Any Discrimination Rule Can Have an Arbitrarily Bad Probability of Error for Finite Sample Size

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn PAMI-4, Issue 2, 1982, Pages 154-157

  Devroye, Luc ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

Bayes risk; consistency; discrimination rule; distribution free inequalities; probability of error

Indexed keywords

PATTERN RECOGNITION SYSTEMS;

EID: 0020098693     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.1982.4767222     Document Type: Article

References (9)

1. T. Cover, “Rates of convergence for nearest neighbor procedures,” in Proc. Hawaii Int. Conf. on Syst. Sci., Honolulu, HI, 1968, pp. 413-415.
2. L. Devroye, “A universal k-nearest neighbor procedure in discrimination,” in Proc. 1978 IEEE Comput. Soc. Conf. on Pattern Recog. and Image Processing, Chicago, IL, 1978, pp. 142-147.
3. L. Devroye and T. J. Wagner, “Distiibution-free consistency results in nonparametric discrimination and regression function estimation,” Ann. Statist., vol. 8, pp. 231-239, 1980.
4. L. Devroye and G. L. Wise, “Consistency of a recursive nearest neighbor regression function estimate,” J. Multivariate Anal., vol. 10, pp. 539-550, 1980.
5. L. Gordon and R. A. Olshen, “Asymptotically efficient solutions to the classification problem,” Ann. Statist., vol. 6, pp. 515-533, 1978.
6. L. Gyorfi, “Recent results on nonparametric regression function estimate and multiple sclassification,” in Problems of Control and Information Theory, 1981.
7. R. A. Olshen, “Comment on a paper by C. J. Stone,” Ann. Statist, vol. 5, pp. 632-633, 1977.
8. C. Spiegelman and J. Sacks, “Consistent window estimation in nonparametric regression,” Ann. Statist., vol. 8, pp. 240-246, 1980.
9. C. J. Stone, “Consistent nonparametric regression,” Ann. Statist., vol. 8, pp. 595-645, 1977.