Rank Regression
نویسندگان
چکیده
منابع مشابه
Low rank Multivariate regression
We consider in this paper the multivariate regression problem, when the target regression matrix A is close to a low rank matrix. Our primary interest is in on the practical case where the variance of the noise is unknown. Our main contribution is to propose in this setting a criterion to select among a family of low rank estimators and prove a non-asymptotic oracle inequality for the resulting...
متن کاملLinear Rank Regression
The errors ei in (1.1) are assumed to be independent and identically distributed, but are not necessarily normal and may be heavy-tailed. Assume for convenience that β is one dimensional. Then (1.1) is a simple linear regression. However, most of the following extends more-or-less easily to higher-dimensional β, in which case (1.1) is a multiple regression. Given β, define Ri(β) as the rank (or...
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We propose an approach to multivariate nonparametric regression that generalizes reduced rank regression for linear models. An additive model is estimated for each dimension of a q-dimensional response, with a shared p-dimensional predictor variable. To control the complexity of the model, we employ a functional form of the Ky-Fan or nuclear norm, resulting in a set of function estimates that h...
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Rank-based estimates are asymptotically efficient when optimal scores are used. This paper describes a method for estimating the optimal score function based on residuals from an initial fit. The resulting adaptive estimate is shown to be asymptotically efficient.
متن کاملHigher-Order Low-Rank Regression
This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension i...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 1988
ISSN: 0090-5364
DOI: 10.1214/aos/1176351044