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Consistent cross-validatory model-selection for dependent data: hv-block cross-validation. (English) Zbl 1011.62118

Summary: This paper considers the impact of J. Shao’s [J. Am. Stat. Assoc. 88, No. 422, 486-494 (1993; Zbl 0773.62051)] recent results regarding the asymptotic inconsistency of model selection via leave-one-out cross-validation on \(h\)-block cross-validation, a cross-validatory method for dependent data proposed by P. Burman, E. Chow and D. Nolan [Biometrika 81, No. 2, 351-358 (1994)]. It is show that \(h\)-block cross-validation is inconsistent in the sense of Shao and therefore is not asymptotically optimal. A modification of the \(h\)-block method, dubbed ‘hv-block’ cross-validation, is proposed which is asymptotically optimal. The proposed approach is consistent for general stationary observations in the sense that the probability of selecting the model with the best predictive ability converges to 1 as the total number of observations approaches infinity.
This extends existing results and yields a new approach which contains leave-one-out cross-validation, leave-\(n_v\)-out cross-validation, and \(h\)-block cross-validation as special cases. Applications are considered.

MSC:

62P20 Applications of statistics to economics
62J05 Linear regression; mixed models

Citations:

Zbl 0773.62051
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References:

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