Title page for ETD etd-122299-184429


Type of Document Dissertation
Author Starnes, Brett Alden
Author's Email Address bstarnes@vt.edu, astarnes@mail.bluefield.edu
URN etd-122299-184429
Title Asymptotic Results for Model Robust Regression
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Birch, Jeffrey B. Committee Chair
Anderson-Cook, Christine M. Committee Member
Coakley, Clint W. Committee Member
Smith, Eric P. Committee Member
Terrell, George R. Committee Member
Keywords
  • Mixing Parameter
  • Nonparametric
  • Parametric
  • Asymptotic
  • Convergence Rates
  • Regression
  • Semiparametric
Date of Defense 1999-12-14
Availability unrestricted
Abstract
Since the mid 1980's many statisticians have studied methods for combining parametric and

nonparametric esimates to improve the quality of fits in a regression problem. Notably in 1987,

Einsporn and Birch proposed the Model Robust Regression estimate (MRR1) in which estimates

of the parametric function, f, and the nonparametric function, g, were combined in a

straightforward fashion via the use of a mixing parameter, l. This technique was studied

extensively at small samples and was shown to be quite effective at modeling various unusual

functions. In 1995, Mays and Birch developed the MRR2 estimate as an alternative to MRR1.

This model involved first forming the parametric fit to the data, and then adding in an estimate of

g according to the lack of fit demonstrated by the error terms. Using small samples, they

illustrated the superiority of MRR2 to MRR1 in most situations. In this dissertation we have

developed asymptotic convergence rates for both MRR1 and MRR2 in OLS and GLS (maximum

likelihood) settings. In many of these settings, it is demonstrated that the user of MRR1 or

MRR2 achieves the best convergence rates available regardless of whether or not the model is

properly specified. This is the "Golden Result of Model Robust Regression". It turns out that the

selection of the mixing parameter is paramount in determining whether or not this result is

attained.

Files
  Filename       Size       Approximate Download Time (Hours:Minutes:Seconds) 
 
 28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access 
  S7994Ch1.PDF 14.85 Kb 00:00:04 00:00:02 00:00:01 < 00:00:01 < 00:00:01
  S7994Ch2a.PDF 27.92 Kb 00:00:07 00:00:03 00:00:03 00:00:01 < 00:00:01
  S7994Ch2b.PDF 19.39 Kb 00:00:05 00:00:02 00:00:02 00:00:01 < 00:00:01
  S7994Ch2c.PDF 23.16 Kb 00:00:06 00:00:03 00:00:02 00:00:01 < 00:00:01
  S7994Ch3a.PDF 58.38 Kb 00:00:16 00:00:08 00:00:07 00:00:03 < 00:00:01
  S7994Ch3b.PDF 44.05 Kb 00:00:12 00:00:06 00:00:05 00:00:02 < 00:00:01
  S7994Ch3c.PDF 39.26 Kb 00:00:10 00:00:05 00:00:04 00:00:02 < 00:00:01
  S7994Ch4a.PDF 47.40 Kb 00:00:13 00:00:06 00:00:05 00:00:02 < 00:00:01
  S7994Ch4b.PDF 45.00 Kb 00:00:12 00:00:06 00:00:05 00:00:02 < 00:00:01
  S7994Ch5a.PDF 53.32 Kb 00:00:14 00:00:07 00:00:06 00:00:03 < 00:00:01
  S7994Ch5b.PDF 39.44 Kb 00:00:10 00:00:05 00:00:04 00:00:02 < 00:00:01
  S7994Ch6.PDF 18.27 Kb 00:00:05 00:00:02 00:00:02 00:00:01 < 00:00:01
  S7994frontmatter.PDF 9.54 Kb 00:00:02 00:00:01 00:00:01 < 00:00:01 < 00:00:01
  S7994frontmatter2.PDF 8.94 Kb 00:00:02 00:00:01 00:00:01 < 00:00:01 < 00:00:01
  S7994rb.pdf 13.71 Kb 00:00:03 00:00:01 00:00:01 < 00:00:01 < 00:00:01
  S7994Vita.PDF 7.18 Kb 00:00:01 00:00:01 < 00:00:01 < 00:00:01 < 00:00:01
  S7994x3a.PDF 19.42 Kb 00:00:05 00:00:02 00:00:02 00:00:01 < 00:00:01
  S7994x3b.PDF 26.41 Kb 00:00:07 00:00:03 00:00:03 00:00:01 < 00:00:01
  S7994x3c.PDF 20.84 Kb 00:00:05 00:00:02 00:00:02 00:00:01 < 00:00:01
  S7994x4a.PDF 42.69 Kb 00:00:11 00:00:06 00:00:05 00:00:02 < 00:00:01
  S7994x4b.PDF 24.11 Kb 00:00:06 00:00:03 00:00:03 00:00:01 < 00:00:01
  S7994x5a.PDF 44.62 Kb 00:00:12 00:00:06 00:00:05 00:00:02 < 00:00:01
  S7994x5b.PDF 34.07 Kb 00:00:09 00:00:04 00:00:04 00:00:02 < 00:00:01

Browse All Available ETDs by ( Author | Department )

dla home
etds imagebase journals news ereserve special collections
virgnia tech home contact dla university libraries

If you have questions or technical problems, please Contact DLA.