Subsampling estimates of the Lasso distribution.

More documents

Recommendations

Info

Bibliography Andersen, P. and R. Gill (1982). Cox’s regression model for counting processes: a large sample study. The annals of statistics 10 (4), 1100–1120. Berg, A., T. McMurry, and D. Politis (2010). Subsampling p-values. Statistics & Probability Letters 80 (17-18), 1358–1364. Bunea, F., A. Tsybakov, and M. Wegkamp (2007). Sparsity oracle inequalities for the lasso. Electronic Journal of Statistics 1, 169–194. Chatterjee, A. and S. Lahiri (2010). Asymptotic properties of the residual bootstrap for lasso estimators. Proceedings of the American Mathematical Society 138 (12), 4497–4509. Chatterjee, A. and S. Lahiri (2011). Bootstrapping lasso estimators. Journal of the American Statistical Association 106 (494), 1–18. Chow, Y. and H. Teicher (1978). Probability Theory : independence, interchangeability, martingales. Springer-Verlag. Dudley, R. (1985). An extended wichura theorem, definitions of donsker class, and weighted empirical distributions. Probability in Banach Spaces V 1153, 141–178. Efron, B., T. Hastie, I. Johnstone, and R. Tibshirani (2004). Least angle regression. The Annals of statistics 32 (2), 407–499. Hjort, N. and D. Pollard (1993). Asymptotics for minimisers of convex processes. Technical report, University of Oslo and Yale University. Huang, J., S. Ma, and C. Zhang (2008). Adaptive lasso for sparse high-dimensional regression models. Statistica Sinica 18 (4), 1603–1618. Kallenberg, O. (2002). Foundations of modern probability. Springer Verlag. Knight, K. and W. Fu (2000). Asymptotics for lasso-type estimators. Annals of Statistics 28 (5), 1356–1378. Lehmann, E. and J. Romano (2005). Testing statistical hypotheses. Springer Verlag. Massart, P. (1990). The tight constant in the dvoretzky-kiefer-wolfowitz inequality. The Annals of Probability 18 (3), 1269–1283. Meinshausen, N. and P. Bühlmann (2006). High-dimensional graphs and variable selection with the lasso. The Annals of Statistics 34 (3), 1436–1462. Politis, D., J. Romano, and M. Wolf (1999). Subsampling. Springer Verlag. 73
74 BIBLIOGRAPHY Pollard, D. (1984). Convergence of stochastic processes. Springer. Pollard, D. (1990). Empirical processes: theory and applications. In NSF-CBMS regional conference series in probability and statistics. JSTOR. Pollard, D. (1991). Asymptotics for least absolute deviation regression estimators. Econometric Theory 7 (2), 186–199. Rockafellar, R. (1970). Convex Analysis, volume 28 of Princeton Mathematics Series. Princeton University Press. Romano, J. and A. Shaikh (2010). On the uniform asymptotic validity of subsampling and the bootstrap. Technical report, Mimeo, University of Chicago. Serfling, Robert, J. (1980). Approximation theorems of mathematical statistics. Wiley. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B (Methodological) 58 (1), 267–288. Van De Geer, S. and P. Bühlmann (2009). On the conditions used to prove oracle results for the lasso. Electronic Journal of Statistics 3, 1360–1392. Van der Vaart, A. (2000). Asymptotic statistics. Cambridge Univ Press. Van der Vaart, A. and J. Wellner (1996). Springer Verlag. Weak convergence and empirical processes. Zhao, P. and B. Yu (2006). On model selection consistency of lasso. The Journal of Machine Learning Research 7, 2541–2563. Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101 (476), 1418–1429.
Page 1:
✄✄ ✄ ✄ ✄ ✄✄ ✄ ✄
Page 4 and 5:
iv Abstract
Page 6 and 7:
vi CONTENTS Contents Notation viii
Page 8 and 9:
viii Notation List of Tables 6.1 Mo
Page 10 and 11:
Chapter 1 Introduction In this thes
Page 12 and 13:
Chapter 2 Minimizers of convex proc
Page 14 and 15:
2.1 Convergence in probability 5 fo
Page 16 and 17:
2.2 Convergence in distribution 7 a
Page 18 and 19:
2.2 Convergence in distribution 9 L
Page 20 and 21:
2.2 Convergence in distribution 11
Page 22 and 23:
2.2 Convergence in distribution 13
Page 24 and 25:
2.3 A continous mapping theorem for
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Chapter 3 Application to the Lasso
Page 32 and 33: 3.2 Limit in distribution 23 almost
Page 34 and 35: 3.2 Limit in distribution 25 We als
Page 36 and 37: 3.2 Limit in distribution 27 3.2.2
Page 38 and 39: 3.2 Limit in distribution 29 Figure
Page 40 and 41: Chapter 4 The adaptive Lasso in a h
Page 42 and 43: 33 B.3 (Adaptive irrepresentable co
Page 44 and 45: 35 exists a constant K d depending
Page 46 and 47: 4.1 Variable selection consistency
Page 48 and 49: 4.2 Partial asymptotic normality 39
Page 50 and 51: 4.3 Marginal regressors as initial
Page 52 and 53: Chapter 5 Subsampling In his semina
Page 54 and 55: 5.1 Pointwise consistency for distr
Page 56 and 57: 5.2 Uniform consistency for quantil
Page 64 and 65: Chapter 6 Numerical results Motivat
Page 66 and 67: 6.1 Low dimensinal setting 57 5. De
Page 68 and 69: 6.1 Low dimensinal setting 59 Figur
Page 70 and 71: 6.2 High dimensional setting 61 3.
Page 72 and 73: 6.2 High dimensional setting 63 (d)
Page 74 and 75: 6.2 High dimensional setting 65 Mod
Page 76 and 77: 6.2 High dimensional setting 67 Mod
Page 78 and 79: 6.2 High dimensional setting 69 Fig
Page 80 and 81: Chapter 7 Concluding remarks We rev
Page 84 and 85: Appendix A R Codes A.1 Simulation c
Page 86 and 87: A.1 Simulation code for the Lasso i
Page 88 and 89: A.2 Simulation code for the adaptiv
Page 90 and 91: A.2 Simulation code for the adaptiv
show all

Subsampling estimates of the Lasso distribution.

Create successful ePaper yourself

Delete template?

Save as template?