Semiparametric analysis of heterogeneous data using varying-scale generalized linear models

Minge Xie, Douglas G. Simpson, Raymond J. Carroll

Research output: Contribution to journalArticlepeer-review


This article describes a class of heteroscedastic generalized linear regression models in which a subset of the regression parameters are rescaled nonparametrically, and develops efficient semiparametric inferences for the parametric components of the models. Such models provide a means to adapt for heterogeneity in the data due to varying exposures, varying levels of aggregation, and so on. The class of models considered includes generalized partially linear models and nonparametrically scaled link function models as special cases. We present an algorithm to estimate the scale function nonparametrically, and obtain asymptotic distribution theory for regression parameter estimates. In particular, we establish that the asymptotic covariance of the semiparametric estimator for the parametric part of the model achieves the semiparametric lower bound. We also describe bootstrap-based goodness-of-scale test. We illustrate the methodology with simulations, published data, and data from collaborative research on ultrasound safety.

Original languageEnglish (US)
Pages (from-to)650-660
Number of pages11
JournalJournal of the American Statistical Association
Issue number482
StatePublished - Jun 2008


  • Generalized linear regression
  • Heteroscedasticity
  • Nonparametric regression
  • Partially linear model
  • Semiparametric efficiency
  • Varying-coefficient model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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