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Modified weighted squared error estimation procedures with special emphasis on the stable laws
Authors:A. S. Paulson  T. A. Delehanty
Affiliation:Rensselaer Polytechnic Institute , Troy, New York, 12181
Abstract:Two families of parameter estimation procedures for the stable laws based on a variant of the characteristic function are provided. The methodology which produces viable computational procedures for the stable laws is generally applicable to other families of distributions across a variety of settings. Both families of procedures may be described as a modified weighted chi-squared minimization procedure, and both explicitly take account of constraints on the parameter space. Influence func-tions for and efficiencies of the estimators are given. If x1, x2, …xn random sample from an unknown distribution F , a method for determining the stable law to which F is attracted is developed. Procedures for regression and autoregres-sion with stable error structure are provided. A number of examples are given.
Keywords:Stable laws  Fourier estimation  empirical characteristic function  domains of attraction  density esti-mation  efficiency  robustness  linear models
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