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In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients.
Variational approximations using Fisher divergence
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Adaptive maximum likelihood estimators of a location parameter
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Asymptotic behavior of general M M -estimates for regression and scale with random carriers
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Correlation functions and computer simulations
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A penalty method for nonparametric estimation of the logarithmic derivative of a density function
Cox, D. D. (1985) · 1985
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Asymptotic behavior of M M estimators of p p regression parameters when p 2 / n p^{2}/n is large; II. normal approximation
Portnoy, S. (1985) · 1985
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On asymptotically efficient estimation in semiparametric models
Schick, A. (1986) · 1986
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Density Estimation
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Order Restricted Statistical Inference
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Empirical Smoothing Parameter Selection in Adaptive Estimation
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Smoothing in adaptive estimation
Faraway, J. J. (1992) · 1992
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Estimating densities, quantiles, quantile densities and density quantiles
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Extremal properties of half-spaces for log-concave distributions
Bobkov, S. G. (1996) · 1996
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Exponential convergence of Langevin distributions and their discrete approximations
Roberts, G. O. and Tweedie, R. L. (1996) · 1996
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Optimal smoothing in adaptive location estimation
Mammen, E. and Park, B. U. (1997) · 1997
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Convex Analysis
Rockafellar, R. T. (1997) · 1997
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Asymptotic theory for M M -estimators over a convex kernel
Arcones, M. A. (1998) · 1998
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Asymptotic Statistics
van der Vaart, A. W. (1998) · 1998
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Real Analysis: Modern Techniques and their Applications
Folland, G. B. (1999) · 1999
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Methods of Information Geometry
Amari, S.-i. and Nagaoka, H. (2000) · 2000
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Maximum likelihood estimation of smooth monotone and unimodal densities
Eggermont, P. P. B. and LaRiccia, V. N. (2000) · 2000
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On parameters of increasing dimensions
He, X. and Shao, Q.-M. (2000) · 2000
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Boyd, S. P. and Vandenberghe, L. (2004) · 2004
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Information Theory and the Central Limit Theorem
Johnson, O. (2004) · 2004
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Fisher information inequalities and the central limit theorem
Density estimation in infinite dimensional exponential families
Sriperumbudur, B., Fukumizu, K., Gretton, A., Hyvärinen, A., and Kumar, R. (2017) · 2017
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Cheng, X., Chatterji, N. S., Bartlett, P. L., and Jordan, M. I. (2018) · 2018
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Double/debiased machine learning for treatment and structural parameters
Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., and Robins, J. (2018) · 2018
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On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators
El Karoui, N. (2018) · 2018
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A general and adaptive robust loss function
Barron, J. T. (2019) · 2019
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Univariate log-concave density estimation with symmetry or modal constraints
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Johnson, O. and Barron, A. (2004) · 2004
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Convergence of the empirical process in Mallows distance, with an application to bootstrap performance
Samworth, R. and Johnson, O. (2004) · 2004
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Estimation of non-normalized statistical models by score matching
Hyvärinen, A. (2005) · 2005
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Elements of Information Theory
Cover, T. M. and Thomas, J. A. (2006) · 2006
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Penalized maximum likelihood and semiparametric second-order efficiency
Dalalyan, A. S., Golubev, G. K., and Tsybakov, A. B. (2006) · 2006
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Nocedal, J. and Wright, S. J. (2006) · 2006
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Doss, C. R. and Wellner, J. A. (2019) · 2019
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Generative modeling by estimating gradients of the data distribution
Song, Y. and Ermon, S. (2019) · 2019
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High-Dimensional Statistics: A Non-Asymptotic Viewpoint
Wainwright, M. J. (2019) · 2019
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Robust statistical learning with Lipschitz and convex loss functions
Chinot, G., Lecué, G., and Lerasle, M. (2020) · 2020
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Goodness-of-fit testing in high dimensional generalized linear models
Janková, J., Shah, R. D., Bühlmann, P., and Samworth, R. J. (2020) · 2020
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Song, Y., Garg, S., Shi, J., and Ermon, S. (2020) · 2020
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Simultaneous inference for pairwise graphical models with generalized score matching
Yu, M., Gupta, V., and Kolar, M. (2020) · 2020
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Local continuity of log-concave projection, with applications to estimation under model misspecification
Barber, R. F. and Samworth, R. J. (2021) · 2021
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Adaptive estimation in symmetric location model under log-concavity constraint
Laha, N. (2021) · 2021
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Loh, P.-L. (2021) · 2021
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How to train your energy-based models
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Score-based generative modeling through stochastic differential equations
Song, Y., Sohl-Dickstein, J., Kingma, D. P., Kumar, A., Ermon, S., and Poole, B. (2021) · 2021
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Fundamental barriers to high-dimensional regression with convex penalties
Celentano, M. and Montanari, A. (2022) · 2022
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Riemannian score-based generative modelling
De Bortoli, V., Mathieu, E., Hutchinson, M., Thornton, J., Teh, Y. W., and Doucet, A. (2022) · 2022
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A modern Gauss–Markov theorem
Hansen, B. E. (2022) · 2022
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Statistical efficiency of score matching: The view from isoperimetry
Koehler, F., Heckett, A., and Risteski, A. (2022) · 2022
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What estimators are unbiased for linear models?
Lei, L. and Wooldridge, J. (2022) · 2022
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Generalized score matching for general domains
Yu, S., Drton, M., and Shojaie, A. (2022) · 2022
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Geodesically convex M M -estimation in metric spaces
Brunel, V.-E. (2023) · 2023
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An empirical Bayes shrinkage method for functional data
Derenski, J., Fan, Y., James, G., and Xu, M. (2023) · 2023
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Finite-sample symmetric mean estimation with Fisher information rate
Gupta, S., Lee, J. C. H., and Price, E. (2023) · 2023
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Extremes in high dimensions: methods and scalable algorithms
Lederer, J. and Oesting, M. (2023) · 2023
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From denoising diffusions to denoising Markov models
Benton, J., Shi, Y., De Bortoli, V., Deligiannidis, G., and Doucet, A. (2024) · 2024
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