کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
7550059 | 1489921 | 2018 | 40 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Asymptotics for high-dimensional covariance matrices and quadratic forms with applications to the trace functional and shrinkage
ترجمه فارسی عنوان
همبستگیها برای ماتریس کوواریانس با ابعاد بزرگ و اشکال درجه دوم با استفاده از برنامه کاربردی برای عملکرد و انقباض ردیابی
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
We establish large sample approximations for an arbitrary number of bilinear forms of the sample variance-covariance matrix of a high-dimensional vector time series using â1-bounded and small â2-bounded weighting vectors. Estimation of the asymptotic covariance structure is also discussed. The results hold true without any constraint on the dimension, the number of forms and the sample size or their ratios. Concrete and potential applications are widespread and cover high-dimensional data science problems such as tests for large numbers of covariances, sparse portfolio optimization and projections onto sparse principal components or more general spanning sets as frequently considered, e.g. in classification and dictionary learning. As two specific applications of our results, we study in greater detail the asymptotics of the trace functional and shrinkage estimation of covariance matrices. In shrinkage estimation, it turns out that the asymptotics differ for weighting vectors bounded away from orthogonality and nearly orthogonal ones in the sense that their inner product converges to 0.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 128, Issue 8, August 2018, Pages 2816-2855
Journal: Stochastic Processes and their Applications - Volume 128, Issue 8, August 2018, Pages 2816-2855
نویسندگان
Ansgar Steland, Rainer von Sachs,