Solving complex regression problems via Algorithmic Inference : a new family of bootstrap algorithms

Regression theory is the hat of various methodologies for approximating a function whose analytical form is typically known up to a finite number of parameters. We use the Algorithmic Inference statistical framework to find regions where non linear functions underlying samples are totally included with a given confidence. The key point is to consider the above parameters and even functions random per se, whose distribution laws we are able to compute either analytically or numerically basing on twisting statistics. The outcoming methods delineate a new family of bootstrap algorithms that are based on replicas consisting of populations compatible with observed statistics in place of dummy samples derived from the observed one. The approach is tested on the problem of estimating the hazard function of non homogeneous negative exponential variables. We discuss both a reconstruction problem and a concrete task arising from benchmarks of leukemia reoccurrence times.