WITHDRAWN: Estimating the Prediction Error in Microarray Classification: Modifications on the .632+ Bootstrap When n < p

• Author(s): Wenyu Jiang and Bingshu E. Chen
• Keywords: .632+ Bootstrap ; Cross-validation ; Gene expression ; Microarray ; Prediction Error ; bias-variance trade off

Abstract

In microarray study, gene expression information is often used to classify patients into pre-determined disease categories. In this paper, we focus on estimating the prediction error for the high dimensional data with relatively small sample size n and very large number of variables p with (n< < p). We explore the idea of pooling the error estimates for training sets of various sizes to achieve a balance in the bias-variance trade-off. We vary the training set sizes through different fold cross-validation to define an adjusted cross-validation method (ACV), and through different bootstrap sample sizes to define an adjusted leave-one-out bootstrap (ALB) method. A learning curve is developed to pool on the estimates for the training sets of different sizes to give an overall prediction error estimate. We adapt the distance argument(Efron, 1983) to form a solid basis for the learning curv