Confidence sets based on sparse estimators are necessarily large

Sankhya: The Indian Journal of Statistics

Volumn 71, Issue 1 SUPPL. 1, 2009, Pages 1-18

  Pötscher, Benedikt M ^a  

^a UNIVERSITY OF VIENNA   (Austria)

Author keywords

Confidence set; Consistent model selection; Coverage probability; Penalized maximum likelihood; Postmodel selection estimator; Sparse estimator

Indexed keywords

EID: 74949103169     PISSN: 09727671     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. Beran, R. (1992). The radial process for confidence sets. Probability in Banach spaces, 8, (Brunswick, ME, 1991), 479-496
2. Beran, R. (1992), Progress in Probability, 30, Birkhäuser Boston, Boston, MA.
3. Bunea, F. (2004). Consistent covariate selection and post model selection inference in semiparametric regression. Ann. Statist., 32, 898-927.
4. Bunea, F. and McKeague, I. W. (2005). Covariate selection for semiparametric hazard function regression models. J. Multivariate Anal., 92, 186-204.
5. Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. J. Amer. Statist. Assoc., 96, 1348-1360.
6. Fan, J. and Li, R. (2002). Variable selection for Cox's proportional hazards model and frailty model. Ann. Statist., 30, 74-99.
7. Fan, J. and Li, R. (2004). New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. J. Amer. Statist. Assoc., 99, 710-723.
8. Kabaila, P. (1995). The effect of model selection on confidence regions and prediction regions. Econometric Theory, 11, 537-549.
9. Kabaila, P. (1998). Valid confidence intervals in regression after variable selection. Econometric Theory 14, 463-482.
10. Kabaila, P. and Leeb, H. (2006). On the large-sample minimal coverage probability of confidence intervals after model selection. J. Amer. Statist. Assoc., 101, 619-629.
11. Kale, B. K. (1985). A note on the super efficient estimator. J. Statist. Plann. Inference, 12, 259-263.
12. Leeb, H. and Pötscher, B.M. (2005). Model selection and inference: facts and fiction. Econometric Theory, 21, 21-59.
13. Leeb, H. and Pötscher, B.M. (2008). Sparse estimators and the oracle property, or the return of Hodges' estimator. J. Econometrics, 142, 201-211.
14. Li, R. and Liang, H. (2008). Variable selection in semiparametric regression modeling. Ann. Statist., 36, 261-286.
15. Pötscher, B. M. (1991). Effects of model selection on inference. Econometric Theory, 7, 163-185.
16. Pötscher, B. M. (1995). Comment on 'The effect of model selection on confidence regions and prediction regions'. Econometric Theory, 11, 550-559.
17. Pötscher, B. M. and Leeb, H. (2009). On the distribution of penalized maximum likelihood estimators: the LASSO, SCAD, and thresholding. J. Multivariate Anal., 100, 2065-2082.
18. Pötscher, B. M. and Schneider, U. (2009). On the distribution of the adaptive LASSO estimator. J. Statist. Plann. Inference, 139, 2775-2790.
19. Wang, H. and Leng, C. (2007). Unified LASSO estimation via least squares approximation. J. Amer. Statist. Assoc., 102, 1039-1048.
20. Wang, H., Li, G. and Tsai, C.L. (2007). Regression coefficient and autoregressive order shrinkage and selection via the lasso. J. Roy. Statist. Soc. B, 69, 63-78.
21. Wang, H., Li, G. and Tsai, C.L. (2007). Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika, 94, 553-568.
22. Yang, Y. (2005). Can the strength of AIC and BIC be shared? A conflict between model identification and regression estimation. Biometrika, 92, 937-950.
23. Zhang, H. H. and Lu, W. (2007). Adaptive lasso for Cox's proportional hazards model. Biometrika 94, 691-703.
24. Zou, H. (2006). The adaptive lasso and its oracle properties. J. Amer. Statist. Assoc., 101, 1418-1429.
25. Zou, H. and Yuan, M. (2008). Composite quantile regression and the oracle model selection theory. Ann. Statist., 36, 1108-1126.