國立高雄大學圖資館 |

Language: English

Back

New findings of functional ANOVA wit...

Liu, Ruixue.

New findings of functional ANOVA with applications to computational finance and statistics.

Record Type:	Electronic resources : Monograph/item
Title/Author:	New findings of functional ANOVA with applications to computational finance and statistics.
Author:	Liu, Ruixue.
Description:	106 p.
Notes:	Advisers: Art Owen; Darrell Duffie.
Notes:	Source: Dissertation Abstracts International, Volume: 66-04, Section: B, page: 2144.
Contained By:	Dissertation Abstracts International66-04B.
Subject:	Statistics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3171779
ISBN:	054208659X

New findings of functional ANOVA with applications to computational finance and statistics.
Liu, Ruixue.

New findings of functional ANOVA with applications to computational finance and statistics. - 106 p.

Advisers: Art Owen; Darrell Duffie.

Thesis (Ph.D.)--Stanford University, 2005.

The ANOVA of [0,1]d involves 2 d - 1 effects and corresponding mean squares. For moderately large d, it becomes difficult to estimate them all. It is much less difficult to estimate certain interpretable weighted sums of these mean squares, which can address such issues as bounds on effective dimensions, and the effectiveness of Quasi-Monte Carlo method.

ISBN: 054208659XSubjects--Topical Terms:

182057
Statistics.

New findings of functional ANOVA with applications to computational finance and statistics.
LDR:03157nmm _2200313 _450 001 167374
005 20061005085916.5
008 090528s2005 eng d
020 $a 054208659X
035 $a 00197990
040 $a UnM $c UnM
100 0 $a Liu, Ruixue. $3 237522
245 1 0 $a New findings of functional ANOVA with applications to computational finance and statistics.
300 $a 106 p.
500 $a Advisers: Art Owen; Darrell Duffie.
500 $a Source: Dissertation Abstracts International, Volume: 66-04, Section: B, page: 2144.
502 $a Thesis (Ph.D.)--Stanford University, 2005.
520 # $a The ANOVA of [0,1]d involves 2 d - 1 effects and corresponding mean squares. For moderately large d, it becomes difficult to estimate them all. It is much less difficult to estimate certain interpretable weighted sums of these mean squares, which can address such issues as bounds on effective dimensions, and the effectiveness of Quasi-Monte Carlo method.
520 # $a The analysis of variance (ANOVA) for square integrable functions on [0, 1]d is becoming a widely used tool for the exploratory analysis of functions in areas from bioinformatics, finance, statistics, and so on. It enables us to quantify the notion that some variables and interactions are much more important than others as well as identifying them. This ANOVA result forms a global sensitivity analysis distinct from local methods based on partial derivatives, and therefore, sheds light on how variables interact with each other on the whole space of [0,1]d. Saltelli, Chan, and Scott (2000) provide a survey of global sensitivity analysis with numerous applications in the physical sciences.
520 # $a This dissertation develops some new theory and algorithms for the ANOVA of [0,1]d. It defines a superset importance measure, which can be useful in studying the full interaction of all variables. One of the larger contributions of this dissertation is that, through some identities, it connects global sensitivity indices and the afore-defined superset importance measure to some weighted sums of mean squares, which significantly reduces computational complexity. Then, grouped ANOVA brings the theoretical study one step further. The dissertation also uses these techniques to investigate various functions, from financial valuation, and extreme value theory to bootstrap.
520 # $a Within the ANOVA formulation, we can measure variable importance for both individuals and groups, via numerical integration. Sobol' and his co-authors (Sobol' 1990; Sobol' 1993; Archer, Saltelli, and Sobol' 1997; Sobol' 2001) have developed unbiased Monte Carlo methods for estimating global sensitivity indices expressed through variances of ANOVA component functions.
590 $a School code: 0212.
650 # 0 $a Statistics. $3 182057
650 # 0 $a Economics, Finance. $3 212585
690 $a 0463
690 $a 0508
710 0 # $a Stanford University. $3 212607
773 0 # $g 66-04B. $t Dissertation Abstracts International
790 $a 0212
790 1 0 $a Duffie, Darrell, $e advisor
790 1 0 $a Owen, Art, $e advisor
791 $a Ph.D.
792 $a 2005
856 4 0 $u http://libsw.nuk.edu.tw:81/login?url=http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3171779 $z http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3171779