Summary
This work is concerned with simultaneous estimation of coefficients and a scale parameter of a p th-order autoregressive process (X t ). The observations are Y t =V t Z t +(1-V t )X t where (Z t) is a contaminating process and (V t ) represents the proportion of contamination. If (X t ) or (Z t ) have heavy tails both least squares estimates and ordinary M-estimates are seriously affected. Under general conditions we prove consistency and asymptotic normality of a general class of M-estimates which contains some M-estimates studied by Denby and Martin [6].
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Bustos, O.H. General M-estimates for contaminated p th-order autoregressive processes: Consistency and asymptotic normality. Z. Wahrscheinlichkeitstheorie verw Gebiete 59, 491–504 (1982). https://doi.org/10.1007/BF00532805
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DOI: https://doi.org/10.1007/BF00532805