The Experts below are selected from a list of 4911 Experts worldwide ranked by ideXlab platform
Peyman Mohajerin Esfahani - One of the best experts on this subject based on the ideXlab platform.
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distributionally robust inverse covariance estimation the wasserstein Shrinkage Estimator
Operations Research, 2021Co-Authors: Viet Anh Nguyen, Daniel Kuhn, Peyman Mohajerin EsfahaniAbstract:Note. The best result in each experiment is highlighted in bold.The optimal solutions of many decision problems such as the Markowitz portfolio allocation and the linear discriminant analysis depen...
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distributionally robust inverse covariance estimation the wasserstein Shrinkage Estimator
2018Co-Authors: Viet Anh Nguyen, Daniel Kuhn, Peyman Mohajerin EsfahaniAbstract:We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model minimizes the worst case (maximum) of Stein's loss across all normal reference distributions within a prescribed Wasserstein distance from the normal distribution characterized by the sample mean and the sample covariance matrix. We prove that this estimation problem is equivalent to a semidefinite program that is tractable in theory but beyond the reach of general purpose solvers for practically relevant problem dimensions $p$. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear Shrinkage Estimator. Besides being invertible and well-conditioned even for $p>n$, the new Shrinkage Estimator is rotation-equivariant and preserves the order of the eigenvalues of the sample covariance matrix. These desirable properties are not imposed ad hoc but emerge naturally from the underlying distributionally robust optimization model. Finally, we develop a sequential quadratic approximation algorithm for efficiently solving the general estimation problem subject to conditional independence constraints typically encountered in Gaussian graphical models.
Michael Wolf - One of the best experts on this subject based on the ideXlab platform.
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nonlinear Shrinkage of the covariance matrix for portfolio selection markowitz meets goldilocks
Review of Financial Studies, 2017Co-Authors: Olivier Ledoit, Michael WolfAbstract:Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many proposals to address the first question exist already. This paper addresses the second question. We promote a new nonlinear Shrinkage Estimator of the covariance matrix that is more flexible than previous linear Shrinkage Estimators and has ‘just the right number’ of free parameters (that is, the Goldilocks principle). In a stylized setting, the nonlinear Shrinkage Estimator is asymptotically optimal for portfolio selection. In addition to theoretical analysis, we establish superior real-life performance of our new Estimator using backtest exercises.
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Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks
Review of Financial Studies, 2017Co-Authors: Olivier Ledoit, Michael WolfAbstract:Markowitz (1952) portfolio selection requires an Estimator of the covariance matrix of returns. To address this problem, we promote a nonlinear Shrinkage Estimator that is more flexible than previous linear Shrinkage Estimators and has just the right number of free parameters (that is, the Goldilocks principle). This number is the same as the number of assets. Our nonlinear Shrinkage Estimator is asymptotically optimal for portfolio selection when the number of assets is of the same magnitude as the sample size. In backtests with historical stock return data, it performs better than previous proposals and, in particular, it dominates linear Shrinkage.
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nonlinear Shrinkage of the covariance matrix for portfolio selection markowitz meets goldilocks
Social Science Research Network, 2017Co-Authors: Olivier Ledoit, Michael WolfAbstract:Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many successful proposals to address the first estimation problem exist by now. This paper addresses the second estimation problem. We promote a nonlinear Shrinkage Estimator of the covariance matrix that is more flexible than previous linear Shrinkage Estimators and has 'just the right number' of free parameters to estimate (that is, the Goldilocks principle). It turns out that this number is the same as the number of assets in the investment universe. Under certain high-level assumptions, we show that our nonlinear Shrinkage Estimator is asymptotically optimal for portfolio selection in the setting where the number of assets is of the same magnitude as the sample size. For example, this is the relevant setting for mutual fund managers who invest in a large universe of stocks. In addition to theoretical analysis, we study the real-life performance of our new Estimator using backtest exercises on historical stock return data. We find that it performs better than previous proposals for portfolio selection from the literature and, in particular, that it dominates linear Shrinkage.
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improved estimation of the covariance matrix of stock returns with an application to portfolio selection
Journal of Empirical Finance, 2003Co-Authors: Olivier Ledoit, Michael WolfAbstract:This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing Estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as Shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our Shrinkage Estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multi-factor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing Estimators, including multi-factor models.
Olivier Ledoit - One of the best experts on this subject based on the ideXlab platform.
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nonlinear Shrinkage of the covariance matrix for portfolio selection markowitz meets goldilocks
Review of Financial Studies, 2017Co-Authors: Olivier Ledoit, Michael WolfAbstract:Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many proposals to address the first question exist already. This paper addresses the second question. We promote a new nonlinear Shrinkage Estimator of the covariance matrix that is more flexible than previous linear Shrinkage Estimators and has ‘just the right number’ of free parameters (that is, the Goldilocks principle). In a stylized setting, the nonlinear Shrinkage Estimator is asymptotically optimal for portfolio selection. In addition to theoretical analysis, we establish superior real-life performance of our new Estimator using backtest exercises.
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Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks
Review of Financial Studies, 2017Co-Authors: Olivier Ledoit, Michael WolfAbstract:Markowitz (1952) portfolio selection requires an Estimator of the covariance matrix of returns. To address this problem, we promote a nonlinear Shrinkage Estimator that is more flexible than previous linear Shrinkage Estimators and has just the right number of free parameters (that is, the Goldilocks principle). This number is the same as the number of assets. Our nonlinear Shrinkage Estimator is asymptotically optimal for portfolio selection when the number of assets is of the same magnitude as the sample size. In backtests with historical stock return data, it performs better than previous proposals and, in particular, it dominates linear Shrinkage.
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nonlinear Shrinkage of the covariance matrix for portfolio selection markowitz meets goldilocks
Social Science Research Network, 2017Co-Authors: Olivier Ledoit, Michael WolfAbstract:Markowitz (1952) portfolio selection requires estimates of (i) the vector of expected returns and (ii) the covariance matrix of returns. Many successful proposals to address the first estimation problem exist by now. This paper addresses the second estimation problem. We promote a nonlinear Shrinkage Estimator of the covariance matrix that is more flexible than previous linear Shrinkage Estimators and has 'just the right number' of free parameters to estimate (that is, the Goldilocks principle). It turns out that this number is the same as the number of assets in the investment universe. Under certain high-level assumptions, we show that our nonlinear Shrinkage Estimator is asymptotically optimal for portfolio selection in the setting where the number of assets is of the same magnitude as the sample size. For example, this is the relevant setting for mutual fund managers who invest in a large universe of stocks. In addition to theoretical analysis, we study the real-life performance of our new Estimator using backtest exercises on historical stock return data. We find that it performs better than previous proposals for portfolio selection from the literature and, in particular, that it dominates linear Shrinkage.
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improved estimation of the covariance matrix of stock returns with an application to portfolio selection
Journal of Empirical Finance, 2003Co-Authors: Olivier Ledoit, Michael WolfAbstract:This paper proposes to estimate the covariance matrix of stock returns by an optimally weighted average of two existing Estimators: the sample covariance matrix and single-index covariance matrix. This method is generally known as Shrinkage, and it is standard in decision theory and in empirical Bayesian statistics. Our Shrinkage Estimator can be seen as a way to account for extra-market covariance without having to specify an arbitrary multi-factor structure. For NYSE and AMEX stock returns from 1972 to 1995, it can be used to select portfolios with significantly lower out-of-sample variance than a set of existing Estimators, including multi-factor models.
Isaac Luginaah - One of the best experts on this subject based on the ideXlab platform.
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Shrinkage estimation in general linear models
Computational Statistics & Data Analysis, 2009Co-Authors: Severien Nkurunziza, Karen Y Fung, Daniel Krewski, Isaac LuginaahAbstract:We propose a James-Stein-type Shrinkage Estimator for the parameter vector in a general linear model when it is suspected that some of the parameters may be restricted to a subspace. The James-Stein Estimator is shown to demonstrate asymptotically superior risk performance relative to the conventional least squares Estimator under quadratic loss. An extensive simulation study based on a multiple linear regression model and a logistic regression model further demonstrates the improved performance of this James-Stein Estimator in finite samples. The application of this new Estimator is illustrated using Ontario newborn infants data spanning four fiscal years.
Viet Anh Nguyen - One of the best experts on this subject based on the ideXlab platform.
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distributionally robust inverse covariance estimation the wasserstein Shrinkage Estimator
Operations Research, 2021Co-Authors: Viet Anh Nguyen, Daniel Kuhn, Peyman Mohajerin EsfahaniAbstract:Note. The best result in each experiment is highlighted in bold.The optimal solutions of many decision problems such as the Markowitz portfolio allocation and the linear discriminant analysis depen...
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distributionally robust inverse covariance estimation the wasserstein Shrinkage Estimator
2018Co-Authors: Viet Anh Nguyen, Daniel Kuhn, Peyman Mohajerin EsfahaniAbstract:We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model minimizes the worst case (maximum) of Stein's loss across all normal reference distributions within a prescribed Wasserstein distance from the normal distribution characterized by the sample mean and the sample covariance matrix. We prove that this estimation problem is equivalent to a semidefinite program that is tractable in theory but beyond the reach of general purpose solvers for practically relevant problem dimensions $p$. In the absence of any prior structural information, the estimation problem has an analytical solution that is naturally interpreted as a nonlinear Shrinkage Estimator. Besides being invertible and well-conditioned even for $p>n$, the new Shrinkage Estimator is rotation-equivariant and preserves the order of the eigenvalues of the sample covariance matrix. These desirable properties are not imposed ad hoc but emerge naturally from the underlying distributionally robust optimization model. Finally, we develop a sequential quadratic approximation algorithm for efficiently solving the general estimation problem subject to conditional independence constraints typically encountered in Gaussian graphical models.
