Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Convex bootstrap error estimation is a popular tool for classifier error estimation in gene expression studies. A basic question is how to determine the ight for the convex combination beten the basic bootstrap estimator and the resubstitution estimator such that the resulting estimator is unbiased at finite sample sizes. The ll-known 0.632 bootstrap error estimator uses asymptotic arguments to propose a fixed 0.632 ight, whereas the more recent 0.632+ bootstrap error estimator attempts to set the ight adaptively. ,  study the finite sample problem in the case of linear discriminant analysis under Gaussian populations.  derive exact expressions for the ight that guarantee unbiasedness of the convex bootstrap error estimator in the univariate and multivariate cases, without making asymptotic simplifications. Using exact computation in the univariate case and an accurate approximation in the multivariate case,  obtain the required ight and show that it can deviate significantly from the constant 0.632 ight, depending on the sample size and Bayes error for the problem. The methodology is illustrated by application on data from a ll-known cancer classification study.
['Thang Vu', 'Chao Sima', 'Ulisses Braga-Neto', 'Edward R. Dougherty']
I am writing a research paper on a idea Unbiased bootstrap error estimation for linear discriminant analysis
[{"from": "human", "value": "I am writing a research paper on a idea Unbiased bootstrap error estimation for linear discriminant analysis"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Convex bootstrap error estimation is a popular tool for classifier error estimation in gene expression studies. A basic question is how to determine the ight for the convex combination beten the basic bootstrap estimator and the resubstitution estimator such that the resulting estimator is unbiased at finite sample sizes. The ll-known 0.632 bootstrap error estimator uses asymptotic arguments to propose a fixed 0.632 ight, whereas the more recent 0.632+ bootstrap error estimator attempts to set the ight adaptively. ,  study the finite sample problem in the case of linear discriminant analysis under Gaussian populations.  derive exact expressions for the ight that guarantee unbiasedness of the convex bootstrap error estimator in the univariate and multivariate cases, without making asymptotic simplifications. Using exact computation in the univariate case and an accurate approximation in the multivariate case,  obtain the required ight and show that it can deviate significantly from the constant 0.632 ight, depending on the sample size and Bayes error for the problem. The methodology is illustrated by application on data from a ll-known cancer classification study."}]