東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Dimension reduction in regression an...

Ye, Zhishen.

FindBook

Google Book

Amazon

博客來

Dimension reduction in regression analysis.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Dimension reduction in regression analysis./
作者:	Ye, Zhishen.
面頁冊數:	121 p.
附註:	Chair: Robert E. Weiss.
Contained By:	Dissertation Abstracts International62-02B.
標題:	Biology, Biostatistics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3005944
ISBN:	049315115X

Dimension reduction in regression analysis.
Ye, Zhishen.

Dimension reduction in regression analysis. - 121 p.

Chair: Robert E. Weiss.

Thesis (Ph.D.)--University of California, Los Angeles, 2001.

Dimension reduction in regression analysis reduces the dimension of the predictor vector p-dimension <bold>x</bold> without specifying a parametric model and without loss of information on the regression of <italic> y</italic> on <bold>x</bold>. The problem is how to identify the low dimensional projection of <bold>x</bold>. The projection can be represented by the <italic> k</italic> eigenvectors corresponding to the nonzero eigenvalues of a <italic> k</italic> rank <italic>p</italic> by <italic>p</italic> matrix with (<italic> k</italic> < <italic>p</italic>).

ISBN: 049315115XSubjects--Topical Terms:

1018416
Biology, Biostatistics.

Dimension reduction in regression analysis.
LDR:03260nam 2200313 a 45 001 929182
005 20110427
008 110427s2001 eng d
020 $a 049315115X
035 $a (UnM)AAI3005944
035 $a AAI3005944
040 $a UnM $c UnM
100 1 $a Ye, Zhishen. $3 1252667
245 1 0 $a Dimension reduction in regression analysis.
300 $a 121 p.
500 $a Chair: Robert E. Weiss.
500 $a Source: Dissertation Abstracts International, Volume: 62-02, Section: B, page: 0634.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2001.
520 $a Dimension reduction in regression analysis reduces the dimension of the predictor vector p-dimension <bold>x</bold> without specifying a parametric model and without loss of information on the regression of <italic> y</italic> on <bold>x</bold>. The problem is how to identify the low dimensional projection of <bold>x</bold>. The projection can be represented by the <italic> k</italic> eigenvectors corresponding to the nonzero eigenvalues of a <italic> k</italic> rank <italic>p</italic> by <italic>p</italic> matrix with (<italic> k</italic> < <italic>p</italic>).
520 $a In this dissertation, we introduce the concepts of a <italic>target matrix </italic>, which is a population <italic>p</italic> by <italic>p</italic> matrix to be estimated, and <italic>estimation methods</italic> which estimate the target matrix from data. We present a new perspective on three existing methods, SIR (Li, 1991), SAVE (Cook and Weisberg, 1991) and pHd (Li, 1992). Their <italic>target matrices</italic> and <italic>estimation methods</italic> are identified and distinguished. A system is built to identify and construct more <italic>target matrices</italic> and therefore more potential methods. SIR, SAVE, and pHd are unified as special cases of a broad new class of methods. In particular, we propose methods based on linear combinations of known <italic> target matrices</italic>.
520 $a Because there are now so many methods of dimension reduction, we introduce methodology to select among different target matrices and estimation methods. A k-dimensional estimate is the first <italic>k</italic> eigenvectors of an estimated <italic>target matrix</italic>. The <italic>variability</italic> of the estimate is defined and assessed using a resampling plan.
520 $a In general, no target matrix is guaranteed to identify the entire k-dimension projection of <bold>x</bold>. Assume the response <italic>y</italic> is categorical and the predictors <bold>x</bold> given <italic>y</italic> are normally distributed, the SAVE target matrix is shown to be able to recover the entire k-dimension projection. We introduce Bayesian modeling techniques as a new estimation method to estimate a target matrix, and study the behavior of various posterior estimates of the SAVE matrix with different priors. Examples with small sample size illustrate that Bayesian techniques can be useful.
590 $a School code: 0031.
650 4 $a Biology, Biostatistics. $3 1018416
650 4 $a Statistics. $3 517247
690 $a 0308
690 $a 0463
710 2 0 $a University of California, Los Angeles. $3 626622
773 0 $t Dissertation Abstracts International $g 62-02B.
790 $a 0031
790 1 0 $a Weiss, Robert E., $e advisor
791 $a Ph.D.
792 $a 2001
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3005944