Fitting a Cm-smooth function to data, I

Fitting a Cm - Smooth Function to Data

Suppose we are given a finite subset E ⊂ R and a function f : E → R. How to extend f to a C function F : R → R with C norm of the smallest possible order of magnitude? In this paper and in [20] we tackle this question from the perspective of theoretical computer science. We exhibit algorithms for constructing such an extension function F , and for computing the order of magnitude of its C norm....

PRELIMINARY VERSION Fitting a C-Smooth Function to Data

Fitting a C-Smooth Function to Data II

We exhibit efficient algorithms to perform the following task: Given a function f defined on a finite subset E ⊂ R, compute a C function F on R, with a controlled C norm, that approximates f on the subset E.

A Note on the Smooth Estimator of the Quantile Function with Left-Truncated Data

This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.

Fitting Aggregation Functions to Data: Part I - Linearization and Regularization

The use of supervised learning techniques for fitting weights and/or generator functions of weighted quasi-arithmetic means – a special class of idempotent and nondecreasing aggregation functions – to empirical data has already been considered in a number of papers. Nevertheless, there are still some important issues that have not been discussed in the literature yet. In the first part of this ...