Nonquadratic estimators of a quadratic functional
By Tommaso Cai, Mark G. Low. 2005
71 citations recorded by the source corpus.
Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate suboptimal. In such cases minimax rate optimal procedures are constructed based on local thresholding. These nonquadratic procedures are sometimes fully efficient even when optimal quadratic rules have slow rates of convergence. Moreover, it is shown that when estimating a quadratic functional nonquadratic procedures may exhibit different elbow phenomena than quadratic procedures.
Subfields: Control and Systems Engineering, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/47b6c5422ad4de8f11ad2ca7924db6ae983364f3
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Control and Systems Engineering
- Yihong Wu
- Pengkun Yang
- Tommaso Cai
- Mark G. Low
- Jiantao Jiao
- Yanjun Han
- Tsachy Weissman
- Kartik Venkat
In Statistics and Probability
- Yanjun Han
- Tommaso Cai
- Yihong Wu
- Pengkun Yang
- Jiantao Jiao
- Tsachy Weissman
- Kartik Venkat
- Mark G. Low
Citations in the corpus
- The Nearest Neighbor Information Estimator is Adaptively Near Minimax Rate-Optimal (2017, background): “We do not attempt to survey the extensive literature in this area, but instead refer to the interested reader to, e.g., [24, 5, 12, 16, 6, 32, 37, 47, 8, 9, 54] and the references therein.”
- 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”
- Testing composite hypotheses, Hermite polynomials and optimal estimation of a nonsmooth functional (2011, background): “See, for example, Cai and Low ( 2005), where upper and lower bounds are constructed for quadratic functionals over many different parameter spaces.”
- Minimax Rates of Entropy Estimation on Large Alphabets via Best Polynomial Approximation (2014, background): “As a consequence, the minimax rate in Theorem 1 implies that to estimate the entropy with an additive error of ǫ , the minimal sample size is given by n ≥ log 2 k ǫ 2 ∨ k ǫ log k .”