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http://dx.doi.org/10.7465/jkdi.2014.25.1.87

Comparison study on kernel type estimators of discontinuous log-variance  

Huh, Jib (Department of Statistics, Duksung Women's University)
Publication Information
Journal of the Korean Data and Information Science Society / v.25, no.1, 2014 , pp. 87-95 More about this Journal
Abstract
In the regression model, Kang and Huh (2006) studied the estimation of the discontinuous variance function using the Nadaraya-Watson estimator with the squared residuals. The local linear estimator of the log-variance function, which may have the whole real number, was proposed by Huh (2013) based on the kernel weighted local-likelihood of the ${\chi}^2$-distribution. Chen et al. (2009) estimated the continuous variance function using the local linear fit with the log-squared residuals. In this paper, the estimator of the discontinuous log-variance function itself or its derivative using Chen et al. (2009)'s estimator. Numerical works investigate the performances of the estimators with simulated examples.
Keywords
Discontinuity point; kernel function; local linear fit; log-squared residual; log-variance;
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Times Cited By KSCI : 5  (Citation Analysis)
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1 Chen, L., Chen, M. and Peng, M. (2009). Conditional variance estimation in heteroscedastic regression models. Journal of Statistical Planning and Inference, 139, 236-245.   DOI   ScienceOn
2 Fan, J. and Gijbels, I. (1996). Local polynomial modelling and its application, Chapman and Hall, London.
3 Gasser, T., Sroka, L. and Jennen-Steinmetz, C. (1986). Residual variance and residual pattern in nonlinear regression. Biometrika, 73, 625-634.   DOI   ScienceOn
4 Gregoire, G. and Hamrouni, Z. (2002). Change point estimation by local linear smoothing. Journal of Multivariate Analysis, 83, 56-83.   DOI   ScienceOn
5 Hall, P. and Carroll, R. J. (1989). Variance function estimation in regression: The effect of estimating the mean. Journal of the Royal Statistical Society B, 51, 3-14.
6 Hall, P., Kay, J. W. and Titterington, D. M. (1990). Asymptotically optimal difference-based estimation of variance in nonparametric regression. Biometrika, 77, 521-528.   DOI   ScienceOn
7 Huh, J. (2005). Nonparametric detection of a discontinuity point in the variance function with the second moment function. Journal of the Korean Data & Information Science Society, 16, 591-601.   과학기술학회마을
8 Huh, J. (2009). Testing a discontinuity point in the log-variance function based on likelihood. Journal of the Korean Data & Information Science Society, 20, 1-9.   과학기술학회마을
9 Huh, J. (2010). Detection of a change point based on local-likelihood. Journal of Multivariate Analysis, 101, 1681-1700.   DOI   ScienceOn
10 Huh, J. (2012a). Bandwidth selection for discontinuity point estimation in density. Journal of the Korean Data & Information Science Society, 23, 79-87.   과학기술학회마을   DOI   ScienceOn
11 Huh, J. (2012b). Bandwidth selections based on cross-validation for estimation of a discontinuity point in density. Journal of the Korean Data & Information Science Society, 23, 765-775.   과학기술학회마을   DOI   ScienceOn
12 Kang, K. H. and Huh, J. (2006). Nonparametric estimation of the variance function with a change point. Journal of the Korean Data & Information Science Society, 35, 1-24.   과학기술학회마을
13 Huh, J. (2013). Estimation of a change point in the variance function based on the ${\chi}^{2}$-distribution. Preprint.
14 Huh, J. and Carriere, 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
15 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
16 Loader, C. R. (1996). Change point estimation using nonparametric regression. Annals of Statistics, 24, 1667-1678.   DOI   ScienceOn
17 Muller, H G. (1992). Change-points in nonparametric regression analysis. Annals of Statistics, 20, 737-761.   DOI   ScienceOn
18 Muller, H. G. and Stadtmuller, U. (1987). Estimation of heteroscedasticity in regression analysis. Annals of Statistics, 15, 610-625.   DOI   ScienceOn
19 Rice, J. (1984). Bandwidth choice for nonparametric regression. Annals of Statistics, 12, 1215-1230.   DOI   ScienceOn
20 Ruppert, D., Wand, M. P., Holst, U. and Hossjer, O. (1997). Local polynomial variance-function estimation. Technomtrics, 39, 262-273.   DOI   ScienceOn
21 Yu, K. and Jones, M. C. (2004). Likelihood-based local linear estimation of the conditional variance function. Journal of the American Statistical Association, 99, 139-144.   DOI   ScienceOn