Asymptotics for Lasso-type estimators

Annals of Statistics

Volumn 28, Issue 5, 2000, Pages 1356-1378

  Knight, Keith ^a   Fu, Wenjiang ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b MICHIGAN STATE UNIVERSITY   (United States)

Author keywords

Epi convergence in distribution; Lasso; Penalized regression; Shrinkage estimation

Indexed keywords

EID: 0034287156     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1015957397     Document Type: Article

References (20)

1. ANDERSON, P. K. and GILL, R. D. (1982). Cox's regression model for counting processes: a large sample study. Ann. Statist. 10 1100-1120.
2. BESAG, J. (1986). On the statistical analysis of dirty pictures (with discussion). J. Roy. Statist. Soc. Ser. B 48 259-302.
3. CHEN, S. S., DONOHO, D. L. and SAUNDERS, M. A. (1999). Atomic decomposition by basis pursuit. SIAM J. Scientific Computing 20 33-61.
4. FAN, J. and LI, R. (1999). Variable selection via penalized likelihood. Unpublished manuscript.
5. FIACCO, A. V. and MCCORMICK, G. P. (1990). Nonlinear Programming: Sequential Unconstrained Minimization Techniques. SIAM, Philadelphia.
6. FRANK, I. E. and FRIEDMAN, J. H. (1993). A statistical view of some chemometrics regression tools (with discussion). Technometrics 35 109-148.
7. FU, W. J. (1998). Penalized regressions: the Bridge versus the Lasso. J. Comput. Graph. Statist. 7 397-416.
8. FU, W. J. (1999). Estimating the effective trends in age-period-cohort studies. Unpublished manuscript.
9. GEYER, C. J. (1994). On the asymptotics of constrained M-estimation. Ann. Statist. 22 1993-2010.
10. GEYER, C. J. (1996). On the asymptotics of convex stochastic optimization. Unpublished manuscript.
11. KIM, J. and POLLARD, D. (1990). Cube root asymptotics. Ann. Statistics 18 191-219.
12. KUPPER, L. L., JANIS, J. M., KARMOUS, A. and GREENBERG, B. G. (1985). Statistical age-period-cohort analysis: a review and critique. J. Chronic Disease 38 811-830.
13. LINHART, H. and ZUCCHINI, W. (1986). Model Selection. Wiley, New York.
14. OSBORNE, M. R., PRESNELL, B. and TURLACH, B. A. (1998). On the Lasso and its dual. Research Report 98/1, Dept. Statistics, Univ. Adelaide.
15. PFLUG, G. CH. (1995). Asymptotic stochastic programs. Math. Oper. Res. 20 769-789.
16. POLLARD, D. (1991). Asymptotics for least absolute deviation regression estimators. Econometric Theory 7 186-199.
17. SARDY, S., BRUCE, A. G. and TSENG, P. (1998). Block coordinate relaxation methods for nonparametric signal denoising with wavelet dictionaries. Technical Report, Dept. Mathematics, EPFL, Lausanne.
18. SRIVASTAVA, M. S. (1971). On fixed width confidence bounds for regression parameters. Ann. Math. Statist. 42 1403-1411.
19. TIBSHIRANI, R. (1996). Regression shrinkage and selection via the Lasso. J. Roy. Statist. Soc. Ser. B 58 267-288.
20. VAN DER VAART, A. W. and WELLNER, J. A. (1996). Weak Convergence and Empirical Processes with Applications to Statistics. Springer, New York.