Deepest condolences

A Letter of Condolences

To late Professor Jung Soon Shin, Sir, we always felt that you would be with us as our mentor to the end. Now that you have suddenly left us, it seems as though our world is caving in and the sky is falling down. Why did you depart your loving family and your disciples so soon? You were a great support to us in this world, but as now you have left for heaven, we, with broken heartedness, are of...

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...

Deepest 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.

Deepest 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...

Asymptotics Of The Deepest Line