NIGERIAN JOURNAL OF SCIENCE AND ENVIRONMENT
Journal of the Faculties of Science and Agriculture, Delta State University, Abraka, Nigeria
ISSN: 1119-9008
DOI: 10.5987/UJ-NJSE
Email: njse@universityjournals.org
HIGHER-ORDER GAUSSIAN KERNEL IN BOOTSTRAP BOOSTING ALGORITHM
DOI: 10.5987/UJ-NJSE.17.112.1 | Article Number: BF07B922 | Vol.12 (1) - May 2013
Authors: Ishiekwene C. C. and Afere B.A. E.
Keywords: boosting, kernel density estimates, bias reduction, higher-order Gaussian kernel, meshsize, noises
The bootstrap boosting algorithm has been shown to be a bias reduction scheme. This paper proposes the use of higher-order Gaussian kernel in a bootstrap boosting algorithm in kernel density estimation. The algorithm uses the higher-order Gaussian kernel instead of the regular fixed kernels. An empirical study for this scheme is conducted and the findings are compared with existing fixed kernel methods.
Bartlett, M.S. (1963). Statistical estimation of density functions. Sankhyā series A,
25: 245 – 254.
Birke, M. (2009). Shape constrained KDE. Journal of Statistical Planning & Inference 139 (8): 2851 – 2862.
Duffy, N. and Hemlbold, D. (2000). Potential bosters? Advances in Neural Information Processing Systems 12: 258 –264.
Freund, Y. (1995). Boosting a weak learning algorithm by majority. Info Comp 121:
256 - 285.
Hazelton, M.L and Turlach, B.A (2007). Reweighted KDE. Computational Statistics
& Data Analysis 5 (6): 3057 – 3069.
Ishiekwene, C. C. and Osemwenkhae, J. E. (2006). A comparison of fourth order window width selectors in Kernel Density Estimation (A Univarate case), ABA-
CUS, 33: 14 - 20.
Ishiekwene, C.C and Afere, B.A.E. (2001). Higher Order Window Width Selectors for Empirical Data. Journal of Nigerian Statistical Association 14: 69 – 82.
Ishiekwene, C.C., Ogbonmwan, S.M and Osemwenkhae, J.E. (2008). A Meshsize
Boosting Algorithm in Kernel Density Estimation. Journal of Science & Technology,
Ghana. 28 (2): 69 – 74.
Ishiekwene, C.C. and Nwelih, E. (2011). Adaptive Kernel in Meshsize Boosting
Algorithm in KDE. African Research Review 5(1): 438-446.
Mannor, S., Meir, R. and Mendelson, S. (2001). On consistency of boosting algorithms; submitted to Adv. In Neural info. Proc. Sys.
Mazio, D. M. and Taylor, C.C. (2004). Boosting Kernel Density estimates: A bias reduction technique? Biometrika 91: 226 - 233.
Parzen, E. (1962). On the estimation of a probability function and the nodes. Annals of Mathematical Statistics. 33: 1065 – 1076.
Ratsch, G., Mika, S., Scholkopf, B. and Muller, K. K. (2000). Construction boosting algorithms from SVM's: An application to-one-class classification. GMD tech report no. 1.
Schapire, R. (1990). The strength of weak learnability. Machine learning 5: 313 –321.
Schapire, R. and Singer, Y. (1999). Improved boosting algorithm using confi-
dence rated prediction. Machine learning 37: 297 – 336.
Schucany, W.R. and Sommers, J.P. (1977). Improvement of kernel-type density estimators. Journal of American Statistical Association 72: 420 -423.
Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London
Wand, M.P. and Jones, M.C. (1995). Kernel Smoothing. Chapman and Hall/CRC,
London.