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2015-07-16 Qu, Annie Qu, Annie Simpson, Douglas G. Chen, Xiaohui Shao, Xiaofeng Shi, Peibei 2015-09-29T20:38:20Z 2015-09-29T20:38:20Z 2015-08 Weak signal identification and inference are very important in the area of penalized model selection, yet they are under-developed and not well-studied. Existing inference procedures for penalized estimators are mainly focused on strong signals. This thesis propose an identification procedure for weak signals in finite samples, and provide a transition phase in-between noise and strong signal strengths. A new two-step inferential method is introduced to construct better confidence intervals for the identified weak signals. Both theory and numerical studies indicate that the proposed method leads to better confidence coverage for weak signals, compared with those using asymptotic inference. In addition, the proposed method outperforms the perturbation and bootstrap resampling approaches. The method is illustrated for HIV antiretroviral drug susceptibility data to identify genetic mutations associated with HIV drug resistance. We also provide signal's inference method based on the exact distribution of penalized estimator. The finite sample distribution is quite different from its asymptotic counterpart, which can be highly non-normal with a point mass at zero. Numerical studies indicate that the density-based approach works well when true parameter is moderately large. However, it cannot provide accurate inference when signal is weak. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2015-09-29 without embargo terms The student, Peibei Shi, accepted the attached license on 2015-07-12 at 17:56. The student, Peibei Shi, submitted this Dissertation for approval on 2015-07-12 at 18:04. This Dissertation was approved for publication on 2015-07-16 at 11:03. DSpace SAF Submission Ingestion Package generated from Vireo submission #8416 on 2015-09-29 at 13:22:39 Made available in DSpace on 2015-09-29T20:38:20Z (GMT). No. of bitstreams: 2 SHI-DISSERTATION-2015.pdf: 894677 bytes, checksum: 154252b923b6125561c15e830533d50a (MD5) LICENSE.txt: 4207 bytes, checksum: 40f7d0a6371bd8036453e9a3c774e1be (MD5) Previous issue date: 2015-07-16 application/pdf http://hdl.handle.net/2142/88025 en Copyright 2015 Peibei Shi model selection weak signal inference Weak signal identification and inference in penalized model selection text text 2015-8 Statistics Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D.