Strong Consistency of the PLS Criterion for Order Determination of Autoregressive Processes

Hemerly, Elder Moreira; Davis, Martin

doi:10.1214/aos/1176347154

Cited by 57 publications

(21 citation statements)

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“…Consistency results for the predictive MDL principle can be found in [15], [17], and [32] for regression models, [23], and [31] for time-series models, and [53] for stochastic regression models. For exponential families, [27] gives a consistency result for BIC.…”

Section: B Consistency Of the MDL Order Estimatesmentioning

confidence: 90%

The minimum description length principle in coding and modeling

Barron

Rissanen

1998

IEEE Trans. Inform. Theory

814

649

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Abstract-We review the principles of Minimum Description Length and Stochastic Complexity as used in data compression and statistical modeling. Stochastic complexity is formulated as the solution to optimum universal coding problems extending Shannon's basic source coding theorem. The normalized maximized likelihood, mixture, and predictive codings are each shown to achieve the stochastic complexity to within asymptotically vanishing terms. We assess the performance of the minimum description length criterion both from the vantage point of quality of data compression and accuracy of statistical inference. Context tree modeling, density estimation, and model selection in Gaussian linear regression serve as examples.

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Section: B Consistency Of the MDL Order Estimatesmentioning

confidence: 90%

The minimum description length principle in coding and modeling

Barron

Rissanen

1998

IEEE Trans. Inform. Theory

814

649

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“…1 it will select the data-generating model, if such a model exists, with probability one (cf. Dawid, 1992;De Luna & Skouras, 2003;Hemerly & Davis, 1989).…”

Section: Pros and Cons Of Accumulating Prediction Errorsmentioning

confidence: 99%

Accumulative prediction error and the selection of time series models

Wagenmakers

Grünwald

Steyvers

2006

Journal of Mathematical Psychology

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“…Examples are [22,10,13,25,17]. In all these papers it is shown that either the regret or the redundancy grows as k 2 ln n + o(ln n), either in expectation or almost surely.…”

Section: Main Result Informallymentioning

confidence: 99%

Asymptotic Log-Loss of Prequential Maximum Likelihood Codes

Grünwald

Rooij

2005

Learning Theory

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We analyze the Dawid-Rissanen prequential maximum likelihood codes relative to oneparameter exponential family models M. If data are i.i.d. according to an (essentially) arbitrary P , then the redundancy grows at rate 1 2 c ln n. We show that c = σ 2 1 /σ 2 2 , where σ 2 1 is the variance of P , and σ 2 2 is the variance of the distribution M * ∈ M that is closest to P in KL divergence. This shows that prequential codes behave quite differently from other important universal codes such as the 2-part MDL, Shtarkov and Bayes codes, for which c = 1. This behavior is undesirable in an MDL model selection setting.

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Strong Consistency of the PLS Criterion for Order Determination of Autoregressive Processes

Cited by 57 publications

References 0 publications

The minimum description length principle in coding and modeling

The minimum description length principle in coding and modeling

Accumulative prediction error and the selection of time series models

Asymptotic Log-Loss of Prequential Maximum Likelihood Codes

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