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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.

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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution

Every year, mainland China sends numerous undergraduate and postgraduate students to study abroad at English-medium universities (Tan & Simpson, 2008), a large number of whom attend Hong Kong universities (Li & Bray, 2007), including the Hong Kong Institute of Education

Abstract—Education is one of the most important ways to protect heritage and to establish an effective transmission mode, Li firewood dance be introduced into school education and protection of heritage, not only for non-material cultural heritage opens a new path, while strengthening the school

Recent studies have called for more integration of educational experiences and closer coopera-tion between high schools and colleges. Students making the transition from high school to college freguently lack library/research skills, which is a major problem for bibliographic in

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