Asymptotic Distributions of Some Scale Estimators in Nonlinear Models With Long Memory Errors Having Infinite Variance

To have scale†invariant M estimators of regression parameters in regression models, there is a need for a robust, scale†invariant estimator of a scale parameter. Two such estimators are the median of the absolute residuals, s1, and the median of the absolute differences of pairwise residuals, s2. The asymptotic distributions of these estimators in regression models when errors have finite variances are known in case the errors are either i.i.d. or form a long†memory stationary process. Since M estimators are robust against heavy†tailed error distributions, it is natural to know whether these scale estimators are consistent under heavy†tailed error distribution assumptions. This article derives their limiting distributions when errors form a linear, long†memory, stationary process with α†stable (1