Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimation of Large Precision Matrices Through Block Penalization   This paper focuses on exploring the sparsity of the inverse covariance matrix
$\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on
each off-diagonal band of the Cholesky factor from its modified Cholesky
decomposition, and penalize each block of parameters using the $L_2$-norm
instead of individual elements. We develop a one-step estimator, and prove an
oracle property which consists of a notion of block sign-consistency and
asymptotic normality. In particular, provided the initial estimator of the
Cholesky factor is good enough and the true Cholesky has finite number of
non-zero off-diagonal bands, oracle property holds for the one-step estimator
even if $p_n \gg n$, and can even be as large as $\log p_n = o(n)$, where the
data $\y$ has mean zero and tail probability $P(|y_j| > x) \leq K\exp(-Cx^d)$,
$d > 0$, and $p_n$ is the number of variables. We also prove an operator norm
convergence result, showing the cost of dimensionality is just $\log p_n$. The
advantage of this method over banding by Bickel and Levina (2008) or nested
LASSO by Levina \emph{et al.} (2007) is that it allows for elimination of
weaker signals that precede stronger ones in the Cholesky factor. A method for
obtaining an initial estimator for the Cholesky factor is discussed, and a
gradient projection algorithm is developed for calculating the one-step
estimate. Simulation results are in favor of the newly proposed method and a
set of real data is analyzed using the new procedure and the banding method.

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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org