ćwik, J., Koronacki, J., 1996b. Multivariate density estimation: a comparative study, Submitted to Neural Comput. Appl.
6. Friedman, J.H., 1987. Exploratory projection pursuit. J. Amer. Statist. Assoc. 82, 249-266.
7. Härdle, W., 1991. Smoothing Techniques. Springer, Berlin.
8. Hartigan, J.A., Wong, M.A., 1979. A k-means algorithm, Applied Statistics 28, 100-108 (also in: P. Griffiths and I.D. Hill (Eds.), Applied Statistics Algorithms, Ellis Horwood, 1981).
9. Hartigan, J.A., Wong, M.A., 1979. A k-means algorithm, Applied Statistics 28, 100-108 (also in: P. Griffiths and I.D. Hill (Eds.), Applied Statistics Algorithms, Ellis Horwood, 1981).
10. Johnson, N.L., Kotz, S., 1972. Distributions in Statistics: Continuous Multivariate Distributions. Wiley, New York.
11. Kowalczyk, T., Tyrcha, J., 1989. Multivariate gamma distributions - properties and shape estimation. Statistics 20, 465-474.
12. MacQueen, J.B., 1967. Some methods for classification and analysis of multivariate observations. In: Proc. 5th Berkeley Symp. Math. Statist. Probab., 1967.
13. Marchette, D.J., Priebe, C.E., Rogers, G.W., Solka, J.L., 1996. Filtered kernel density estimation. Comput. Statist., to appear.
14. Park, B.U., Turlach, B.A., 1992. Practical performance of several data driven bandwidth selectors. Comput. Statist. 7, 251-270 and discussion.
15. Priebe, C.E., 1994. Adaptive mixtures. J. Amer. Statist. Assoc. 89, 796-806.
16. Ruppert, D., Cline, D.B.H., 1994. Bias reduction in kernel density estimation by smoothed empirical transformations. Ann. Statist. 22, 185-210.
17. Sain, S., Baggerly, K., Scott, D.W., 1994. Cross-validation of multivariate densities. J. Amer. Statist. Assoc. 89, 807-817.
18. Scott, D.W., 1992. Multivariate Density Estimation: Theory, practice, and Visualization. Wiley, New York.
19. Sheather, S.J., 1992. The performance of six popular bandwidth selection methods on some real data sets. Comp. Statist. 7, 225-250 and discussion.
20. Sheather, S.J., Jones, M.C., 1991. A reliable data-based bandwidth selection method for kernel density estimation. J. Roy. Statist. Soc. Ser. B 53, 683-690.
21. Silverman, B.W., 1986. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
22. Solka, J.L., Poston, W.L., Wegman, E.J., 1995. A visualization technique for studying the iterative estimation of mixture densities. J. Comput. Graph. Statist. 4, 180-197.
23. Solka, J.L., Wegman, E.J., Priebe, C.E., Poston, W.L., Rogers, G.W., 1996. Mixture structure analysis using the Akaike information criterion and the bootstrap. Statist. Comput., to appear.
24. Titterington, D.M., Smith, A.F.M., Makov, U.E., 1985. Statistical Analysis of Finite Mixture Distributions. Wiley, New York.
25. Tråvén, H.G.C., 1991. A neural network approach to statistical pattern classification by semi-parametric estimation of probability density functions. IEEE Trans. Neural Networks 2, 366-377.
26. Wand, M.P., 1992. Error analysis for general multivariate kernel estimators. J. Nonpar. Statist. 2, 1-15.
27. Wand, M.P., Jones, M.C., 1991. Comparison of smoothing parametrizations in bivariate kernel density estimation, Technical Report, Department of Statistics, Rice University.
28. Wand, M.P., Jones, M.C., 1993. Comparison of smoothing parametrizations in bivariate kernel density estimation. J. Amer. Statist. Assoc. 88, 520-528.
29. Wand, M.P., Jones, M.C., 1994. Multivariate plug-in bandwidth selection. Comput. Statist. 9, 97-116.
30. Wand, M.P., Marron, J.S., Ruppert, D., 1991. Transformations in density estimation. J. Amer. Statist. Assoc. 86, 343-353 and discussion.