The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation

Ledoit, Olivier; Wolf, Michael

doi:10.1093/jjfinec/nbaa007

Cited by 76 publications

(21 citation statements)

References 68 publications

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“…The estimation of was obtained by comparing several candidate estimators from the cvCovEst R package and by selecting the estimator having the smallest estimation error. In this application, the combination of the sample covariance matrix and a dense target matrix ( denseLinearShrinkEst ) derived by [ 18 ] provides the smallest estimation error. Figure 8 (left) displays the estimated and highlights the strong correlation between the genes.…”

Section: Application To Transcriptomic and Proteomic Datamentioning

confidence: 99%

Identification of prognostic and predictive biomarkers in high-dimensional data with PPLasso

2023

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In clinical trials, identification of prognostic and predictive biomarkers has became essential to precision medicine. Prognostic biomarkers can be useful for the prevention of the occurrence of the disease, and predictive biomarkers can be used to identify patients with potential benefit from the treatment. Previous researches were mainly focused on clinical characteristics, and the use of genomic data in such an area is hardly studied. A new method is required to simultaneously select prognostic and predictive biomarkers in high dimensional genomic data where biomarkers are highly correlated. We propose a novel approach called PPLasso, that integrates prognostic and predictive effects into one statistical model. PPLasso also takes into account the correlations between biomarkers that can alter the biomarker selection accuracy. Our method consists in transforming the design matrix to remove the correlations between the biomarkers before applying the generalized Lasso. In a comprehensive numerical evaluation, we show that PPLasso outperforms the traditional Lasso and other extensions on both prognostic and predictive biomarker identification in various scenarios. Finally, our method is applied to publicly available transcriptomic and proteomic data.

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Section: Application To Transcriptomic and Proteomic Datamentioning

confidence: 99%

Identification of prognostic and predictive biomarkers in high-dimensional data with PPLasso

2023

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“…The estimation of Σ was obtained by comparing several candidate estimators from the cvCovEst R package and by selecting the estimator having the smallest estimation error. In this application, the combination of the sample covariance matrix and a dense target matrix (denseLinearShrinkEst) derived by Ledoit and Wolf (2020) provides the smallest estimation error. Figure 7 displays the estimated Σ and highlights the strong correlation between the genes.…”

Section: Application To Gene Expression Data In Breast Cancermentioning

confidence: 99%

Identification of prognostic and predictive biomarkers in high-dimensional data with PPLasso

Zhu,

Lévy-Leduc,

Ternès

2022

Preprint

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In clinical trials, identification of prognostic and predictive biomarkers is essential to precision medicine. Prognostic biomarkers can be useful for the prevention of the occurrence of the disease, and predictive biomarkers can be used to identify patients with potential benefit from the treatment. Previous researches were mainly focused on clinical characteristics, and the use of genomic data in such an area is hardly studied. A new method is required to simultaneously select prognostic and predictive biomarkers in high dimensional genomic data where biomarkers are highly correlated. We propose a novel approach called PPLasso (Prognostic Predictive Lasso) integrating prognostic and predictive effects into one statistical model. PPLasso also takes into account the correlations between biomarkers that can alter the biomarker selection accuracy. Our method consists in transforming the design matrix to remove the correlations between the biomarkers before applying the generalized Lasso. In a comprehensive numerical evaluation, we show that PPLasso outperforms the traditional Lasso approach on both prognostic and predictive biomarker identification in various scenarios. Finally, our method is applied to publicly available transcriptomic data from clinical trial RV144. Our method is implemented in the PPLasso R package which will be soon available from the Comprehensive R Archive Network (CRAN).

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“…erefore, before the problem is studied, the data needs to be normalized and standardized. e problem of economic aggregates does not exist independently, and the study of economic structure is inseparable from the study of aggregates [15]. It is not enough to know the total national economy; we need to understand what the total economy consists of and what factors influence it.…”

Section: Macroeconomic Multivariate Statistical Analysis With Random ...mentioning

confidence: 99%

Macroeconomic Multivariate Statistics and Regionalization Management Strategy Based on Random Matrix

Tan

2022

Mathematical Problems in Engineering

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This paper adopts the method of the random matrix to conduct an in-depth study and analysis of the management of macroeconomic multivariate statistics and regionalization, and to design its management strategy based on a random matrix. A combination of theoretical and applied research, combined with the experience of other cities, is used to study regional economic management using literature analysis, comparative analysis, and deductive induction by summarizing the results achieved in community management, studying its experience, exploring the significance of community management in ETDZs for social development, analyzing the current obstacles and contradictions affecting community management in Suqian ETDZ, and proposing relevant countermeasures for the problems arising therein to enrich the relevant theories and thus promote the level of community management in ETDZs to a higher level. Macroeconomic uncertainty refers to the changes that cannot be accurately observed, analyzed, and foreseen, i.e., the deviation of the expected value of the economy from the actual value. Not all macroeconomic fluctuations belong to the category of macroeconomic uncertainty, only unpredictable economic fluctuations are uncertain. It can be seen from the above that there is a corresponding relationship between the financial income correlation matrix and the random correlation matrix, and both are affected by the same random factors. The importance of uncertainty for macroeconomic policy making is undeniable, and its quantification is a key step. In this paper, we propose an econometric model to eliminate expectations and compare the advantages and disadvantages of different measurement models; we measure a system of fourteen macroeconomic indicators to reflect macroeconomic uncertainty and provide quantitative measurement results for the correct understanding of macroeconomic uncertainty and economic policy making. Factor analysis is used to analyze these six comprehensive aspects to obtain the six-dimensional comprehensive scores of each province and city, and the scores are normalized and visualized. Based on a certain understanding of the economic equilibrium structure of each province and city in China, and a certain control of the overall development of each region itself at this stage, the future economic development trend is studied.

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The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation

Cited by 76 publications

References 68 publications

Identification of prognostic and predictive biomarkers in high-dimensional data with PPLasso

Identification of prognostic and predictive biomarkers in high-dimensional data with PPLasso

Identification of prognostic and predictive biomarkers in high-dimensional data with PPLasso

Macroeconomic Multivariate Statistics and Regionalization Management Strategy Based on Random Matrix

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