High dimensional robust M-estimation: asymptotic variance via approximate message passing
نویسندگان
چکیده
منابع مشابه
HIGH DIMENSIONAL ROBUST M-ESTIMATION: ASYMPTOTIC VARIANCE VIA APPROXIMATE MESSAGE PASSING By
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n. Using numerical simulations and ‘highly plausible’ heuristic arguments, they unveil a striking new phenomenon. Namely, the regression coefficients contain an ...
متن کاملHigh Dimensional Robust M-Estimation: Asymptotic Variance via Approximate Message Passing
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n. Using numerical simulations and ‘highly plausible’ heuristic arguments, they unveil a striking new phenomenon. Namely, the regression coefficients contain an ...
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In this note, I summarize Sections 5.1 and 5.2 of Arian Maleki’s PhD thesis. 1 Notation We denote scalars by small letters e.g. a, b, c, . . ., vectors by boldface small letters e.g. λ,α,x, . . ., matrices by boldface capital letter e.g. A,B,C, . . ., (subsets of) natural numbers by capital letters e.g. N,M, . . .. We denote i’th element of a vector a by ai and (i, j)’th entry of a matrix A by ...
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ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2015
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-015-0675-z