## Data Depth: Robust Multivariate Analysis, Computational Geometry, and ApplicationsThe 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). |

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### Contents

xi | |

1 | |

Rank tests for multivariate scale difference based on data depth | 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

affine 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 equivariant error rate estimate example Figure finite functional data given halfspace depth hyperplane hyperplane arrangement integer programs intersection points iterations kernel Lemma linear location depth logistic regression lower bound Mathematics Mathematics Subject Classification matrix methods Multivariate Analysis multivariate data observations optimal outlyingness parameter pixel point set primal-dual problem PROOF properties quantile function random rank tests regression depth robust Rousseeuw sample scale curve Section Serfling simplicial depth simplicial median simulated Singh spatial spherical depth spherical median stencil buffer subset support vector machine symmetric Theorem triangles trimmed mean Tukey univariate weak convergence zonoid depth