The Determination of the Order of an Autoregression

Hannan, E. J.; Quinn, Barry

doi:10.1111/j.2517-6161.1979.tb01072.x

Cited by 2,082 publications

(1,007 citation statements)

References 10 publications

Supporting

Mentioning

976

Contrasting

Unclassified

Order By: Relevance

“…In our framework, this means that s belongs to some model S m with minimal dimension that we want to find: this is the consistency point of view. The following criteria have been designed to find it with probability tending to one when ε goes to zero (and the list of models remains fixed): BIC (Akaike, [5] or equivalently Schwarz, [35]) and Hannan and Quinn [20]. For a recent analysis of such criteria, see Guyon and Yao [19].…”

Section: Some Historical Remarks About Model Selectionmentioning

confidence: 99%

Minimal Penalties for Gaussian Model Selection

Birgé

Massart

2006

Probab. Theory Relat. Fields

233

344

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This paper is mainly devoted to a precise analysis of what kind of penalties should be used in order to perform model selection via the minimization of a penalized least-squares type criterion within some general Gaussian framework including the classical ones. As compared to our previous paper on this topic (Birgé and Massart in J. Eur. Math. Soc. 3, 203-268 (2001)), more elaborate forms of the penalties are given which are shown to be, in some sense, optimal. We indeed provide more precise upper bounds for the risk of the penalized estimators and lower bounds for the penalty terms, showing that the use of smaller penalties may lead to disastrous results. These lower bounds may also be used to design a practical strategy that allows to estimate the penalty from the data when the amount of noise is unknown. We provide an illustration of the method for the problem of estimating a piecewise constant signal in Gaussian noise when neither the number, nor the location of the change points are known.

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Section: Some Historical Remarks About Model Selectionmentioning

confidence: 99%

Minimal Penalties for Gaussian Model Selection

Birgé

Massart

2006

Probab. Theory Relat. Fields

233

344

View full text Add to dashboard Cite

show abstract

“…Our examples are misspecified regression models for univariate data Yt, 1 <_ t ~ N, which are estimated, given column vector regressors xt, Hannan and Quinn (1979), WN =-21oglogN. When two competing regressor processes x~ 1) and x~ 2) are being compared by (1.2), the one with the smaller criterion value is favored.…”

Section: Introductionmentioning

confidence: 99%

Counterexamples to parsimony and BIC

Findley

1991

Ann Inst Stat Math

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“…The Fig. 1 The discrete wavelet transform of a function and function + Gaussian white noise, respectively asymptotic properties and consistency of BIC are well known and have been described extensively in the literature (Hannan and Quinn 1979;Haughton 1988). The optimum number of clusters minimizes the quantity…”

Section: Cem Algorithm (Classification Expectation Aximization)mentioning

confidence: 99%

DWT–CEM: an algorithm for scale-temporal clustering in fMRI

et al. 2007

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The number of studies using functional magnetic resonance imaging (fMRI) has grown very rapidly since the first description of the technique in the early 1990s. Most published studies have utilized data analysis methods based on voxel-wise application of general linear models (GLM). On the other hand, temporal clustering analysis (TCA) focuses on the identification of relationships between cortical areas by measuring temporal common properties. In its most general form, TCA is sensitive to the low signal-to-noise ratio of BOLD and is dependent on subjective choices of filtering parameters. In this paper, we introduce a method for wavelet-based clustering of time-series data and show that it may be useful in data sets with low signal-to-noise ratios, allowing the automatic selection of the optimum number of clusters. We also provide examples of the technique applied to simulated and real fMRI datasets.

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The Determination of the Order of an Autoregression

Cited by 2,082 publications

References 10 publications

Minimal Penalties for Gaussian Model Selection

Minimal Penalties for Gaussian Model Selection

Counterexamples to parsimony and BIC

DWT–CEM: an algorithm for scale-temporal clustering in fMRI

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