Abstract
The autoregressive orders selected by the criterion autoregressive transfer function (CAT) of Parzen (1974), a new version, CAT$^\\ast$, of CAT introduced by Parzen (1977), and the CAT$_2$ criterion of Bhansali (1985) are shown to be asymptotically efficient in the sense defined by Shibata (1980, 1981). A generalization of the penalty function considered by Shibata (1980) is introduced. The order selected by the CAT$_\\alpha$ criterion of Bhansali (1985), with any fixed $\\alpha > 1$, is asymptotically efficient with respect to this generalized penalty function.
Keywords
MathematicsAutoregressive modelGeneralizationApplied mathematicsFunction (biology)Selection (genetic algorithm)Asymptotically optimal algorithmStatisticsMathematical optimizationMathematical analysisArtificial intelligence
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Publication Info
- Year
- 1986
- Type
- article
- Volume
- 14
- Issue
- 1
- Citations
- 22
- Access
- Closed
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Cite This
R. J. Bhansali
(1986).
Asymptotically Efficient Selection of the Order by the Criterion Autoregressive Transfer Function.
The Annals of Statistics
, 14
(1)
.
https://doi.org/10.1214/aos/1176349858
Identifiers
- DOI
- 10.1214/aos/1176349858