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Statistical inference for single-ind...

Lin, Wei.

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Statistical inference for single-index models.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Statistical inference for single-index models./
作者:	Lin, Wei.
面頁冊數:	149 p.
附註:	Adviser: K. B. Kulasekera.
Contained By:	Dissertation Abstracts International67-05B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3215795
ISBN:	9780542674143

Statistical inference for single-index models.
Lin, Wei.

Statistical inference for single-index models. - 149 p.

Adviser: K. B. Kulasekera.

Thesis (Ph.D.)--Clemson University, 2006.

With the rapid increase in computing power, nonparametric methods in regression analysis have gained more and more popularity. One major difficulty in a general nonparametric regression model comes from the so-called "curse-of-dimensionality"; the difficulty and inefficiency of smoothing in high-dimensional settings. Hence, scientists seek techniques to reduce the model dimension in order to keep a reasonable level of accuracy for all practical purposes. The single-index model, where the regression function takes the form m(x) = g(theta' x), is a natural generalization of the classical linear regression models and a restrictive version of a completely nonparametric model. Most of the statistical analysis in the literature for the single-index models focuses on estimating the index vector theta and the link function g(·). In this work, we present some research results for the following issues regarding the single-index models. These are: the identifiability of the single-index models and their generalizations; the error variance estimation in the single-index models; testing for the equality of two single-index models; variable selection in a single-index model; and a goodness-of-fit (GOF) test for the single-index models (checking whether or not a sample follows a single-index model).

ISBN: 9780542674143Subjects--Topical Terms:

515831
Mathematics.

Statistical inference for single-index models.
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520 $a With the rapid increase in computing power, nonparametric methods in regression analysis have gained more and more popularity. One major difficulty in a general nonparametric regression model comes from the so-called "curse-of-dimensionality"; the difficulty and inefficiency of smoothing in high-dimensional settings. Hence, scientists seek techniques to reduce the model dimension in order to keep a reasonable level of accuracy for all practical purposes. The single-index model, where the regression function takes the form m(x) = g(theta' x), is a natural generalization of the classical linear regression models and a restrictive version of a completely nonparametric model. Most of the statistical analysis in the literature for the single-index models focuses on estimating the index vector theta and the link function g(·). In this work, we present some research results for the following issues regarding the single-index models. These are: the identifiability of the single-index models and their generalizations; the error variance estimation in the single-index models; testing for the equality of two single-index models; variable selection in a single-index model; and a goodness-of-fit (GOF) test for the single-index models (checking whether or not a sample follows a single-index model).
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