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Inspired by the well-known linear shrinkage estimation, we propose a novel second-order Stein-type regularization strategy to generate well-conditioned covariance matrix estimators. We model the second-order Stein-type regularization as a quadratic polynomial concerning the sample covariance matrix and a given target matrix, representing the prior information of the actual covariance structure. To obtain available covariance matrix estimators, we choose the spherical and diagonal target matrices and develop unbiased estimates of the theoretical mean squared errors, which measure the distances between the actual covariance matrix and its estimators. We formulate the second-order Stein-type regularization as a convex optimization problem, resulting in the optimal second-order Stein-type estimators. Numerical simulations reveal that the proposed estimators can significantly lower the Frobenius losses compared with the existing Stein-type estimators. Moreover, a real data analysis in portfolio selection verifies the performance of the proposed estimators.<\/jats:p>","DOI":"10.3390\/e25010053","type":"journal-article","created":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T08:38:19Z","timestamp":1672216699000},"page":"53","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Estimation of Large-Dimensional Covariance Matrices via Second-Order Stein-Type Regularization"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7654-5072","authenticated-orcid":false,"given":"Bin","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0511-6902","authenticated-orcid":false,"given":"Hengzhen","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianbin","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1111\/rssb.12016","article-title":"Large covariance estimation by thresholding principal orthogonal complements","volume":"75","author":"Fan","year":"2013","journal-title":"J. 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