Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We consider kernel density estimation in the multivariate case, focusing on the use of some elements of parametric estimation. We present a two-step method, based on a modification of the EM algorithm and the generalized kernel density estimator, and compare this method with a couple of well known multivariate kernel density estimation methods.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
41--55
Opis fizyczny
Bibliogr. 17 poz., rys., wykr., tab.
Twórcy
autor
- AGH University of Science and Technology, Faculty of Applied Mathematics, Mickiewicza 30, 30-059 Cracow, Poland, jarnicka@wms.mat.agh.edu.pl
Bibliografia
- [1] I.S. Abramson, Arbitrariness of the pilot estimator in adaptive kernel methods, J. Multivariate Anal. 12 (1982), 562-567.
- [2] L. Breiman, W. Meisel, E. Purcell, Variable kernel estimates of multivariate densities, Technometrics, 1977, 135-144.
- [3] A.P. Dempster, N.M. Laird, D.B. Rubin, Maximum-likelihood from incomplete data via EM algorithm, J. Roy. Statist. Soc. Ser. B 39 (1977), 1-38.
- [4] L. Devroye, L. Gjorfi, Nonparametric density estimation: the L1 view, Willey, New York, 1985.
- [5] P. Hall, J.S. Marron, Choice of kernel order in density estimation, Ann. Statis. 16 (1987), 161-173.
- (6] N.L. Hjort, I.K. Glad, Nonparametric density estimation with a parametric start, Ann. Statist. 23 (1995), 882-904.
- [7] J. Jarnicka, On some two-step density estimation method, Univ. Iagel. Acta Math. 43 (2005), 67-91.
- [8] J. .Jarnicka, Density estimation - the two-step method, Thesis, the Jagiellonian University, Cracow, 2006 [in Polish].
- [9] J.S. Marron, M.P. Wand, Exact mean integrated squared error, Ann. Statist. 20 (1992), 712-736.
- [10] B.U. Park, J.S. Marron, Comparison of data-driven bandwidth selectors, J. Amer. Statist. Assoc. 85 (1990), 66-72.
- [11] E. Parzen, On estimation of a probability density function and mode, Ann. Math. Statist. 33 (1962), 1065-1076.
- [12] M. Rosenblatt, Remarks on some nonparametrics estimates of a density function, Ann. Math. Statist. 27 (1956), 827-837.
- [13] S.J. Sheater, M.C. Jones, A reliable data-based bandwidth selection method for kernel density estimation, J. Roy. Statist. Soc B 53 (1991), 683-690.
- [14] B.W. Silverman, Density estimation for statistics and data analysis, Chapman and Hall, London, New York, 1986.
- [15] J.S. Simonoff, Smoothing methods in statistics, Springer-Verlag, 1996.
- [16] G.R. Terrel, D.W. Scott, Variable kernel density estimation, Ann. Statist. 20 (1992), 1236-1265.
- [17] Z.R. Yang, M. Zwolinski, Mutual information theory for adaptive mixture models, Trans. Pattern Anal. Machine Intellegence 23, 40 (2001), 396-403.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGHB-0002-0004