相关论文: Locally minimax optimal confidence sets for the be…

In this paper, we study the detection boundary for minimax hypothesis testing in the context of high-dimensional, sparse binary regression models. Motivated by genetic sequencing association studies for rare variant effects, we investigate…

In this paper, we propose an improved numerical algorithm for solving minimax problems based on nonsmooth optimization, quadratic programming and iterative process. We also provide a rigorous proof of convergence for our algorithm under…

We consider the problem of recovering an unknown matching between a set of $n$ randomly placed points in $\mathbb{R}^d$ and random perturbations of these points. This can be seen as a model for particle tracking and more generally, entity…

We consider exact asymptotics of the minimax risk for global testing against sparse alternatives in the context of high dimensional linear regression. Our results characterize the leading order behavior of this minimax risk in several…

This paper considers an ML inspired approach to hypothesis testing known as classifier/classification-accuracy testing ($\mathsf{CAT}$). In $\mathsf{CAT}$, one first trains a classifier by feeding it labeled synthetic samples generated by…

We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a…

Recently, a new local optimality concept for minimax problems, termed calm local minimax points, has been introduced. In this paper, we extend this concept to a general class of nonsmooth, nonconvex nonconcave minimax problems with coupled…

We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…

The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years. To gain insights…

Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. We consider sequential algorithms that…

We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…

Learning discrete distributions from i.i.d. samples is a well-understood problem. However, advances in generative machine learning prompt an interesting new, non-i.i.d. setting: after receiving a certain number of samples, an estimated…

This paper revisits a fundamental problem in statistical inference from a non-asymptotic theoretical viewpoint $\unicode{x2013}$ the construction of confidence sets. We establish a finite-sample bound for the estimator, characterizing its…

We consider the problem of finding a proper confidence interval for the mean based on a single observation from a normal distribution with both mean and variance unknown. Portnoy (2017) characterizes the scale-sign invariant rules and shows…

We consider the problem of testing a particular type of composite null hypothesis under a nonparametric multivariate regression model. For a given quadratic functional $Q$, the null hypothesis states that the regression function $f$…

Let $(Y,X_1,...,X_m)$ be a random vector. It is desired to predict $Y$ based on $(X_1,...,X_m)$. Examples of prediction methods are regression, classification using logistic regression or separating hyperplanes, and so on. We consider the…

The aim of this paper is to recover the regression function with sup norm loss. We construct an asymptotically sharp estimator which converges with the spatially dependent rate r\_{n, \mu}(x) = P \big(\log n / (n \mu(x)) \big)^{s / (2s +…

In the first part, we develop a general framework for projection structures and study several inference problems within this framework. We propose procedures based on data dependent measures (DDM) and make connections with empirical Bayes…

For any class of one-sided $1-\alpha$ confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two…

We propose a method to remedy finite sample coverage problems and improve upon the efficiency of commonly employed procedures for the construction of nonparametric confidence intervals in regression kink designs. The proposed interval is…