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oai:www.ideals.illinois.edu:2142/24348 2023-07-10 col_2142_5131 col_2142_17362 com_2142_5130 com_2142_17361 com_2142_8903

Chen, Yuguo Chen, Yuguo He, Xuming Liang, Feng Portnoy, Stephen L. Feng, Yang 2011-05-25T14:37:47Z 2011-05-25T14:37:47Z 2013-05-26T10:00:21Z 2011-05-25T14:37:47Z 2011-05 Quantile regression, as a supplement to the mean regression, is often used when a comprehensive relationship between the response variable and the explanatory variables is desired. The traditional frequentists’ approach to quantile regression was well developed with asymptotic theories and efficient algorithms. However not much work has been done under the Bayesian framework. The most challenging problem for Bayesian quantile regression is that the likelihood is usually not available unless a certain distribution for the error is assumed. In this dissertation, we propose two Bayesian quantile regression methods: the data generating process based method (DG) and the linearly interpolated density based method (LID). Markov chain Monte Carlo algorithms are developed to implement the proposed methods. We provide the convergence property of the algorithms and numerically verify the theoretical results. We compare the proposed methods with some existing methods through simulation studies, and apply our method to the birth weight data. Unlike most of the existing methods which aim at tackling one quantile at a time, our proposed methods aim at estimating the joint posterior distribution of multiple quantiles and achieving global efficiency for all quantiles of interest and functions of those quantiles. From the simulation results, we found that LID could produce more efficient estimates than some existing methods. In particular, for estimating the difference of quantiles, LID has a big advantage over other existing methods. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2011-04-14T14:29:02Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Feng_Yang.pdf: 374153 bytes, checksum: 5a47714671ad2148c27ef2609feddabf (MD5) Made available in DSpace on 2011-05-25T14:37:47Z (GMT). No. of bitstreams: 2 Feng_Yang.pdf: 374153 bytes, checksum: 5a47714671ad2148c27ef2609feddabf (MD5) license.txt: 4057 bytes, checksum: fea818015997dd574aecd1525dcdcdbe (MD5) Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by William Ingram (wingram2@illinois.edu) on 2011-05-25T14:41:29Z Item is restricted until 2013-05-25T14:41:28Z Item reinstated by Sarah Shreeves (sshreeve@illinois.edu) on 2013-05-26T10:00:21Z Item was in collections: University of Illinois Dissertations and Theses (ID: 204) Dissertations and Theses - Statistics (ID: 774) No. of bitstreams: 3 Feng_Yang.pdf.txt: 125119 bytes, checksum: 1a91559edf80631271ad23f0f61566f4 (MD5) Feng_Yang.pdf: 374153 bytes, checksum: 5a47714671ad2148c27ef2609feddabf (MD5) license.txt: 4057 bytes, checksum: fea818015997dd574aecd1525dcdcdbe (MD5) Item released from any restrictions by Sarah Shreeves (sshreeve@illinois.edu) on 2013-05-26T10:00:21Z http://hdl.handle.net/2142/24348 en Copyright 2011 Yang Feng Bayesian inference Markov chain Monte Carlo (MCMC) Quantile regression Linearly interpolated density (LID) Bayesian quantile linear regression Statistics 1583 Statistics 0329 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Statistics -UIUC 10KS0329PHD