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We develop an efficient estimation procedure for identifying and estimating the central subspace. Using a new way of parameterization, we convert the problem of identifying the central subspace to the problem of estimating a finite dimensional parameter in a semiparametric model. This conversion allows us to derive an efficient estimator which reaches the(More)
Summarizing the effect of many covariates through a few linear combinations is an effective way of reducing covariate dimension and is the backbone of (sufficient) dimension reduction. Because the replacement of high-dimensional covariates by low-dimensional linear combinations is performed with a minimum assumption on the specific regression form, it(More)
This article considers a wide class of semiparametric regression models in which interest focuses on population-level quantities that combine both the parametric and the nonparametric parts of the model. Special cases in this approach include generalized partially linear models, generalized partially linear single-index models, structural measurement error(More)
We provide a novel and completely different approach to dimension-reduction problems from the existing literature. We cast the dimension-reduction problem in a semiparametric estimation framework and derive estimating equations. Viewing this problem from the new angle allows us to derive a rich class of estimators, and obtain the classical dimension(More)
We consider a class of generalized skew-normal distributions that is useful for selection modeling and robustness analysis and derive a class of semiparametric estimators for the location and scale parameters of the central part of the model. We show that these estimators are consistent and asymptotically normal. We present the semiparametric efficiency(More)
We derive constructive locally efficient estimators in semiparametric measurement error models. The setting is one where the likelihood function depends on variables measured with and without error, where the variables measured without error can be modelled nonpara-metrically. The algorithm is based on backfitting. We show that if one adopts a parametric(More)
Huntington's disease (HD) is a progressive neurodegenerative disorder caused by an expansion of CAG repeats in the IT15 gene. The age-at-onset (AAO) of HD is inversely related to the CAG repeat length and the minimum length thought to cause HD is 36. Accurate estimation of the AAO distribution based on CAG repeat length is important for genetic counseling(More)
SUMMARY A local likelihood estimator for a nonparametric nuisance function is proposed in the context of semiparametric skew-normal distributions. Constraints imposed on such functions result in a nonparametric estimator with a different target function for maximization from classical local likelihood estimators. The optimal asymptotic semiparametric(More)