کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4949253 1440042 2017 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
High dimensional covariance matrix estimation by penalizing the matrix-logarithm transformed likelihood
ترجمه فارسی عنوان
برآورد ماتریس کوواریانس با ضریب مجاز ماتریس-لگاریتم احتمال تبدیل شده
کلمات کلیدی
برآورد ماتریس کوواریانس، تبدیل لگاریتم ماتریس، مجازات،
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
چکیده انگلیسی
It is well known that when the dimension of the data becomes very large, the sample covariance matrix S will not be a good estimator of the population covariance matrix Σ. Using such estimator, one typical consequence is that the estimated eigenvalues from S will be distorted. Many existing methods tried to solve the problem, and examples of which include regularizing Σ by thresholding or banding. In this paper, we estimate Σ by maximizing the likelihood using a new penalization on the matrix logarithm of Σ (denoted by A) of the form: ‖A−mI‖F2=∑i(log(di)−m)2, where di is the ith eigenvalue of Σ. This penalty aims at shrinking the estimated eigenvalues of A toward the mean eigenvalue m. The merits of our method are that it guarantees Σ to be non-negative definite and is computational efficient. The simulation study and applications on portfolio optimization and classification of genomic data show that the proposed method outperforms existing methods.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computational Statistics & Data Analysis - Volume 114, October 2017, Pages 12-25
نویسندگان
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