Statistical Inference from Estimating Equations

Mon. 4-5,  Rm  Mth 1308                                                Spring '08
 

Eric Slud        Statistics Program , Math Department        Rm 2314       x5-5469

                  Interested participants should send email to    evs@math.umd.edu

Reading list

Schedule of Talks

Research Focus: A great deal of current research in parametric and semiparametric statistical
inference is organized around Estimating Equations. This includes

  • martingale estimating equations arising in Survival Analysis;
  • Horvitz-Thompson type estimating equations to account for mechanisms of biased sampling
  • quasilikelihood based estimating equations arising in Generalized Linear Models;
  • Generalized Estimating Equations (GEE's) arising in inference for longitudinal data;
    plus many other topics. We will study papers from a few of these areas, focusing in areas of
    interest to the RIT attendees.

    Graduate Prerequisites: To benefit from this research activity, a graduate student
    should have completed Stat 700 and Stat 600-601.

    Graduate Program: Graduate students will be involved in reading and presenting
    papers from the statistical literature concerning provable properties of estimators from
    Estimating Equations.

    Work Schedule: We will meet weekly in the spring of 2008. Students will choose
    from the following list of Topics and Papers (which will regularly be augmented on
    this web-page) and present the material in subsequent weeks, after an introductory
    couple of weeks' talks by me. Presentations can be informal, but should be detailed
    enough and present enough background that we can understand the issues and ideas
    clearly. It is expected that many presentations will extend to a second week.
     


    Topics by Keyword:

  • misspecified regression models,
  • robustness under misspecifications, `double robustness'
  • random-effect GLM's,
  • errors-in-variables (`measurement error') models,
  • longitudinal models & GEE methods (Generalized Estimating Equations),
  • biased sampling & survey-weighted models


    • Reading List

    Chen, Jinbo and Norman Breslow (2004) Semiparametric efficient estimation for the auxiliary outcome
              problem with the conditional mean model     Canad. Jour. Statist. 32, 1-14. Click here for pdf.

    Diggle, Heagerty, Liang and Zeger book (2002, 2nd ed.) "Analysis of Longitudinal Data"

    Fitzmaurice, Laird & Ware (2004) "Applied Longitudinal Analysis"

    V. P. Godambe classic paper on optimal estimating equations,
             An Optimum Property of Regular Maximum Likelihood Estimation, pp. 1208-1211, Ann. Math. Stat. 31
    Stable URL: http://links.jstor.org/sici?sici=0003-4851%28196012%2931%3A4%3C1208%3AAOPORM%3E2.0.CO%3B2-K

    Heyde, C. (1997) book, "Quasilikelihood and its Application"

    Jiang, Jiming (1999) Conditional inference about generalized linear mixed models.
    Ann. Statist. 27 , 1974-2007. Click here for pdf.

    Li, Haihong, Lindsay, Bruce G. and Waterman, Richard P. (2003) Efficiency of projected
             score methods in rectangular array asymptotics.     J. Roy. Statist. Soc. Ser. B 65, 191-208.

    Huber, P. (1956?) classic paper on M-estimation from Berkeley Symposium

    Liang, K. and Zeger, S. (1986) Biometrika paper on GEE's

    Lindsay, Bruce, Clogg, C., and Grego, J. (1991) Semiparametric estimation in the Rasch
             model and related exponential response models, including a simple latent class model
             for item analysis.     J. Amer. Statist. Assoc. 86, 96-107.

    Pfeffermann, D. and Sverchkov, M. work on survey data with semiparametrically modelled informative nonresponse

    Rotnitzky and Robins papers (some with other co-authors) on inverse-probability weighted estimating equations for
             longitudinal studies (eg AIDS) with informative dropout patterns

    Tsiatis book on Estimating Equations

    White, Halbert (1982) Maximum likelihood estimation of misspecified models.
             Econometrica 50, no. 1, 1-25.

    Schedule of Talks ---