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It is a common phenomenon that for high-dimensional and nonparametric statistical models, rate-optimal estimators balance squared bias and variance.
A new lower bound for Kullback-Leibler divergence based on Hammersley-Chapman-Robbins bound
Nishiyama, T · 1907
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Inadmissibility of the usual estimator for the mean of a multivariate normal distribution
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Maximum entropy and the nearly black object
Donoho, D. L., Johnstone, I. M., Hoch, J. C., and Stern, A. S · 1992
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Neural networks and the bias/variance dilemma
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Nonexistence of informative unbiased estimators in singular problems
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Bias-variance tradeoffs in functional estimation problems
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A constrained risk inequality with applications to nonparametric functional estimation
Brown, L. D., and Low, M. G · 1996
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Superefficiency in nonparametric function estimation
Brown, L. D., Low, M. G., and Zhao, L. H · 1997
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Matrix analysis and applied linear algebra
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A nonparametric asymptotic version of the Cramér-Rao bound
Pfanzagl, J · 2001
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Entropies, convexity, and functional inequalities: on Φ \Phi -entropies and Φ \Phi -Sobolev inequalities
Chafaï, D · 2004
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Notes on the bias-variance trade-off phenomenon
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Stable recovery of sparse overcomplete representations in the presence of noise
Donoho, D. L., Elad, M., and Temlyakov, V. N · 2006
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Theory of point estimation
Lehmann, E. L., and Casella, G · 2006
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The elements of statistical learning
Hastie, T., Tibshirani, R., and Friedman, J · 2009
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Introduction to non-parametric estimation
Tsybakov, A. B · 2009
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Complexity theoretic lower bounds for sparse principal component detection
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Optimal detection of sparse principal components in high dimension
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Efficient estimation of functionals in nonparametric boundary models
Reiß M., and Selk, L · 2017
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A Modern Take on the Bias-Variance Tradeoff in Neural Networks
Neal, B., Mittal, S., Baratin, A., Tantia, V., Scicluna, M., Lacoste-Julien, S., and Mitliagkas, I · 2018
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Gaussian estimation: Sequence and wavelet models, September 2019
Johnstone, I. M · 2019
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Fano’s Inequality for Random Variables
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Asymptotic equivalence for nonparametric regression with non-regular errors
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On asymptotically optimal confidence regions and tests for high-dimensional models
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