منابع مشابه
On matrix estimation under monotonicity constraints
Abstract: We consider the problem of estimating an unknown n1×n2 matrix θ∗ from noisy observations under the constraint that θ∗ is nondecreasing in both rows and columns. We consider the least squares estimator (LSE) in this setting and study its risk properties. We show that the worst case risk of the LSE is n−1/2, up to multiplicative logarithmic factors, where n = n1n2 and that the LSE is mi...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1974
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1974-0352116-0