Truncated sequential estimation of the parameter of a first order autoregressive process with dependent noises |
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Authors: | D Fourdrinier V Konev S Pergamenshchikov |
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Institution: | (1) LITIS EA 4108, Univ. Rouen, Rouen, France;(2) Dept. Appl. Math. and Cybernetics, Tomsk State University, Tomsk, Russia;(3) Laboratoire de Math. R. Salem, Univ. Rouen, Rouen, France |
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Abstract: | For a first-order non-explosive autoregressive process with dependent noise, we propose a truncated sequential procedure with
a fixed mean-square accuracy. The asymptotic distribution of the estimator depends on the type of the noise distribution:
it is normal when the noise has a Kotz’s distribution, while it is a mixture of normal distributions if the noise distribution
is a variance mixture of normal distrbutions as well. In both cases, the convergence to the limiting distribution is uniform
in the unknown parameter.
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Keywords: | autoregression model truncated sequential estimators uniform normality |
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