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Optimal M-estimation in high-dimensional regression.

ABSTRACT: We consider, in the modern setting of high-dimensional statistics, the classic problem of optimizing the objective function in regression using M-estimates when the error distribution is assumed to be known. We propose an algorithm to compute this optimal objective function that takes into account the dimensionality of the problem. Although optimality is achieved under assumptions on the design matrix that will not always be satisfied, our analysis reveals generally interesting families of dimension-dependent objective functions.

SUBMITTER: Bean D

PROVIDER: S-EPMC3767535 | biostudies-literature | 2013 Sep

REPOSITORIES: biostudies-literature

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Optimal M-estimation in high-dimensional regression.

Bean Derek D Bickel Peter J PJ El Karoui Noureddine N Yu Bin B

Proceedings of the National Academy of Sciences of the United States of America 20130816 36

We consider, in the modern setting of high-dimensional statistics, the classic problem of optimizing the objective function in regression using M-estimates when the error distribution is assumed to be known. We propose an algorithm to compute this optimal objective function that takes into account the dimensionality of the problem. Although optimality is achieved under assumptions on the design matrix that will not always be satisfied, our analysis reveals generally interesting families of dimen ...[more]

PMID: 23954907

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