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Related Concept Videos

Bootstrapping01:24

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The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is...
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Updated: Mar 7, 2026

Assisted Selection of Biomarkers by Linear Discriminant Analysis Effect Size LEfSe in Microbiome Data
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Unbiased bootstrap error estimation for linear discriminant analysis.

Thang Vu1, Chao Sima2, Ulisses M Braga-Neto1,2

  • 1Department of Electrical and Computer Engineering, Texas A&M University, 3128 TAMU, College Station, 77843 TX USA.

EURASIP Journal on Bioinformatics & Systems Biology
|February 15, 2017
PubMed
Summary
This summary is machine-generated.

This study finds optimal weights for convex bootstrap error estimation in gene expression studies, ensuring unbiasedness at finite sample sizes. The derived weights differ from the standard 0.632 bootstrap, improving classifier accuracy.

Keywords:
BiasBootstrapError estimationGene expression classificationLinear discriminant analysis

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Area of Science:

  • Bioinformatics
  • Statistical Learning
  • Computational Biology

Background:

  • Convex bootstrap error estimation is widely used for classifier accuracy in gene expression studies.
  • Determining optimal weights for convex bootstrap is crucial for unbiased finite sample error estimation.
  • Existing methods like 0.632 and 0.632+ bootstrap estimators rely on asymptotic arguments or adaptive weights.

Purpose of the Study:

  • To derive exact expressions for weights that ensure unbiased convex bootstrap error estimation at finite sample sizes.
  • To investigate the finite sample problem for linear discriminant analysis under Gaussian populations.
  • To compare derived weights with the fixed 0.632 weight and adaptive 0.632+ bootstrap.

Main Methods:

  • Derivation of exact unbiased weight expressions for univariate and multivariate cases.
  • Application of exact computation for univariate and accurate approximation for multivariate scenarios.
  • Analysis of weight dependency on sample size and Bayes error.

Main Results:

  • Exact expressions for unbiased convex bootstrap weights were derived without asymptotic simplifications.
  • The optimal weight can significantly deviate from the fixed 0.632 value.
  • Weight deviation depends on sample size and Bayes error, impacting classifier performance.

Conclusions:

  • The study provides a method for obtaining unbiased convex bootstrap error estimators at finite sample sizes.
  • The derived weights offer a more accurate alternative to fixed or adaptively set weights in specific scenarios.
  • The methodology is validated through application to a cancer classification dataset.