Data Depth: Robust Multivariate Analysis, Computational Geometry, and ApplicationsRegina Y. Liu, Robert Joseph Serfling, Diane L. Souvaine American Mathematical Soc. - 246 pages The book is a collection of some of the research presented at the workshop of the same name held in May 2003 at Rutgers University. The workshop brought together researchers from two different communities: statisticians and specialists in computational geometry. The main idea unifying these two research areas turned out to be the notion of data depth, which is an important notion both in statistics and in the study of efficiency of algorithms used in computational geometry. Many ofthe articles in the book lay down the foundations for further collaboration and interdisciplinary research. Information for our distributors: Co-published with the Center for Discrete Mathematics and Theoretical Computer Science beginning with Volume 8. Volumes 1-7 were co-published with theAssociation for Computer Machinery (ACM). |
From inside the book
Results 6-10 of 82
Page 7
... dimensional unit ball , and define Odn ( x , X ) = || Q21 ( x || , i.e. , the magnitude of the centered rank of x in the data set ( we elaborate on quantile and centered rank functions later ) . Using the spatial quantile function [ 9 ] ...
... dimensional unit ball , and define Odn ( x , X ) = || Q21 ( x || , i.e. , the magnitude of the centered rank of x in the data set ( we elaborate on quantile and centered rank functions later ) . Using the spatial quantile function [ 9 ] ...
Page 9
... dimensions 2 and 3 , using contours along with rays to outlying points . They answer questions like : where is the " middle half " of the data ? ( See [ 29 ] , [ 46 ] . ) DD , PP , QQ PLOTS , ETC. One may compare two samples by a plot ...
... dimensions 2 and 3 , using contours along with rays to outlying points . They answer questions like : where is the " middle half " of the data ? ( See [ 29 ] , [ 46 ] . ) DD , PP , QQ PLOTS , ETC. One may compare two samples by a plot ...
Page 11
... dimensional median . The quantile function QF ( · ) has an inverse Q1 ( x ) , x Є Rd , satisfying QFQF1 ( x ) ) . We may interpret this inverse as a centered rank function in Rd . Its magnitude || Q1 ( x ) || in [ 0 , 1 ) measures the ...
... dimensional median . The quantile function QF ( · ) has an inverse Q1 ( x ) , x Є Rd , satisfying QFQF1 ( x ) ) . We may interpret this inverse as a centered rank function in Rd . Its magnitude || Q1 ( x ) || in [ 0 , 1 ) measures the ...
Page 12
... dimensional space as analogues of rank and order statistics in univariate inference was introduced by Tukey ( 1975 ) , formulating the halfspace depth on the data space . The properties and performance of this depth function have been ...
... dimensional space as analogues of rank and order statistics in univariate inference was introduced by Tukey ( 1975 ) , formulating the halfspace depth on the data space . The properties and performance of this depth function have been ...
Contents
xi | |
1 | |
17 | |
On scale curves for nonparametric description of dispersion | 37 |
Data analysis and classification with the zonoid depth | 49 |
On some parametric nonparametric and semiparametric discrimination rules | 61 |
Regression depth and support vector machine | 71 |
Spherical data depth and a multivariate median | 87 |
Impartial trimmed means for functional data | 121 |
Geometric measures of data depth | 147 |
Computation of halfspace depth using simulated annealing | 159 |
Primaldual algorithms for data depth | 171 |
An improved definition analysis and efficiency for the finite sample case | 195 |
Fast algorithms for frames and point depth | 211 |
Statistical data depth and the graphics hardware | 223 |
Depthbased classification for functional data | 103 |
Common terms and phrases
algorithm Annals of Statistics bivariate breakdown point buffer cell center-outward central region classification Computational Geometry Computer Science containing convergence convex hull Data Analysis data depth data points data set defined denote density depth contours depth function depth measures depth-based dimensional distribution dual error rate estimate example Figure finite functional data given halfspace depth hyperplane hyperplane arrangement integer programs iterations kernel Lemma linear location depth logistic regression lower bound Mathematics Mathematics Subject Classification matrix methods Multivariate Analysis multivariate data ncomplete O(n² optimal outlyingness parameter pixel point set problem PROOF properties quantile function random rank tests regression depth robust Rousseeuw sample scale curve Section Serfling simplicial depth simplicial median simulated spatial spherical depth spherical median stencil buffer subset support vector machine symmetric Theorem triangles trimmed mean Tukey univariate weak convergence zonoid depth
Popular passages
Page 17 - The discussion on aviation safety in this paper reflects the views of the authors, who are solely responsible for the accuracy of the analysis results presented herein, and does not necessarily reflect the official view or policy of the FAA.
Page 189 - K. Miller, S. Ramaswami, P. Rousseeuw, T. Sellares, D. Souvaine, I. Streinu and A. Struyf, Fast implementation of depth contours using topological sweep, Proceedings of the Twelfth ACM-SIAM Symposium on Discrete Algorithms, Washington, DC (2001), 690-699.
Page 157 - S. Jadhav and A. Mukhopadhyay. Computing a centerpoint of a finite planar set of points in linear time.
Page 34 - R. Liu, J. Parelius, and K. Singh, Multivariate analysis by data depth: descriptive statistics, graphics and inference (with discussions), Annals of Statistics 27 (1999), 783-858.
Page 188 - A. Marzetta, K. Fukuda and J. Nievergelt, The parallel search bench ZRAM and its applications, Annals of Operations Research (1999), 45-63.
Page 34 - Structural properties and convergence results for contours of sample statistical depth functions.
Page 168 - I. Ruts, and PJ Rousseeuw, Computing depth contours of bivariate point clouds, Computational Statistics and Data Analysis 23 (1996), 153-168.
Page 118 - Computing depth contours of bivariate point clouds. Computational Statistics and Data Analysis, 23, pp. 153-168. Struyf, A. and Rousseeuw, PJ (2000). High-dimensional computation of the deepest location. Computational Statistics and Data Analysis, to appear. Tukey, JW (1975), Mathematics and the picturing of data.
Page 85 - Steinwart. On the influence of the kernel on the consistency of support vector machines. Journal of Machine Learning Research, 2:67-93, 2002.