We propose a new estimator of the regression coefficients for a high-dimensional linear regression model, which is de rived by replacing the sample predictor covariance matrix in the OLS estimator with a different predictor covariance matrix estimate obtained by a nuclear norm plus l1 norm penalization. We call the estimator ALCE-reg. We make a direct theoretical comparison of the expected mean square error of ALCE-reg with OLS and RIDGE. We show in a sim ulation study that ALCE-reg is particularly effective when both the dimension and the sample size are large, due to its ability to find a good compromise between the large bias of shrinkage estimators (like RIDGE and LASSO) and the large variance of estimators conditioned by the sample predictor covariance matrix (like OLS and POET).

High‐dimensional regression coefficient estimation by nuclear norm plus l1 norm penalization / Farne, Matteo; Montanari, Angela. - In: STAT. - ISSN 2049-1573. - ELETTRONICO. - 12:1(2023), pp. 1-11. [10.1002/sta4.548]

High‐dimensional regression coefficient estimation by nuclear norm plus l1 norm penalization

Farne, Matteo
Primo
Formal Analysis
;
Montanari, Angela
Secondo
Conceptualization
2023

Abstract

We propose a new estimator of the regression coefficients for a high-dimensional linear regression model, which is de rived by replacing the sample predictor covariance matrix in the OLS estimator with a different predictor covariance matrix estimate obtained by a nuclear norm plus l1 norm penalization. We call the estimator ALCE-reg. We make a direct theoretical comparison of the expected mean square error of ALCE-reg with OLS and RIDGE. We show in a sim ulation study that ALCE-reg is particularly effective when both the dimension and the sample size are large, due to its ability to find a good compromise between the large bias of shrinkage estimators (like RIDGE and LASSO) and the large variance of estimators conditioned by the sample predictor covariance matrix (like OLS and POET).
2023
High‐dimensional regression coefficient estimation by nuclear norm plus l1 norm penalization / Farne, Matteo; Montanari, Angela. - In: STAT. - ISSN 2049-1573. - ELETTRONICO. - 12:1(2023), pp. 1-11. [10.1002/sta4.548]
Farne, Matteo; Montanari, Angela
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/916366
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