Semiparametric Statistics

Fridays 1-2 pm,  Rm  Mth 2400                                                Spring '09
 

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: Semiparametric statistical theory, which is broadly speaking about the estimation of
finite-dimensional (`structural') parameters like regression coefficients in the presence of infinite-
dimensional `nuisance ' parameters like unknown error distributions in regression or like unknown
baseline hazard functions and censoring distributions in survival regression problems.

Much of the research in this field has been done in a biostatistical setting; econometricians have also
worked heavily in it. We will cover some of the basic examples (Cox model, `accelerated failure
models' as an instance of right-censored regression models), which I hope will be presented by RIT
participants after a couple of introductory lectures. After that we will proceed according to the interests
of participants, but with at least some attention to "biased sampling" semiparametric models which
relate to survey weights.

For those that are new to the Semiparametrics topic, the essential introductory reading is
Chapter 25 of the van der Vaart book, Sections 25.1-25.5. That is what the introductory talks
are based on. From there, the Examples will be expanded using journal papers and (for some
topics) the Tsiatis book.

Graduate-student Prerequisites: To benefit from this research activity, a graduate student
should have completed Stat 700-701 and Stat 600-601.

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

Work Schedule: We will meet weekly in the spring of 2009. 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:

  • semiparametric efficiency via inversion of operators
  • survival data & frailty models
  • semiparametric efficiency via estimating equations
  • robustness under misspecifications, `double robustness'
  • estimation of structural parameters from data, sampled either with missing data
              or by a biased sampling design,
  • partially linear, GAM, and other semiparametric models involving kernel and
              spline density estimation techniques.


    • Reading List

    Books

    (i) Bickel, P., Klaassen, C., Ritov, Y. Wellner, J. (1993), Efficient and Adaptive Estimation for
    Semiparametric Models,     Johns Hopkins Univ. Press: Baltimore.
    This is now re-issued as a Springer paperback, but is very difficult to read.

    (ii) LeCam, L. & Yang, G. (1990), Asymptotics in Statistics: Some Basic Concepts, Springer-Verlag: New York.
    A good and readable text on contiguity theory, local asymptotic normality and applications.

    (iii) Van der Vaart, A. (1998, paperback edition 2000) Asymptotic Statistics, Cambridge Univ. Press.
    This text was used in Stat 710 a couple of years ago and will be used now in introducing the semiparametrics
    topic. It contains excellent introductory chapters on contiguity and empirical processes and semiparametrics.

    (iv) Tsiatis, A. (2006) Semiparametric Theory and Missing Data (Springer Series in Statistics).

    (v) Hastie, T. J. and Tibshirani, R. J. (1990). Generalized Additive Models. Chapman & Hall/CRC.

    Papers

    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.

    Gilbert, Peter B. (2000) Large sample theory of maximum likelihood estimates in semiparametric
             biased sampling models    . Ann. Statist. 28, 151--194.

    Godambe, V.P. and Heyde, C. 1987 ISI review paper on Quasi-likelihood and optimal estimation.

    Kosorok, M., Lee, B., and Fine, J. (2004) Robust inference for proportional hazards univariate frailty
            regression models    . Ann. Statist. 32, 1448-1491.

    Lai, T.L. and Ying, Z. (1992) Asymptotically efficient estimation in censored and truncated
              regression models    . Statistica Sinica 2, 17-46.
    http://www3.stat.sinica.edu.tw/statistica/oldpdf/A2n12.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.

    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.

    Parner, E. (1998) Asymptotic theory for the correlated gamma-frailty model. Ann. Statist. 26, 183-214.

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

    Qin, J. (1994?) Ann. Statist. papers on empirical likelihood

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

    Slud, E. and Vonta, I. (2005) Efficient semiparametric estimators via modified profile likelihood. Jour. Statist.
             Planning & Inference 129, 339-367.

    Schedule of Talks ---