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1

Tsukuma, Hisayuki, and Tatsuya Kubokawa. Shrinkage Estimation for Mean and Covariance Matrices. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1596-5.

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2

Jong, Robert M. de. Consistency of kernel estimators of heteroscedastic and autocorrelated covariance matrices. Cardiff: Cardiff Business School, 1996.

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3

Srivastava, M. S. Classification with a preassigned error rate when two covariance matrices are equal. Toronto: University of Toronto, Dept. of Statistics, 1998.

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4

Woodruff, David. A note on a relationship between covariance matrices and consistently estimated variance components. Iowa City, Iowa: American College Testing Program, 1995.

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5

U.S. Nuclear Regulatory Commission. Division of Systems Analysis and Regulatory Effectiveness. and Oak Ridge National Laboratory, eds. PUFF-III: A code for processing ENDF uncertainty data into multigroup covariance matrices. Washington, DC: U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, 2000.

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6

U.S. Nuclear Regulatory Commission. Division of Systems Analysis and Regulatory Effectiveness. and Oak Ridge National Laboratory, eds. PUFF-III: A code for processing ENDF uncertainty data into multigroup covariance matrices. Washington, DC: U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, 2000.

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7

Kubokawa, T. Robust improvements in estimation of mean and covariance matrices in elliptically contoured distribution. Toronto: University of Toronto, Dept. of Statistics, 1997.

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8

Pynnönen, Seppo. Testing for additional information in variables in multivariate normal classification with unequal covariance matrices. Vaasa: Universitas Wasaensis, 1988.

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9

Bose, Arup, and Monika Bhattacharjee. Large Covariance and Autocovariance Matrices. Taylor & Francis Group, 2018.

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10

Bose, Arup. Large Covariance and Autocovariance Matrices. Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9780203730652.

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11

Bose, Arup, and Monika Bhattacharjee. Large Covariance and Autocovariance Matrices. Taylor & Francis Group, 2018.

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12

Bose, Arup, and Monika Bhattacharjee. Large Covariance and Autocovariance Matrices. Taylor & Francis Group, 2020.

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13

Large Covariance and Autocovariance Matrices. Taylor & Francis Group, 2018.

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14

Bose, Arup, and Monika Bhattacharjee. Large Covariance and Autocovariance Matrices. Taylor & Francis Group, 2018.

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15

Bose, Arup, and Monika Bhattacharjee. Large Covariance and Autocovariance Matrices. Taylor & Francis Group, 2018.

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16

Tsukuma, Hisayuki, and Tatsuya Kubokawa. Shrinkage Estimation for Mean and Covariance Matrices. Springer, 2020.

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17

Tsukuma, Hisayuki, and Tatsuya Kubokawa. Shrinkage Estimation for Mean and Covariance Matrices. Springer, 2020.

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18

Bai, Zhidong, Jianfeng Yao, and Shurong Zheng. Large Sample Covariance Matrices and High-Dimensional Data Analysis. Cambridge University Press, 2015.

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19

Large Sample Covariance Matrices and High-Dimensional Data Analysis. Cambridge University Press, 2015.

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20

Zinn-Justin, Paul, and Jean-Bernard Zuber. Multivariate statistics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.28.

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This article considers some classical and more modern results obtained in random matrix theory (RMT) for applications in statistics. In the classic paradigm of parametric statistics, data are generated randomly according to a probability distribution indexed by parameters. From this data, which is by nature random, the properties of the deterministic (and unknown) parameters may be inferred. The ability to infer properties of the unknown Σ (the population covariance matrix) will depend on the quality of the estimator. The article first provides an overview of two spectral statistical techniques, principal components analysis (PCA) and canonical correlation analysis (CCA), before discussing the Wishart distribution and normal theory. It then describes extreme eigenvalues and Tracy–Widom laws, taking into account the results obtained in the asymptotic setting of ‘large p, large n’. It also analyses the results for the limiting spectra of sample covariance matrices..
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21

PUFF-III: A code for processing ENDF uncertainty data into multigroup covariance matrices. Washington, DC: U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, 2000.

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22

A Linear Algebra Primer for Financial Engineering: Covariance Matrices, Eigenvectors, OLS, and more. FE Press, LLC, 2014.

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23

Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. Relativistic Wave Equations. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0006.

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Relativistically covariant wave equations for scalar, spinor, and vector fields. Plane wave solutions and Green’s functions. The Klein–Gordon equation. The Dirac equation and the Clifford algebra of γ‎ matrices. Symmetries and conserved currents. Hamiltonian and Lagrangian formulations. Wave equations for spin-1 fields.
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24

Chirembo, Anderson Mayotcha. Direct versus indirect methods for the estimation of variance-covariance matrices and regression parameters when data are skewed and incomplete. 1995.

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25

Back, Kerry E. Factor Models. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0006.

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The CAPM and factor models in general are explained. Factors can be replaced by the returns or excess returns that are maximally correlated (the projections of the factors). A factor model is equivalent to an affine representation of an SDF and to spanning a return on the mean‐variance frontier. The use of alphas for performance evaluation is explained. Statistical factor models are defined as models in which factors explain the covariance matrix of returns. A proof is given of the Arbitrage Pricing Theory, which states that statistical factors are approximate pricing factors. The CAPM and the Fama‐French‐Carhart model are evaluated relative to portfolios based on sorts on size, book‐to‐market, and momentum.
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