Related papers: Testing composite hypotheses, Hermite polynomials …
In this paper, we present explicit and computable error bounds for the asymptotic expansions of the Hermite polynomials with Plancherel--Rotach scale. Three cases, depending on whether the scaled variable lies in the outer or oscillatory…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
We develop a technique for establishing lower bounds on the sample complexity of Least Squares (or, Empirical Risk Minimization) for large classes of functions. As an application, we settle an open problem regarding optimality of Least…
This note establishes a theoretical framework for finding (potentially overparameterized) approximations of a function on a compact set with a-priori bounds for the generalization error. The approximation method considered is to choose,…
We discuss a number of estimates of the hazard under the assumption that the hazard is monotone on an interval [0,a]. The usual isotonic least squares estimators of the hazard are inconsistent at the boundary points 0 and a. We use…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…
We consider a broad class of permutation invariant statistical problems by extending the standard decision theoretic definition to allow also selective inference tasks, where the target is specified only after seeing the data. For any such…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…
In this paper, we observe a sparse mean vector through Gaussian noise and we aim at estimating some additive functional of the mean in the minimax sense. More precisely, we generalize the results of (Collier et al., 2017, 2019) to a very…
During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…
We propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$…
An algorithm is proposed, analyzed, and tested for minimizing locally Lipschitz objective functions that may be nonconvex and/or nonsmooth. The algorithm, which is built upon the gradient-sampling methodology, is designed specifically for…
The problem of Bayes minimax estimation for the mean of a multivariate normal distribution under quadratic loss has attracted significant attention recently. These estimators have the advantageous property of being admissible, similar to…
Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…
Composite minimization involves a collection of functions which are aggregated in a nonsmooth manner. It covers, as a particular case, smooth approximation of minimax games, minimization of max-type functions, and simple composite…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
Inverse optimization (Inverse optimal control) is the task of imputing a cost function such that given test points (trajectories) are (nearly) optimal with respect to the discovered cost. Prior methods in inverse optimization assume that…
We develop a finite-sample optimal estimator for regression discontinuity design when the outcomes are bounded, including binary outcomes as the leading case. Our estimator achieves minimax mean squared error among linear shrinkage…