Related papers: Root-$n$ Asymptotically Normal Maximum Score Estim…
This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…
There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence…
In this work we study the semi-supervised framework of confidence set classification with controlled expected size in minimax settings. We obtain semi-supervised minimax rates of convergence under the margin assumption and a H{\"o}lder…
We consider stochastic optimization problems which use observed data to estimate essential characteristics of the random quantities involved. Sample average approximation (SAA) or empirical (plug-in) estimation are very popular ways to use…
In many randomized trials, outcomes such as essays or open-ended responses must be manually scored as a preliminary step to impact analysis, a process that is costly and limiting. Model-assisted estimation offers a way to combine surrogate…
For the problem of nonparametric regression of smooth functions, we reconsider and analyze a constrained variational approach, which we call the MultIscale Nemirovski-Dantzig (MIND) estimator. This can be viewed as a multiscale extension of…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
We propose a novel study of the stochastic proximal gradient method for minimizing the sum of two convex functions, one of which is smooth. Under suitable assumptions and without requiring any boundedness or control of the variance of the…
Binary classification is a common statistical learning problem in which a model is estimated on a set of covariates for some outcome indicating the membership of one of two classes. In the literature, there exists a distinction between hard…
Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…
In this paper we consider large-scale smooth optimization problems with multiple linear coupled constraints. Due to the non-separability of the constraints, arbitrary random sketching would not be guaranteed to work. Thus, we first…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
In statistical learning theory, convex surrogates of the 0-1 loss are highly preferred because of the computational and theoretical virtues that convexity brings in. This is of more importance if we consider smooth surrogates as witnessed…
In this paper, we study the problem of maximizing continuous submodular functions that naturally arise in many learning applications such as those involving utility functions in active learning and sensing, matrix approximations and network…
Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…
One of the most commonly used methods for forming confidence intervals for statistical inference is the empirical bootstrap, which is especially expedient when the limiting distribution of the estimator is unknown. However, despite its…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
The exact maximum likelihood estimate (MLE) provides a test statistic for the unit root test that is more powerful \citep[p. 577]{Fuller96} than the usual least squares approach. In this paper a new derivation is given for the asymptotic…
This paper is concerned with the estimating problem of response quantile with high dimensional covariates when response is missing at random. Some existing methods define root-n consistent estimators for the response quantile. But these…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…