Reweighting approximate GM estimators: Asymptotics and residual-based graphics

Douglas G. Simpson, Yuan Chin Ivan Chang

Research output: Contribution to journalArticlepeer-review


The iterative weighted least squares algorithm is handy for solving generalized estimating equations. In some situations it may be desirable to limit the number of iterations to a fixed finite number, for instance, to keep the breakdown point under control. Such a scheme is called reweighting. Usually reweighting leads to a different large sample theory than full iteration, and the reweighted estimator may inherit deficiencies of the starting value. When might the reweighting scheme work? To answer this question we define a broad class of estimators, namely, approximate GM estimators, and we show that reweighting leads to the same large sample theory as full iteration within this class. As an example, we provide conditions under which one-step Newton-Raphson estimators are approximate GM estimators. We then use the reweighting to construct residual-based graphics for approximate GM estimates, adapting weighted residual plots that have been proposed previously, and developing new plots to provide complementary views of the data.

Original languageEnglish (US)
Pages (from-to)273-293
Number of pages21
JournalJournal of Statistical Planning and Inference
Issue number2
StatePublished - Feb 1 1997


  • Added variable plot
  • Generalized estimating equation
  • One-step estimator
  • Regression diagnostics
  • Robust methods

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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