Related papers: Breakdown and groups

A half century ago, Huber evaluated the minimax asymptotic variance in scalar location estimation, $ \min_\psi \max_{F \in {\cal F}_\epsilon} V(\psi, F) = \frac{1}{I(F_\epsilon^*)} $, where $V(\psi,F)$ denotes the asymptotic variance of the…

The notion of maximal-spacing in several dimensions was introduced and studied by Deheuvels (1983) for data uniformly distributed on the unit cube. Later on, Janson (1987) extended the results to data uniformly distributed on any bounded…

We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recent construction of an equivariant spectral flow by the…

Neural networks are an indispensable model class for many complex learning tasks. Despite the popularity and importance of neural networks and many different established techniques from literature for stabilization and robustification of…

The minimum density power divergence estimator (MDPDE) has gained significant attention in the literature of robust inference due to its strong robustness properties and high asymptotic efficiency; it is relatively easy to compute and can…

Recent works at the interface of algebraic combinatorics, algebraic geometry, number theory, and topology have provided new integer-valued invariants on integer partitions. It is natural to consider the distribution of partitions when…

Discussion of ``Breakdown and groups'' by P. L. Davies and U. Gather [math.ST/0508497]

Discussion of ``Breakdown and groups'' by P. L. Davies and U. Gather [math.ST/0508497]

Discussion of ``Breakdown and groups'' by P. L. Davies and U. Gather [math.ST/0508497]

Discussion of ``Breakdown and groups'' by P. L. Davies and U. Gather [math.ST/0508497]

Discussion of ``Breakdown and groups'' by P. L. Davies and U. Gather [math.ST/0508497]

Discussion of ``Breakdown and groups'' by P. L. Davies and U. Gather [math.ST/0508497]

Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures how good of a regression hyperplane a given query hyperplane is with respect to a set of data points. Under projective duality, this can be interpreted…

Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…

The notion of divergence information of an ensemble of probability distributions was introduced by Jain, Radhakrishnan, and Sen in the context of the ``substate theorem''. Since then, divergence has been recognized as a more natural measure…

The discussion focuses on metric covariance, a new association measure between paired random objects in a metric space, developed by Dubey and M\"uller, and on its relationship with other similar concepts which have previously appeared in…

We consider the problem of breakpoint detection in a regression modeling framework. To that end, we introduce a novel method, the max-EM algorithm which combines a constrained Hidden Markov Model with the Classification-EM (CEM) algorithm.…

This paper studies multivariate nonparametric change point localization and inference problems. The data consists of a multivariate time series with potentially short range dependence. The distribution of this data is assumed to be…

Derivators, introduced independently by Grothendieck and Heller in the 1980s, provide a categorical framework for studying homotopy theory. They are based on the idea that, while the homotopy 1-category of a single model category or…

We present proofs of basic results, including those developed by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by…