The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Geometrizing Rates of Convergence, II
Open accessAbstract
Consider estimating a functional $T(F)$ of an unknown distribution $F \in \mathbf{F}$ from data $X_1, \cdots, X_n$ i.i.d. $F$. Let $\omega(\varepsilon)$ denote the modulus of continuity of the functional $T$ over $\mathbf{F}$, computed with respect to Hellinger distance. For well-behaved loss functions $l(t)$, we show that $\inf_{T_n \sup_\mathbf{F}} E_Fl(T_n - T(F))$ is equivalent to $l(\omega(n^{-1/2}))$ to within constants, whenever $T$ is linear and $\mathbf{F}$ is convex. The same conclusion holds in three nonlinear cases: estimating the rate of decay of a density, estimating the mode and robust nonparametric regression. We study the difficulty of testing between the composite, infinite dimensional hypotheses $H_0: T(F) \leq t$ and $H_1: T(F) \geq t + \Delta$. Our results hold, in the cases studied, because the difficulty of the full infinite-dimensional composite testing problem is comparable to the difficulty of the hardest simple two-point testing subproblem.
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Cites
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Self-citationOptimal Rates of Convergence for Nonparametric Estimators
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Estimation of entropy and mutual information
Paninski, L. (2003) · Neural Computation · doi:10.1162/089976603321780272 · Cited by 1,442
On the Optimal Rates of Convergence for Nonparametric Deconvolution Problems
Fan, J. (1991) · The Annals of Statistics · doi:10.1214/aos/1176348248 · Cited by 845
Elements of Large-Sample Theory
Strawderman, W. E., Lehmann, E. L., & Holmes, S. P. (2012) · Selected Works of E. L. Lehmann · doi:10.1007/978-1-4614-1412-4_97 · Cited by 818
Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk Minimization
Nguyen, X., Wainwright, M. J., & Jordan, M. I. (2010) · IEEE Transactions on Information Theory · doi:10.1109/tit.2010.2068870 · Cited by 379
Test of Significance Based on Wavelet Thresholding and Neyman's Truncation
Fan, J. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476936 · Cited by 288
Metadata
- Authors
- Donoho, D. L., & Liu, R. C.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1991-06-01
- Volume
- 19
- Issue
- 2
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2070086983
- Cited by
- 261
- References
- 28
- FWCI
- 9.35
- Type
- journal article
- Language
- en
- Open access
- bronze
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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