منابع مشابه
The Deepest Regression Method
Deepest regression (DR) is a method for linear regression introduced by Rousseeuw and Hubert [20]. The DR method is defined as the fit with largest regression depth relative to the data. In this paper we show that DR is a robust method, with breakdown value that converges almost surely to 1/3 in any dimension. We construct an approximate algorithm for fast computation of DR in more than two dim...
متن کاملDeepest Regression in Analytical Chemistry
Recently the concept of regression depth has been introduced [1]. The deepest regression (DR) is a method for linear regression which is defined as the fit with the best depth relative to the data. In this paper we explain the properties of the DR and give some applications of deepest regression in analytical chemistry which involve regression through the origin, polynomial regression, the Mich...
متن کاملConsistency and Robustness of Kernel Based Regression
We investigate properties of kernel based regression (KBR) methods which are inspired by the convex risk minimization method of support vector machines. We first describe the relation between the used loss function of the KBR method and the tail of the response variable Y . We then establish a consistency result for KBR and give assumptions for the existence of the influence function. In partic...
متن کاملOn Robustness in Kernel Based Regression
It is well-known that Kernel Based Regression (KBR) with a least squares loss has some undesirable properties from robustness point of view. KBR with more robust loss functions, e.g. Huber or logistic losses, often give rise to more complicated computations and optimization problems. In classical statistics, robustness is improved by reweighting the original estimate. We study reweighting the K...
متن کاملDeepest Neural Networks
This paper shows that a long chain of perceptrons (that is, a multilayer perceptron, or MLP, with many hidden layers of width one) can be a universal classifier. The classification procedure is not necessarily computationally efficient, but the technique throws some light on the kind of computations possible with narrow and deep MLPs.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 2000
ISSN: 0047-259X
DOI: 10.1006/jmva.1999.1870