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NONPARAMETRIC ESTIMATION BY CONVEX PROGRAMMING
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DOI：10.1214/08-AOS654.png)
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Abstract
En 中文
The problem we concentrate on is as follows: given (1) a convex compact set X in R-n, an affine mapping x bar right arrow A(x), a parametric family {p(mu)(.)} of probability densities and (2) N i.i.d. observations of the random variable omega, distributed with the density p(A(x)) (.) for some (unknown) x is an element of X, estimate the value g(T)x of a given linear form at x. For several families {p(mu)(.)} with no additional assumptions on X and A, we develop computationally efficient estimation routines which are minimax optimal, within an absolute constant factor. We then apply these routines to recovering x itself in the Euclidean norm.
Keywords:
Estimation of linear functional
minimax estimation
oracle inequalities
convex optimization
PE tomography
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