Issue No. 02 - February (1982 vol. 4)
P. A. Devijver , Philips Research Laboratory, Brussels, Belgium.
J. Kittler , Technology Division, SERC Rutherford and Appleton Laboratories, Chilton, England.
The problem of estimating the error probability of a given classification system is considered. Statistical properties of the empirical error count (C) and the average conditional error (R) estimators are studied. It is shown that in the large sample case the R estimator is unbiased and its variance is less than that of the C estimator. In contrast to conventional methods of Bayes error estimation the unbiasedness of the R estimator for a given classifier can be obtained only at the price of an additional set of classified samples. On small test sets the R estimator may be subject to a pessimistic bias caused by the averaging phenomenon characterizing the functioning of conditional error estimators.
P. A. Devijver, J. Kittler, "Statistical Properties of Error Estimators in Performance Assessment of Recognition Systems", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 4, no. , pp. 215-220, February 1982, doi:10.1109/TPAMI.1982.4767229