An AM estimate phi of the AR(1) parameter phi is a solution of the M- estimate equation sum from 1 to n of x sub(t-1) Ps (Y sub t - phi (x sub(t-1)/S sub t), where x sub t-1, t=0,2, satisfies the robust filter recursion x' sub t = phi (x' sub t-1) + s sub t psi* ( L y sub t) -psi (x' sub t -1)/s sub b) ...
A new class of robust estimates, called tau-estimates, is introduced in this paper. These estimates have simultaneously the following properties: (1) they are qualitatively robust; (2) their breakdown point is 0.5; and (3) they are highly efficient for regression models with normal errors. These estimates are defined by minimizing a new scale estimate, tau, applied to the residuals. Asymptotically, a tau-estimate is equivalent to an M-estimate with a psi- function ...
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