Bridge estimators and the adaptive lasso under heteroscedasticity

H. Akaike, “Information Theory and an Extension of the Maximum Likelihood Principle”, In 2nd Internat. Symp. on Inform. Theory, Tsahkadsor, Armenian SSR (1973), pp. 267–281.

L. Breiman, “Better Subset Regression Using the Nonnegative Garrote”, Technometrics 37, 373–384 (1995).

E. Candes and T. Tao, “The Dantzig Selector: Statistical Estimation when p is Much Larger than n”, Ann. Statist. 35, 2313–2351 (2007).

G. Claeskens and N. L. Hjort, “The Focused Information Criterion (with Discussion)”, J. Amer. Statist. Assoc. 98, 900–916 (2003).

P. Craven and G. Wahba, “Smoothing Noisy Data with Spline Function: Estimating the Correct Degree of Smoothing by the Method of Generalized Cross Validation”, NumerischeMathematik 31, 337–403 (1979).

H. Dette and A. Munk, “Testing Heteroscedasticity in Nonparametric Regression”, J. Roy. Statist. Soc. B 60, 693–708 (1998).

B. Efron, T. Hastie, and R. Tibshirani, “Least Angle Regression (with Discussion)”, Ann. Statist. 32, 407–451 (2004).

J. Fan and R. Li, “Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties”, J. Amer. Statist. Assoc. 96, 1348–1360 (2001).

J. Fan and H. Peng, “Nonconcave Penalized Likelihood with a Diverging Number of Parameters”, Ann. Statist. 32, 928–961 (2004).

I. E. Frank and J. H. Friedman, “A Statistical View of Some Chemometrics Regression Tools (with Discussion)”, Technometrics 35, 109–148 (1993).

C. J. Geyer, On the Asymptotics of Convex Stochastic Optimization (1996), Manuscript.

J. Huang, J. L. Horowitz, and S. Ma, “Asymptotic properties of bridge estimators in sparse high dimensional regression models”, Ann. Statist. 36, 587–613 (2008).

J. Huang, S. Ma, and C. Zhang, “Adaptive Lasso for Sparse High-Dimensional Regression Models”, Statistica Sinica 18, 1603–1618 (2008).

G. M. James, P. Radchenko, and J. Lv, “DASSO: Connections between the Dantzig Selector and Lasso”, J. Roy. Statist. Soc. B 71, 127–142 (2009).

Y. Kim, H. Choi, and H.-S. Oh, “Smoothly Clipped Absolute Deviation on High Dimensions”, J. Amer. Statist. Assoc. 103, 1665–1673 (2008).

K. Knight and W. Fu, (2000). “Asymptotics for Lasso-type Estimators”, Ann. Statist, 28, 1356–1378 (2000).

H. Leeb and B. M. Pötscher, “Model Selection and Inference: Facts and Fiction”, Econometric Theory 21, 21–59 (2005).

H. Leeb and B. M. Pötscher, “Sparse Estimators and the Oracle Property, or the Return of Hodges’ Estimator”, J. Econometrics 142, 201–211 (2008).

J. Nocedal and S. J. Wright, Numerical Optimization, in Springer Series in Operations Research and Financial Engineering (Springer, New York, 2006), 2nd ed.

B. M. Pötscher and H. Leeb, “On the Distribution of Penalized Maximum Likelihood Estimators: The LASSO, SCAD, and Thresholding”, J.Multivar.Anal. 100, 2065–2082 (2009).

R Development Core Team, R: A language and environment for statistical computing (R Foundation for Statistical Computing, Vienna, Austria, 2009) ISBN 3-900051-07-0, URL http://www.R-project.org

D. Ruppert, S. J. Sheather, and M. P. Wand, “An Effective Bandwidth Selector for Local Least Squares Regression”, J. Amer. Statist. Assoc. 90, 1257–1270 (1995).

G. Schwarz, “Estimating the Dimension of a Model”, Ann. Statist. 6, 461–464 (1978).

J. Shao, “An Asymptotic Theory for Linear Model Selection”, Statistica Sinica 7, 221–264 (1997).

R. Tibshirani, “Regression Shrinkage and Selection via the Lasso”, J. Roy. Statist. Soc. B 58, 267–288 (1996).

M. P. Wand and M. C. Jones, Kernel Smoothing (Chapman and Hall, London, 1995).

H. Wang, R. Li, and C.-L. Tsai, “Tuning Parameter Selectors for the Smoothly Clipped Absolute Deviation Method”, Biometrika 94, 553–568 (2007).

P. Zhao and B. Yu, “On Model Selection Consistency of Lasso”, J. Machine Learning Research 7, 2541–2563 (2006).

H. Zou, “The Adaptive Lasso and Its Oracle Properties”, J. Amer. Statist. Assoc. 101, 1418–1429 (2006).

H. Zou and T. Hastie, “Regularization and Variable Selection via the Elastic Net”, J. Roy. Statist. Soc. B 67, 301–320 (2005).