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07/05/2023
The distribution of Ridgeless least squares interpolators
The Ridgeless minimum ℓ_2-norm interpolator in overparametrized linear r...
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12/11/2022
Gaussian random projections of convex cones: approximate kinematic formulae and applications
Understanding the stochastic behavior of random projections of geometric...
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07/27/2022
Exact spectral norm error of sample covariance
Let X_1,…,X_n be i.i.d. centered Gaussian vectors in ℝ^p with covariance...
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06/16/2022
Universality of regularized regression estimators in high dimensions
The Convex Gaussian Min-Max Theorem (CGMT) has emerged as a prominent th...
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01/20/2022
Noisy linear inverse problems under convex constraints: Exact risk asymptotics in high dimensions
In the standard Gaussian linear measurement model Y=Xμ_0+ξ∈ℝ^m with a fi...
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07/15/2021
Nonparametric, tuning-free estimation of S-shaped functions
We consider the nonparametric estimation of an S-shaped regression funct...
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06/14/2021
Generalized kernel distance covariance in high dimensions: non-null CLTs and power universality
Distance covariance is a popular dependence measure for two random vecto...
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02/10/2021
Multiplier U-processes: sharp bounds and applications
The theory for multiplier empirical processes has been one of the centra...
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01/26/2021
A general method for power analysis in testing high dimensional covariance matrices
Covariance matrix testing for high dimensional data is a fundamental pro...
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10/07/2020
High dimensional asymptotics of likelihood ratio tests in Gaussian sequence model under convex constraint
In the Gaussian sequence model Y=μ+ξ, we study the likelihood ratio test...
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06/18/2020
Inference for local parameters in convexity constrained models
We consider the problem of inference for local parameters of a convex re...
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04/23/2020
On a phase transition in general order spline regression
In the Gaussian sequence model Y= θ_0 + ε in R^n, we study the fundament...
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01/20/2020
Confidence intervals for multiple isotonic regression and other monotone models
We consider the problem of constructing pointwise confidence intervals i...
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10/21/2019
Berry-Esseen bounds for Chernoff-type non-standard asymptotics in isotonic regression
This paper derives Berry-Esseen bounds for an important class of non-sta...
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05/30/2019
Limit distribution theory for multiple isotonic regression
We study limit distributions for the tuning-free max-min block estimator...
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05/30/2019
Complex sampling designs: uniform limit theorems and applications
In this paper, we develop a general approach to proving global and local...
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05/30/2019
Global empirical risk minimizers with "shape constraints" are rate optimal in general dimensions
Entropy integrals are widely used as a powerful tool to obtain upper bou...
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05/07/2018
Robustness of shape-restricted regression estimators: an envelope perspective
Classical least squares estimators are well-known to be robust with resp...
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12/15/2015