Skip to search formSkip to main contentSkip to account menu
Least angle regression
TLDR
A publicly available algorithm that requires only the same order of magnitude of computational effort as ordinary least squares applied to the full set of covariates is described.
View PDF on arXiv
Ideal spatial adaptation by wavelet shrinkage
SUMMARY With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline,…
View via Publisher
Adapting to Unknown Smoothness via Wavelet Shrinkage
Abstract We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet…
View via Publisher
On the distribution of the largest eigenvalue in principal components analysis
Let x (1) denote the square of the largest singular value of an n x p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x (1) is the largest principal component…
View via Publisher
Minimax estimation via wavelet shrinkage
TLDR
A nonlinear method which works in the wavelet domain by simple nonlinear shrinkage of the empirical wavelet coefficients is developed, andVariants of this method based on simple threshold nonlinear estimators are nearly minimax.
View via Publisher
Needles and straw in haystacks: Empirical Bayes estimates of possibly sparse sequences
An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at…
View PDF on arXiv
On Consistency and Sparsity for Principal Components Analysis in High Dimensions
  • I. Johnstone, A. Lu
  • Computer Science, Mathematics
    Journal of the American Statistical Association
  • 1 June 2009
TLDR
A simple algorithm for selecting a subset of coordinates with largest sample variances is provided, and it is shown that if PCA is done on the selected subset, then consistency is recovered, even if p(n) ≫ n.
View on Taylor & Francis
Sure independence screening for ultrahigh dimensional feature space Discussion
Wavelet Shrinkage: Asymptopia?
TLDR
A method for curve estimation based on n noisy data: translate the empirical wavelet coefficients towards the origin by an amount √(2 log n) /√n and draw loose parallels with near optimality in robustness and also with the broad near eigenfunction properties of wavelets themselves.
View via Publisher
Density estimation by wavelet thresholding
Density estimation is a commonly used test case for nonparametric estimation methods. We explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients.…
View via Publisher
...
...
By clicking accept or continuing to use the site, you agree to the terms outlined in our Privacy Policy, Terms of Service, and Dataset License