Bias, Variance and Prediction Error for Classification Rules

We study the notions of bias and variance for classiication rules. Following Efron (1978) we develop a decomposition of prediction error into its natural components. Then we derive bootstrap estimates of these components and illustrate how they can be used to describe the error behaviour of a classiier in practice. In the process we also obtain a bootstrap estimate of the error of a \bagged" classiier.