Browse > Article
http://dx.doi.org/10.7465/jkdi.2012.23.1.079

Bandwidth selection for discontinuity point estimation in density  

Huh, Jib (Department of Information & Statistics, Duksung Women's University)
Publication Information
Journal of the Korean Data and Information Science Society / v.23, no.1, 2012 , pp. 79-87 More about this Journal
Abstract
In the case that the probability density function has a discontinuity point, Huh (2002) estimated the location and jump size of the discontinuity point based on the difference between the right and left kernel density estimators using the one-sided kernel function. In this paper, we consider the cross-validation, made by the right and left maximum likelihood cross-validations, for the bandwidth selection in order to estimate the location and jump size of the discontinuity point. This method is motivated by the one-sided cross-validation of Hart and Yi (1998). The finite sample performance is illustrated by simulated example.
Keywords
Maximum likelihood cross-validation; one-sided kernel function; smoothing parameter;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Huh, J. and Carri`ere, K. C. (2002). Estimation of regression functions with a discontinuity in a derivative with local polynomial fits. Statistics and Probability Letters, 56, 329-343.   DOI   ScienceOn
2 Huh, J. and Park, B. U. (2004). Detection of change point with local polynomial fits for random design case. Australian and New Zealand Journal of Statistics, 46, 425-441.   DOI   ScienceOn
3 Jose, C. T. and Ismail, B. (1999). Change points in nonparametric regression functions. Communication in Statistics-Theory and Methods, 28, 1883-1902.   DOI
4 Kim, J. T., Choi, H. and Huh, J. (2003). Detection of change-points by local linear regression fit. The Korean Communications in Statistics, 10, 31-38.   DOI   ScienceOn
5 Lee, C. S., Chang, C. and Park, Y. W. (2010). Estimates for parameter changes in a uniform model with a generalized uniform outlier. Journal of the Korean Data & Information Science Society, 21, 581-687.
6 Loader, C. R. (1996). Change point estimation using nonparametric regression. Annals of Statistics, 24, 1667-1678.   DOI
7 Muller, H G. (1992). Change-points in nonparametric regression analysis. Annals of Statistics, 20, 737-761.   DOI   ScienceOn
8 Muller, H. G. and Wang, J. L. (1990). Nonparametric analysis of changes in hazard rates for censored survival data: An alternative to change-point models. Biometrika, 77, 305-314.   DOI
9 Otsu, T and Xu, K.-L. (2010). Estimation and inference of discontinuity in density. preprint.
10 Schuster, E. F. (1985). Incorporating support constraints into nonparametric estimators of densities. Communications in Statistics-Theory and Methods, 14, 1123-1136.   DOI   ScienceOn
11 Cline, D. B. H. and Hart, J. D. (1991). Kernel estimation of densities with discontinuities or discontinuous derivatives. Statistics, 22, 69-84.   DOI
12 Gijbels, I. and Goderniaux, A. C. (2004a). Bandwidth selection for change point estimation in nonparametric regression. Technometrics, 46, 76-86.   DOI   ScienceOn
13 Gijbels, I. and Goderniaux, A. C. (2004a). Bootstrap test for change points in nonparametric regression. Journal of Nonparametric Statistics, 16, 591-611.   DOI   ScienceOn
14 Gijbels, I. and Goderniaux, A. C. (2005). Data-driven discontinuity detection in derivatives of a regression function. Communications in Statistics-Theory and Methods, 33, 851-871.   DOI   ScienceOn
15 Hart, J. D. and Yi, S. (1998). One-sided cross-validation. Journal of the American Statistical Association, 93, 620-631.   DOI   ScienceOn
16 Huh, J. (2002). Nonparametric discontinuity point estimation in density or density derivatives. Journal of the Korean Statistical Society, 31, 261-276.
17 Huh, J. (2007). Nonparametric detection algorithm of discontinuity points in the variance function. Journal of the Korean Data & Information Science Society, 18, 669-678.
18 Huh, J. (2010a). Estimation of the number of discontinuity points based on likelihood. Journal of the Korean Data & Information Science Society, 21, 51-59.
19 Huh, J. (2010b). Detection of a change point based on local-likelihood. Journal of Multivariate Analysis, 101, 1681-1700.   DOI   ScienceOn
20 Huh, J. (2011). Likelihood based estimation of the log-variance function with a change point. Submitted to Journal of Statistical Planning and Inference.