Bandwidth selection in nonparametric estimator of density derivative by smoothed cross-validation method1

Automation and Remote Control

Volumn 71, Issue 2, 2010, Pages 209-224

  Dobrovidov, A V ^a   Rud'Ko, I M ^a  

^a TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATION; CONTROL ENGINEERING; CONTROL;

BANDWIDTH SELECTIONS; CROSS-VALIDATION METHODS; DENSITY DERIVATIVES; INDEPENDENT SAMPLES; KERNEL ESTIMATION; NONPARAMETRIC ESTIMATORS; PROBABILITY DENSITIES; RATE OF CONVERGENCE;

BANDWIDTH;

EID: 77950646791     PISSN: 00051179     EISSN: None     Source Type: Journal    
DOI: 10.1134/S0005117910020050     Document Type: Article

References (15)

1. Opsomer, J., Wang, Y., and Yang, Y., Nonparametric Regression with Correlated Errors, Stat. ScL, 2001, vol. 16, no. 2, pp. 134-153.
2. Vasil'ev, V.A., Dobrovidov, A.V., and Koshkin, CM., Neparametricheskoe otsenivanie funktsionalov ot raspredelenii statsionarnykh posledovatel'nostei (Nonparametric Estimation of the Functionals of the Distributions of Stationary Sequences), Moscow: Nauka, 2004.
3. Nemirovskii, A.S. and Tsypkin, Ya.Z., Optimal Adaptive Control Algorithms, Autom. Remote Control. 1984, no. 12, pp. 1589-1600.
4. Härdle, W., Hart, J., Marron, J.S., and Tsybakov, A.B., Bandwidth Choice for Average Derivative Estimation, J. Am. Statist. Assoc., 1992, vol. 87, no. 417, pp. 218-226.
5. Bowman, A., An Alternative Method of Cross-validation for the Smoothing of Density Estimates, Biometrica, 1984, vol. 71, pp. 353-360.
6. Rudemo, M., Empirical Choice of Histograms and Kernel Density Estimators, Scand. J. Statist., 1982, vol. 9, pp. 65-78.
7. Hall, P., Marron, J., and Park, B., Smoothed Cross-validation, Prob. Theory Related Fields, 1992, vol. 90, pp. 1-20.
8. Park, B. and Marron, J., Comparison of Data-driven Bandwidth Selectors, J. Am. Statist. Assoc., 1990, vol. 85, pp. 66-72.
9. Duong, T. and Hazelton, M.L., Cross-validation Bandwidth Matrices for Multivariate Kernel Density Estimation, Scand. J. Statist., 2005, vol. 32, pp. 485-506.
10. Devroye, L. and Györfi, L., Nonparametric Density Estimation. The L\ View., New York: Wiley, 1985. Translated under the title Neparametricheskoe otsenivanie plotnosti. L\-podkhod, Moscow: Mir, 1988.
11. Marron, J.S. and Wand, M.P., Exact Mean Integrated Squared Errors, Ann. Statist., 1992, vol. 20, pp. 712-736.
12. Härdl, W., Marron, J.S., and Wand, M.P., Bandwidth Choice for Density Derivatives, J. Royal Statist. Soc., 1990, vol. 52, no. 1, pp. 223-232.
13. Jones, M., Marron, J., and Park, B., A Simple Root n Bandwidth Selector, Ann. Statist., 1991, vol. 19, pp. 1919-1932.
14. Duong, T. and Hazelton, M.L., Convergence Rates for Unconstrained Bandwidth Matrix Selectors in Multivariate Kernel Density Estimation, J. Multivariate Anal., 2005, vol. 93(2), pp. 417-433.
15. Cramer, H., Mathematical Methods of Statistics, Princeton: Princeton Univ. Press, 1937. Translated under the title Matematicheskie metody statistiki, Moscow: Mir, 1975.