Extends covariance estimation with multiple targets for better performance.
problem Improving covariance estimation for multiple targets.
method Combines multiple constant matrices with sample covariance matrix, derives estimators and proves convergence.
result The multi-target linear shrinkage estimator outperforms other estimators in various situations.
WeSpeR speeds up non-linear shrinkage for high-dimensional weighted covariance.
problem Computing non-linear shrinkage formulas for high-dimensional weighted sample covariance.
method Derive extit{WeSpeR} algorithm using asymptotic sample spectrum properties.
result Significantly speeds up non-linear shrinkage in dimensions higher than 1000.
New method improves covariance estimation for weighted samples.
problem Improving covariance estimation for weighted sample data.
method Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
result Asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators of weighted sample covariances.
Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on factor models and shrinkage. Recent work of Ledoit and Wolf has extended the sh…
Paper proposes a new method for covariance estimation using M-estimators with eigenvalue shrinkage.
problem Estimating covariance matrices in heavy-tailed distributions.
method Replaces shrinkage sample covariance matrix with M-estimator of scatter matrix and optimizes shrinkage parameter.
result Shrinkage M-estimators outperform shrinkage SCM in heavy-tailed distributions.
Improved covariance matrix forecasting for S&P 500 using factor models and shrinkage.
problem Forecasting large covariance matrices of returns in finance.
method Decompose covariance matrix into firm-level factors and sectoral restrictions. Estimate using VHAR models with LASSO.
result Significantly improved forecasting precision compared to benchmarks.
This work extends Ledoit-Wolf shrinkage to unknown mean covariance estimation.
problem Large dimensional covariance matrix estimation with unknown mean under Kolmogorov asymptotics.
method Extending Ledoit-Wolf linear shrinkage to translation-invariant estimators, proving their convergence properties.
result A new estimator outperforms other standard estimators empirically.
Self-distillation optimally improves model performance in spiked covariance models.
problem Improving model performance in spiked covariance models.
method Developed spectral shrinkage estimators and analyzed self-distillation.
result Self-distillation achieves optimal performance among spectral shrinkage estimators for spiked covariance matrices.
In this work we construct an optimal linear shrinkage estimator for the covariance matrix in high dimensions. The recent results from the random matrix theory allow us to find the asymptotic deterministic equivalents of the optimal shrinkage intensities and estimate them consistently. The developed distribution-free es…
SCOPE estimator improves covariance and precision matrix estimation.
problem Estimating covariance and precision matrices accurately.
method Distributionally robust optimization with convex spectral divergence.
result SCOPE estimator reduces spectral bias and improves condition number.
This study evaluates shrinkage estimators for improving mean and covariance in portfolio optimization.
problem Estimation errors in expected returns and covariance matrix in mean-variance model.
method Examined five shrinkage estimators for expected returns and eleven for covariance matrix across six datasets.
result GMV model with Ledoit Wolf COV2 outperforms traditional methods in most scenarios.
Covariance shrinkage via stochastic interpolation
problem High-dimensional covariance estimation
method Recasting shrinkage as empirical risk minimization
result Reduces statistical risk through scheduling, flow maps, and early stopping
Non-linear shrinkage isn't optimal for portfolio optimization, especially when asset dependence is non-stationary.
problem Optimizing portfolios with non-stationary asset dependence structures.
method Derived and compared non-linear shrinkage with an optimal target for covariance matrix estimation.
result Non-linear shrinkage can be significantly improved for portfolio optimization.
Estimates covariance matrices with correlations between samples.
problem Estimating large-dimensional covariance matrices with correlated samples.
method Generalized Marcenko-Pastur equation and Ledoit-Peche shrinkage estimator using random matrix theory and free probability. Developed an efficient algorithm based on Ledoit-Wolf kernel estimation.
result Efficient algorithm for estimating large covariance matrices with correlations.
New method estimates covariance matrices without restrictive assumptions.
problem Estimating high-dimensional covariance matrices under restrictive assumptions.
method Distributionally robust covariance estimation problems with mild conditions.
result Robust estimators are efficient, consistent, and perform well.
New estimator improves covariance matrix estimation under distributional uncertainty.
problem Estimating inverse covariance matrix under distributional uncertainty.
method Distributionally robust optimization with Wasserstein ambiguity set.
result Analytical solution as nonlinear shrinkage estimator.
The paper calibrates shrinkage covariance estimators for spectral functionals in high dimensions.
problem Calibrating shrinkage covariance estimators for spectral functionals in high dimensions.
method Derives first-order null laws, distribution-free Davis-Kahan bands, and calibrated tests for spectral functionals under shrinkage.
result Calibrated tests and intervals for spectral functionals are provided, addressing the issue of estimation noise and shrinkage bias.
Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits out-of-sample instabilities of the sample covariance matrix, is not an alternativ…
Extended study improves covariance matrix estimation for portfolio managers.
problem Limited sample sizes and poor performance of PCA estimator in high-dimensional returns.
method Developed a more general shrinkage framework targeting further information.
result Improves the PCA estimator of beta by shrinking it toward a target.
Developed shrinkage methods for Poisson regression models with experts to handle multicollinearity.
problem Multicollinearity in Poisson regression models with experts.
method Ridge and Liu-type shrinkage methods.
result Shrinkage methods offer more reliable estimates for coefficients in multicollinearity.
Nash integrates covariate-specific side info into sparse regression via neural networks.
problem Sparse linear regression struggles with covariates exhibiting structure or coming from heterogeneous sources.
method Neural Adaptive Shrinkage (Nash) framework that integrates side information into sparse regression via neural networks. Uses split variational empirical Bayes algorithm.
result Nash improves accuracy and adaptability over existing methods in real data experiments.
Improved portfolio optimization method reduces risk and improves performance.
problem Minimizing risk in large portfolios with limited data.
method Combines Tikhonov regularization and direct shrinkage of portfolio weights.
result Significantly reduces out-of-sample variance and Sharpe ratio compared to existing methods.
Enhances UPSA to reduce noise in financial data.
problem Noise in financial data affects UPSA's performance.
method Time-averaging optimal penalty weights and using Average Oracle correlation eigenvalues.
result Combining time-averaging and Average Oracle correlation eigenvalues improves UPSA's performance.
New covariance estimator for financial portfolios.
problem Estimating large financial covariances in non-stationary environments.
method Exponentially weighted averages and cross-validation for nonlinearly shrinking sample eigenvalues.
result Our estimator performs well in large dimensions compared to existing estimators.
Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target. In a general framework, independent of a specific estimator, we extend the shrink…
Average Oracle outperforms DCC+NLS in portfolio optimization.
problem Optimizing portfolio performance in volatile markets.
method Comparing the Average Oracle to various DCC+NLS variants.
result The Average Oracle consistently yields higher Sharpe ratios.
Develops a sparsity-inducing Bayesian Causal Forest for estimating heterogeneous treatment effects.
problem Estimating heterogeneous treatment effects using observational data with varying degrees of sparsity.
method Introduces a sparsity-inducing version of Bayesian Causal Forests with additional priors to adjust covariate weights.
result Improves adaptability to sparse data generating processes and uncovering moderating factors driving heterogeneity.
Study compares different covariance estimation methods for portfolio allocation.
problem Comparing methods for estimating covariance and precision matrices in portfolio allocation.
method Gaussian Graphical Model (GGM), Shrinkage, Thresholding, Random Matrix Theory (RMT) methods.
result GGM methods outperform other methods in predictive ability for portfolio allocation.
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables p→∞ and the sample size n→∞ so that p/n→c∈(0,+∞). The precision matrix is estimated directly, wit…
The study optimizes portfolios under transaction costs and model uncertainty, showing the effectiveness of turnover penalization.
problem Optimizing portfolios under transaction costs and model uncertainty.
method Theoretical and empirical analysis linking turnover penalization to covariance shrinkage, incorporating transaction costs and parameter uncertainty.
result Turnover penalization is more effective than shrinkage methods in constructing well-performing portfolios.
We study the design of portfolios under a minimum risk criterion. The performance of the optimized portfolio relies on the accuracy of the estimated covariance matrix of the portfolio asset returns. For large portfolios, the number of available market returns is often of similar order to the number of assets, so that t…
Improved estimation of higher order integrals using shrinkage techniques.
problem Estimating higher order Bochner integrals in non-parametric settings.
method Shrinkage of U-statistic towards a target element, considering kernel degeneracy.
result Consistent shrinkage estimators with fast rates of convergence, even for non-degenerate kernels.
EigenBayes: A fast, adaptive Bayesian shrinkage approach for high-dimensional matrix factorization
problem Choosing the latent dimension k in factor models method Adaptive spectral shrinkage and empirical Bayes calibration
result Adapts to signal-to-noise ratio and shrinks superfluous components
Flexible co-data learning improves clinical prediction models.
problem High-dimensional clinical data challenges prediction accuracy.
method Combining domain knowledge and external studies to estimate adaptive multi-group ridge penalties.
result Improves prediction performance and variable selection stability.
New methods improve portfolio risk minimization by estimating covariance matrix more accurately.
problem Uncertainty in estimating covariance matrix leads to unreliable hedge trades.
method Proposes two new estimators of the inverse covariance matrix using l2 and l1 norms.
result Portfolio formed using proposed estimators achieves substantial risk reduction and improved returns.
Optimizes high-dimensional portfolios using joint shrinkage.
problem Optimizing portfolios with many assets where classical methods fail.
method Regression-based joint shrinkage method for estimating partial correlations.
result Superior performance in variance, weight, and risk estimation compared to other methods.
New method for estimating financial covariance matrices efficiently.
problem Noisy covariance matrix estimation in high-dimensional financial data.
method Cluster financial time series into groups, apply shrinkage to ensure positive definiteness.
result Proposed methods provide reliable estimates and outperform other estimators.
Predicts user session length in streaming services with hierarchical modeling and shrinkage.
problem Predicting user session length in streaming services is challenging due to external factors and lack of covariates.
method Inspired by hierarchical Bayesian modeling, the approach incorporates flexible parametric/nonparametric models and uses hierarchical shrinkage.
result The method outperforms state-of-the-art estimators in efficiency and predictive performance.
New method cleans cross-covariance matrices for better financial forecasting.
problem Asymptotically optimal cross-covariance cleaners fail in real-world, time-varying markets.
method Physics-informed neural network that learns from empirical singular values.
result Trained model outperforms analytical cleaners in out-of-sample cross-covariance prediction.
We present the FuSSO, a functional analogue to the LASSO, that efficiently finds a sparse set of functional input covariates to regress a real-valued response against. The FuSSO does so in a semi-parametric fashion, making no parametric assumptions about the nature of input functional covariates and assuming a linear f…
Inflating the minimum norm interpolator improves linear regression generalization error.
problem Highly anisotropic covariances and diverging d/n in linear regression. method Inflating the minimum ℓ2 norm interpolator by a constant greater than one. result Inflating the minimum norm interpolator improves generalization error.
New shrinkage estimator for GMV portfolio reduces risk in high-dimensional asset settings.
problem Estimating the global minimum variance portfolio in high-dimensional settings with limited data.
method Dynamic shrinkage of the GMV portfolio using previous data as a target.
result The new estimator outperforms traditional methods in high-dimensional asset settings.
New research shows shrinkage methods re-scale portfolio efficient frontiers under distributional misspecification.
problem Poor performance of mean-variance portfolio decisions under distributional assumptions.
method Investigation of shrinkage methods under different distributional assumptions (auto-correlation, skewness, excess kurtosis).
result Shrinkage methods re-scale the sample efficient frontier, implying standard comparison methods are flawed.
Study tests GMVP weights in high-dimensional settings, comparing sample and shrinkage estimators.
problem Testing GMVP weights in high-dimensional settings with varying sample size and asset count.
method Developed two tests based on sample and shrinkage estimators of GMVP weights.
result Shrinkage estimator test performs well even for high asset counts.
The article proposes a new portfolio allocation method using network theory.
problem Portfolio allocation problem by improving network theory tools.
method Enhancing network theory tools to construct risk-based models and using two covariance matrix estimators.
result Network-based portfolios consistently outperform standard portfolios in terms of performance and risk.
KG-WDRO optimizes transfer learning with external knowledge.
problem Over-pessimism in WDRO for small target samples.
method KG-WDRO incorporates multiple sources of external knowledge to construct smaller Wasserstein ambiguity sets.
result KG-WDRO improves transfer learning performance and adaptivity.
Unified framework for fast large-scale portfolio optimization.
problem Efficient portfolio optimization for large-scale financial data.
method Incorporates shrinkage and regularization techniques, addressing multiple objectives.
result AP-Trees and PCA-based factor models consistently outperform other approaches in out-of-sample portfolio performance.
The paper analyzes how factorized Gaussian approximations underestimate uncertainty in variational inference.
problem Underestimation of uncertainty in variational inference using factorized Gaussian approximations.
method Examined the trade-off between shrinkage and delinking in approximating a Gaussian with a diagonal covariance matrix.
result Entropy of the factorized Gaussian approximation underestimates both componentwise variance and entropy of the original Gaussian.