General M-estimates for contaminated p th-order autoregressive processes: Consistency and asymptotic normality |
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| Authors: | Oscar H Bustos |
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| Institution: | (1) IMPA, Estrada Dona Castorina 110, 22460 Rio de Janeiro, Brazil |
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| Abstract: | 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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| Keywords: | |
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