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- W2063122409 abstract "In this paper, we will consider the estimation of a monotone regression (or density) function in a fixed point by the least-squares (Grenander) estimator. We will show that this estimator is locally asymptotic minimax, in the sense that, for each $f_0$, the attained rate of the probabilistic error is uniform over a shrinking $L^2$-neighborhood of $f_0$ and there is no estimator that attains a significantly better uniform rate over these shrinking neighborhoods. Therefore, it adapts to the individual underlying function, not to a smoothness class of functions. We also give general conditions for which we can calculate a (non-standard) limiting distribution for the estimator." @default.
- W2063122409 created "2016-06-24" @default.
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- W2063122409 date "2011-05-01" @default.
- W2063122409 modified "2023-10-14" @default.
- W2063122409 title "Adaptivity and optimality of the monotone least-squares estimator" @default.
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- W2063122409 doi "https://doi.org/10.3150/10-bej289" @default.
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