A Fast and Globally Convergent Method for Estimating General Scale-Shape Distributions

• Activity Number: 680
• Type: Contributed
• Date/Time: Thursday, August 5, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Kai-Sheng Song Song*+
• Companies: University of North Texas
• Keywords: Algorithms ; Global Convergence ; Fixed Point ; Real-time ; Signal Processing ; Scale-shape

Abstract

Many applications in real-time signal processing such as in implantable medical devices require automatic algorithms for rapid characterizations of noisy source signals through fast and accurate estimation of parametric distributions. We present a fast and globally convergent algorithm for estimating general scale-shape distributions. It is based on a scale-independent shape equation with desirable global properties. We demonstrate that the equation has a unique global root on its domain at the true parameter value and the root of the sample estimating equation is consistent for estimating the true parameter. We establish that with probability tending to one the Newton-Raphson algorithm for computing the root of the sample estimating equation converges globally to the root from any starting value. Finite-sample performance of the method is demonstrated through numerical examples.