ON BLOCK THRESHOLDING IN WAVELET REGRESSION: ADAPTIVITY, BLOCK SIZE, AND THRESHOLD LEVEL

By Tommaso Cai. 2002

125 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c83ecd281a5dc52909d88be74cfc06946a38874d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Incorporating Information on Neighboring Coefficients Into Wavelet Estimation (2001, background): “for for and ( 6 ) Theorem 2 Define to be the NeighCoeff estimator of the array . Then, for ,a s ,”
Adaptive Confidence Balls (2006, background): “LOW It follows from [5] that this local block thresholding rule has strong adaptivity under both global and local risk measures.”
Block thresholding for density estimation: local and global adaptivity (2005, methodology): “Motivated by the analysis of block thresholding rules for nonparametric regression in Cai [6], the block size is chosen to be log n.”
Some theoretical results on the Grouped Variables Lasso (2008, background): “This construction enjoys powerful theoretical properties in various statistical approaches (oracle inequalities, (near) minimax optimality, ...) . See, for instance, [ 6 ] and [8].”
Bayesian model choice and information criteria in sparse generalized linear models (2011, unknown): “…exp {∑ i `i(φ̂J) }∣∣∣HJ(φ̂J)∣∣∣−1/2 (λ2λ−11 )|J|/2 ∫ ‖ξ‖22>2 log(np) exp { −1 2 ‖ξ‖22 } dξ = F1 exp {∑ i `i(φ̂J) }∣∣∣HJ(φ̂J)∣∣∣−1/2 (λ2λ−11 )|J|/2 · (2π)|J|/2P{χ2|J| > 2 log(np)} ≤ F1 exp {∑ i `i(φ̂J) }∣∣∣HJ(φ̂J)∣∣∣−1/2 (λ2λ−11 )|J|/2 · (2π)|J|/2 · e− log(np)/2 , by the chi-square tail bounds…”
General maximum likelihood empirical Bayes estimation of normal means (2009, background): “Johnstone and Silverman [24] reported results of an extensive simulation study of 18 threshold estimators, including eight options of their EBThresh, the SURE and adaptive SURE [14], the FDR [1] at three levels, three block threshold methods [7, 8] and the soft and”