Adaptive Posterior Mode Estimation of a Sparse Sequence for Model Selection
For the problem of estimating a sparse sequence of coefficients of a parametric or non-parametric generalized linear model, posterior mode estimation with a Subbotin("λ","ν") prior achieves thresholding and therefore model selection when "ν" is an element of <b>[0,1]</b> for a class of likelihood functions. The proposed estimator also offers a continuum between the (forward/backward) best subset estimator ("ν" = <b>0</b>), its approximate convexification called lasso ("ν" = <b>1</b>) and ridge regression ("ν" = <b>2</b>). Rather than fixing "ν", selecting the two hyperparameters "λ" and "ν" adds flexibility for a better fit, provided both are well selected from the data. Considering first the canonical Gaussian model, we generalize the Stein unbiased risk estimate, SURE("λ","ν"), to the situation where the thresholding function is not almost differentiable (i.e. "ν" ⩽ <b>1</b>). We then propose a more general selection of "λ" and "ν" by deriving an information criterion that can be employed for instance for the lasso or wavelet smoothing. We investigate some asymptotic properties in parametric and non-parametric settings. Simulations and applications to real data show excellent performance. Copyright (c) 2009 Board of the Foundation of the Scandinavian Journal of Statistics.
Year of publication: |
2009
|
---|---|
Authors: | SARDY, SYLVAIN |
Published in: |
Scandinavian Journal of Statistics. - Danish Society for Theoretical Statistics, ISSN 0303-6898. - Vol. 36.2009, 4, p. 577-601
|
Publisher: |
Danish Society for Theoretical Statistics Finnish Statistical Society Norwegian Statistical Association Swedish Statistical Association |
Saved in:
freely available
Saved in favorites
Similar items by person
-
Stochastic optimization of sailing trajectories in an upwind regatta
Dalang, Robert C, (2015)
-
Density Estimation by Total Variation Penalized Likelihood Driven by the Sparsity ℓ
SARDY, SYLVAIN, (2010)
-
Moments structure of ℓ <Subscript>1</Subscript>-stochastic volatility models
Neto, David, (2012)
- More ...