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Model Selection and Estimation in Ge...

Wang, Dong.

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Model Selection and Estimation in Generalized Additive Models and Generalized Additive Mixed Models.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Model Selection and Estimation in Generalized Additive Models and Generalized Additive Mixed Models./
作者:	Wang, Dong.
面頁冊數:	124 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
Contained By:	Dissertation Abstracts International74-07B(E).
標題:	Statistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3538507
ISBN:	9781303013669

Model Selection and Estimation in Generalized Additive Models and Generalized Additive Mixed Models.
Wang, Dong.

Model Selection and Estimation in Generalized Additive Models and Generalized Additive Mixed Models. - 124 p.

Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.

Thesis (Ph.D.)--North Carolina State University, 2013.

In this dissertation, we propose a method of model selection and estimation in generalized additive models (GAMs) for data from a distribution in the exponential family. The linear mixed model representation of the smoothing spline estimators of the nonparametric functions is constructed, where the inverse of the smoothing parameters are treated as extra variance components and the importance of these nonparametric functions is controlled by the induced variance components. By maximizing the penalized quasi-likelihood with the adaptive LASSO, we could effectively select the important nonparametric functions. Approximate EM algorithms are applied to achieve the goal of model selection and estimation. In addition, we also calculate the approximate pointwise frequentist and Bayesian confidence intervals for selected functions. The eigenvalue-eigenvector decomposition approach is used to approximate the induced random effects from the nonparametric functions in order to reduce the dimensions of matrices and speed up the computation.

ISBN: 9781303013669Subjects--Topical Terms:

517247
Statistics.

Model Selection and Estimation in Generalized Additive Models and Generalized Additive Mixed Models.
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245 1 0 $a Model Selection and Estimation in Generalized Additive Models and Generalized Additive Mixed Models.
300 $a 124 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-07(E), Section: B.
500 $a Adviser: Daowen Zhang.
502 $a Thesis (Ph.D.)--North Carolina State University, 2013.
520 $a In this dissertation, we propose a method of model selection and estimation in generalized additive models (GAMs) for data from a distribution in the exponential family. The linear mixed model representation of the smoothing spline estimators of the nonparametric functions is constructed, where the inverse of the smoothing parameters are treated as extra variance components and the importance of these nonparametric functions is controlled by the induced variance components. By maximizing the penalized quasi-likelihood with the adaptive LASSO, we could effectively select the important nonparametric functions. Approximate EM algorithms are applied to achieve the goal of model selection and estimation. In addition, we also calculate the approximate pointwise frequentist and Bayesian confidence intervals for selected functions. The eigenvalue-eigenvector decomposition approach is used to approximate the induced random effects from the nonparametric functions in order to reduce the dimensions of matrices and speed up the computation.
520 $a In the case of longitudinal data, we apply the generalized additive mixed models (GAMMs) to model the relationship. The subject-specific random effects are introduced to accommodate the correlation among the responses. Similarly, we propose the adaptive LASSO for generalized additive mixed models to perform model selection and estimation.
520 $a To evaluate the method, we investigate simulation studies and provide real data applications.
590 $a School code: 0155.
650 4 $a Statistics. $3 517247
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710 2 $a North Carolina State University. $b Statistics. $3 2098676
773 0 $t Dissertation Abstracts International $g 74-07B(E).
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791 $a Ph.D.
792 $a 2013
793 $a English
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