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RateOptimal Estimation for a General Class of Nonparametric Regression Models with Unknown Link Functions
 ANNALS OF STATISTICS
, 2007
"... This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of onedimensional transformations and can be estimated with a onedimensional rate of convergence. The model contains the generalized additive model with unk ..."
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Cited by 13 (2 self)
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This paper discusses a nonparametric regression model that naturally generalizes neural network models. The model is based on a finite number of onedimensional transformations and can be estimated with a onedimensional rate of convergence. The model contains the generalized additive model with unknown link function as a special case. For this case, it is shown that the additive components and link function can be estimated with the optimal rate by a smoothing spline that is the solution of a penalized least squares criterion.
Additive isotone regression
 In: Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom. IMS
, 2007
"... This paper is dedicated to Piet Groeneboom on the occasion of his 65th birthday Abstract: This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimat ..."
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Cited by 11 (0 self)
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This paper is dedicated to Piet Groeneboom on the occasion of his 65th birthday Abstract: This paper is about optimal estimation of the additive components of a nonparametric, additive isotone regression model. It is shown that asymptotically up to first order, each additive component can be estimated as well as it could be by a least squares estimator if the other components were known. The algorithm for the calculation of the estimator uses backfitting. Convergence of the algorithm is shown. Finite sample properties are also compared through simulation experiments. 1.
Smooth backfitting in generalized additive models
, 2007
"... Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with nonGaussian responses including binary and count data. In this paper, a new likelihood approach for fitting generalized additive models is proposed. It aims to maximize ..."
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Cited by 9 (6 self)
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Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with nonGaussian responses including binary and count data. In this paper, a new likelihood approach for fitting generalized additive models is proposed. It aims to maximize a smoothed likelihood. The additive functions are estimated by solving a system of nonlinear integral equations. An iterative algorithm based on smooth backfitting is developed from the Newton–Kantorovich theorem. Asymptotic properties of the estimator and convergence of the algorithm are discussed. It is shown that our proposal based on local linear fit achieves the same bias and variance as the oracle estimator that uses knowledge of the other components. Numerical comparison with the recently proposed twostage estimator [Ann. Statist. 32 (2004) 2412–2443] is also made.
Nonparametric additive . . . Measured Data
, 2009
"... We develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems. Our methodology easily copes with various settings, such as when some covariates are the same over repeated response measurements. We allow for a working covariance matrix for the reg ..."
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We develop an easily computed smooth backfitting algorithm for additive model fitting in repeated measures problems. Our methodology easily copes with various settings, such as when some covariates are the same over repeated response measurements. We allow for a working covariance matrix for the regression errors, showing that our method is most efficient when the correct covariance matrix is used. The component functions achieve the known asymptotic variance lower bound for the scalar argument case. Smooth backfitting also leads directly to designindependent biases in the local linear case. Simulations show our estimator has smaller variance than the usual kernel estimator. This is also illustrated by an example from nutritional epidemiology.
A Service of zbw Additive Models: Extensions and Related Models
"... StandardNutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, ..."
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StandardNutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter OpenContentLizenzen (insbesondere CCLizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract We give an overview over smooth backfitting type estimators in additive models. Moreover we illustrate their wide applicability in models closely related to additive models such as nonparametric regression with dependent error variables where the errors can be transformed to white noise by a linear transformation, nonparametric regression with repeatedly measured data, nonparametric panels with fixed effects, simultaneous nonparametric equation models, and nonand semiparametric autoregression and GARCHmodels. We also discuss extensions to varying coefficient models, additive models with missing observations, and the case of nonstationary covariates. Terms of use: Documents in EconStor may
Electronic Journal of Statistics
, 2008
"... Uniform limit laws of the logarithm for estimators of the additive regression function in the presence of right censored data ..."
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Uniform limit laws of the logarithm for estimators of the additive regression function in the presence of right censored data