## Data Depth: Robust Multivariate Analysis, Computational Geometry, and ApplicationsRegina Y. Liu, Robert Joseph Serfling, Diane L. Souvaine 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). |

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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 affine transformations algorithm analysis applications approach arrangement assume bounds buffer cell central classification complexity compute consider containing contours convergence convex hull corresponding curves data depth data points data set defined definition denote depth function described dimension discussed distance distribution dual error estimate example exists Figure follows formed frame geometry given halfspace depth hyperplane implementation intersection introduced Journal linear Mathematics matrix mean measure median methods multivariate nonparametric Note notion observations obtained operations optimal outlyingness parameter performance pixel plane position present probability problem procedure PROOF properties proposed quantile random rank regions regression respect robust robust estimate Rousseeuw rule sample scale scale curve Science simplicial depth space spherical Statistics Table Theorem univariate vector volume zonoid