Bootstrap Methods for Error Rate Estimation in Discriminant Analysis

Unbiased bootstrap error estimation for linear discriminant analysis

Convex bootstrap error estimation is a popular tool for classifier error estimation in gene expression studies. A basic question is how to determine the weight for the convex combination between the basic bootstrap estimator and the resubstitution estimator such that the resulting estimator is unbiased at finite sample sizes. The well-known 0.632 bootstrap error estimator uses asymptotic argume...

A comparison of bootstrap methods and an adjusted bootstrap approach for estimating prediction error in microarray classification Short title: Bootstrap Prediction Error Estimation

SUMMARY This paper first provides a critical review on some existing methods for estimating prediction error in classifying microarray data where the number of genes greatly exceeds the number of specimen. Special attention is given to the bootstrap-related methods. When the sample size n is small, we find that all the reviewed methods suffer from either substantial bias or variability. We intr...

Multiple group discriminant analysis: Robustness and error rate

Multiple Group Linear Discriminant Analysis: Robustness and Error Rate

Abstract: Discriminant analysis for multiple groups is often done using Fisher’s rule, and can be used to classify observations into different populations. In this paper, we measure the performance of classical and robust Fisher discriminant analysis using the Error Rate as a performance criterion. We were able to derive an expression for the optimal error rate in the situation of three groups....

A Bootstrap Method for Error Estimation in Randomized Matrix Multiplication

In recent years, randomized methods for numerical linear algebra have received growing interest as a general approach to large-scale problems. Typically, the essential ingredient of these methods is some form of randomized dimension reduction, which accelerates computations, but also creates random approximation error. In this way, the dimension reduction step encodes a tradeoff between cost an...