Asymptotic theory for description of regions in which Newton-Raphson iterations converge to location M-estimators

Clarke, B.R. (1986) Asymptotic theory for description of regions in which Newton-Raphson iterations converge to location M-estimators. Journal of Statistical Planning and Inference , 15 (C). pp. 71-85.

Abstract

By examination of properties of the function of the sample and location parameter that describes the M-estimating equation for location a detailed probabilistic description of regions from which the Newton-Raphson algorithm converges to the location M-estimator is given. In finite samples an asymptotic distribution can be used to approximate the size of the region from which convergence occurs. This gives experimenters an idea of the tolerance acceptable for an initial estimate to begin an iteration. Empirical evidence is given which highlights the results.