On Kolmogorov asymptotics of estimators of the misclassification error rate in linear discriminant analysis
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Spatio-Temporal Statistics and Data Analysis Group
Permanent link to this recordhttp://hdl.handle.net/10754/562770
MetadataShow full item record
AbstractWe provide a fundamental theorem that can be used in conjunction with Kolmogorov asymptotic conditions to derive the first moments of well-known estimators of the actual error rate in linear discriminant analysis of a multivariate Gaussian model under the assumption of a common known covariance matrix. The estimators studied in this paper are plug-in and smoothed resubstitution error estimators, both of which have not been studied before under Kolmogorov asymptotic conditions. As a result of this work, we present an optimal smoothing parameter that makes the smoothed resubstitution an unbiased estimator of the true error. For the sake of completeness, we further show how to utilize the presented fundamental theorem to achieve several previously reported results, namely the first moment of the resubstitution estimator and the actual error rate. We provide numerical examples to show the accuracy of the succeeding finite sample approximations in situations where the number of dimensions is comparable or even larger than the sample size.
PubMed Central IDPMC3840470
- Moments and Root-Mean-Square Error of the Bayesian MMSE Estimator of Classification Error in the Gaussian Model.
- Authors: Zollanvari A, Dougherty ER
- Issue date: 2014 Jun 1
- Unbiased bootstrap error estimation for linear discriminant analysis.
- Authors: Vu T, Sima C, Braga-Neto UM, Dougherty ER
- Issue date: 2014 Dec
- Estimation of error rates in discriminant analysis with selection of variables.
- Authors: Snapinn SM, Knoke JD
- Issue date: 1989 Mar
- Smooth estimation of the reliability function.
- Authors: Kulasekera KB, Williams CL, Coffin M, Manatunga A
- Issue date: 2001 Dec
- Sieve Estimation of Constant and Time-Varying Coefficients in Nonlinear Ordinary Differential Equation Models by Considering Both Numerical Error and Measurement Error.
- Authors: Xue H, Miao H, Wu H
- Issue date: 2010 Jan 1