Using a stopping rule to determine the size of the training sample in a classification problem. (English) Zbl 0910.62077
Summary: The problem of determining the size of the training sample needed to achieve sufficiently small misclassification probability is considered. The appropriate sample size is approximated using a stopping rule. The proposed procedure is asymptotically optimal.
MSC:
| 62L10 | Sequential statistical analysis |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
| 62L15 | Optimal stopping in statistics |
References:
| [1] | Chernoff, H., Sequential Analysis and Optimal Design (1972), Society for Industrial and Applied Mathematics: Society for Industrial and Applied Mathematics Philadelphia · Zbl 0265.62024 |
| [2] | Devroye, L.; Wagner, T. J., Nonparametric discrimination and density estimation, (Tech. Report (1976), Information Systems Research Laboratory, University of Texas at Austin) · Zbl 0511.62069 |
| [3] | Devroye, L.; Györfi, L., Nonparametric Density Estimation: the \(L_1\) View (1985), Wiley: Wiley New York · Zbl 0546.62015 |
| [4] | Greblicki, W., Asymptotically optimal pattern recognition procedures with density estimates, IEEE Trans. Inform. Theory IT-24, 250-251 (1978) · Zbl 0371.68027 |
| [5] | Greblicki, W., Pattern recognition procedures with nonparametric density estimates, IEEE Trans. Systems Man. Cybernet., 8, 809-812 (1978) · Zbl 0392.68075 |
| [6] | Greblicki, W.; Pawlak, M., Almost sure convergence of classification procedures using Hermite series density estimates, Pattern Recogn. Lett., 2, 13-17 (1983) · Zbl 0523.62060 |
| [7] | Györfi, L., Estimation of probability density and optimal decision function in RKHS, (Gani, J.; Srakadi, K.; Vincze, T., Progress in Statistics (1974), North-Holland: North-Holland Amsterdam), 281-301 · Zbl 0302.62050 |
| [8] | Kundu, S.; Martinsek, A. T., Bounding the \(L_1\) distance in nonparametric density estimation, Ann. Inst. Statist. Math. (1994), submitted |
| [9] | Krzyzak, A., Classification procedures using multivariate variable kernel density estimate, Pattern Recogn. Lett., 1, 293dash29 (1983) · Zbl 0524.62061 |
| [10] | Parzen, E., On estimation of a probability density function and mode, Ann. Math. Statist., 33, 1065-1076 (1962) · Zbl 0116.11302 |
| [11] | Rosenblatt, M., Remarks on some nonparametric estimates of a density function, Ann. Math. Statist., 27, 832-837 (1956) · Zbl 0073.14602 |
| [12] | Siegmund, D., On moments of the maximum of normed sums, Ann. Math. Statist., 40, 527-531 (1969) · Zbl 0177.21704 |
| [13] | Van Ryzin, J., Bayes risk consistency of classification procedures using density estimation, Sankhyā, Ser. A, 28, 261-270 (1966) · Zbl 0192.25703 |
| [14] | Wolverton, C. T.; Wagner, T. J., Asymptotically optimal discriminant functions for pattern recognition, IEEE Trans. Inform. Theory, 15, 258-265 (1969) · Zbl 0172.43404 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
