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    <title>Pinboard (cshalizi)</title>
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    <description>recent bookmarks from cshalizi</description>
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  </channel><item rdf:about="http://arxiv.org/abs/1206.0867">
    <title>[1206.0867] Testing linear hypotheses in high-dimensional regressions</title>
    <dc:date>2012-06-07T15:43:09+00:00</dc:date>
    <link>http://arxiv.org/abs/1206.0867</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say $ple 20$. On the other hand, assuming that the data dimension $p$ as well as the number $q$ of regression variables are fixed while the sample size $n$ grows, several asymptotic approximations are proposed in the literature for Wilk's $bLa$ including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension $p$ and a large sample size $n$. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large $p$ and large $n$ context, but also for moderately large data dimensions like $p=30$ or $p=50$. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in MANOVA which is valid for high-dimensional data."]]></description>
<dc:subject>to:NB statistics model_selection likelihood re:model_selection_for_networks high-dimensional_statistics to_read</dc:subject>
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<dc:identifier>https://pinboard.in/u:cshalizi/b:b0bd5626ab41/</dc:identifier>
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    <title>[0805.3906] Inference for Multivariate Normal Mixtures</title>
    <dc:date>2012-02-29T16:12:24+00:00</dc:date>
    <link>http://arxiv.org/abs/0805.3906</link>
    <dc:creator>cshalizi</dc:creator><description><![CDATA["Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical likelihood-based methods, which may have nice practical properties, are inconsistent. In this paper, we recommend a penalized likelihood method for estimating the mixing distribution. We show that the maximum penalized likelihood estimator is strongly consistent when the number of components has a known upper bound. We also explore a convenient EM-algorithm for computing the maximum penalized likelihood estimator. Extensive simulations are conducted to explore the effectiveness and the practical limitations of both the new method and the ratified maximum likelihood estimators. Guidelines are provided based on the simulation results."]]></description>
<dc:subject>statistics mixture_models in_NB have_read re:model_selection_for_networks</dc:subject>
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<dc:identifier>https://pinboard.in/u:cshalizi/b:78c2829656bf/</dc:identifier>
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<item rdf:about="http://www.jstor.org/stable/2333273?seq=1">
    <title>&quot;The power of the Poisson index of dispersion&quot; (JSTOR: Biometrika, Vol. 44, No. 1/2 (Jun., 1957), pp. 286-289)</title>
    <dc:date>2012-02-08T21:11:02+00:00</dc:date>
    <link>http://www.jstor.org/stable/2333273?seq=1</link>
    <dc:creator>cshalizi</dc:creator><dc:subject>statistics re:model_selection_for_networks</dc:subject>
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<dc:identifier>https://pinboard.in/u:cshalizi/b:4988dc870eb0/</dc:identifier>
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