Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Exact Performance of CoD Estimators in Discrete Prediction | Hindawi Publishing Corporation EURASIP Journal on Advances in Signal Processing Volume 2010 Article ID 487893 13 pages doi 2010 487893 Research Article Exact Performance of CoD Estimators in Discrete Prediction Ting Chen and Ulisses Braga-Neto Department of Electrical Engineering Texas A M University College Station TX 77843 USA Correspondence should be addressed to Ulisses Braga-Neto ulisses@ Received 1 April 2010 Accepted 9 July 2010 Academic Editor Haris Vikalo Copyright 2010 T. Chen and U. Braga-Neto. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. The coefficient of determination CoD has significant applications in genomics for example in the inference of gene regulatory networks. We study several CoD estimators based upon the resubstitution leave-one-out cross-validation and bootstrap error estimators. We present an exact formulation of performance metrics for the resubstitution and leave-one-out CoD estimators assuming the discrete histogram rule. Numerical experiments are carried out using a parametric Zipf model where we compute exact performance metrics of resubstitution and leave-one-out CoD estimators using the previously derived equations for varying actual CoD sample size and bin size. These results are compared to approximate performance metrics of 10-repeated 2-fold cross-validation and bootstrap CoD estimators computed via Monte Carlo sampling. The numerical results lead to a perhaps surprising conclusion under the Zipf model under consideration and for moderate and large values of the actual CoD the resubstitution CoD estimator is the least biased and least variable among all CoD estimators especially at small number of predictors. We also observed that the leave-one-out and cross-validation CoD estimators tend to perform the worst whereas the performance of the
