On Adaptive Estimation of Linear Functionals

By T. Cai, Mark G. Low. 2005

51 citations recorded by the source corpus.

Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single para, meter space. A general construction of optimally adaptive estimators based on an ordered modulus of continuity is given. The results are complemented by several illustrative examples.

Subfields: Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/11f46a76e68e81e12930c66e0c33e38aa199cbb3

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In Control and Systems Engineering

In Statistics and Probability

Citations in the corpus

Maximum Likelihood Estimation of Functionals of Discrete Distributions (2014, background): “Khasminskii, 1978; Ibragimov, Nemirovskii and Khas’ minskii, 1987;Hall and Marron, 1987; Bickel and Ritov, 1988;Donoho and Nussbaum,1990;Fan, 1991; Efromovich and Low, 1996; Birg´e and Massart, 1995; Cai and Low, 2005b, 2006), among others. Estimation of non-smooth functionals is an extremely diﬃcul”
Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity (2015, background): “In the Gaussian sequence model, the problem of estimating the sum of sparse means has been considered in [5, 7] and more recently in [12].”