Growth Tranformations for General Functions

Last decade the new discrimination technique for estimating of parameters became popular. It is based on the transformation formula for continuous parameters [9]. This formula was obtained as approximation of the Baum-Eagon like growth transformation formula for rational functions of discrete parameters that was introduced in [5]. The paper deals mostly with theoretical aspects related to [5]. One of the goal of this paper is to give several proofs for growth transformations for these transformation formula in the case of continuous parameters. The first proof is based on the modification of the basic principle of adding specific constants that was introduced in [5] and that allowed to extend to rational functions Baum-Eagon like growth transformations for polynomial functions. The other proof is based on the linearization of the problem for nonlinear functions and computing explicitly the growth estimate for linear forms of Gaussians using a sufficiently large specific constant. In the paper we also give a new proof of the growth of Baum-Eagon like transformation formula for arbitrary objective functions of discrete parameters generalizing [5]. And finally, we derive new transformation formula for continuous parameters case and run simulation experiments to compare growth for different transformation formula.

By: Dimitri Kanevsky

Published in: RC22919 in 2003


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