Related papers: The Minimax Risk in Testing Uniformity over Large …

We investigate the problem of continuous-time causal estimation under a minimax criterion. Let $X^T = \{X_t,0\leq t\leq T\}$ be governed by the probability law $P_{\theta}$ from a class of possible laws indexed by $\theta \in \Lambda$, and…

We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…

We consider the classical problem of sequential probability assignment under logarithmic loss while competing against an arbitrary, potentially nonparametric class of experts. We obtain tight bounds on the minimax regret via a new approach…

This article provides, through theoretical analysis, an in-depth understanding of the classification performance of the empirical risk minimization framework, in both ridge-regularized and unregularized cases, when high dimensional data are…

We observe a sample of $n$ independent $p$-dimensional Gaussian vectors with Toeplitz covariance matrix $ \Sigma = [\sigma_{|i-j|}]_{1 \leq i,j \leq p}$ and $\sigma_0=1$. We consider the problem of testing the hypothesis that $\Sigma$ is…

The problem of estimating the missing mass or total probability of unseen elements in a sequence of $n$ random samples is considered under the squared error loss function. The worst-case risk of the popular Good-Turing estimator is shown to…

In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…

In this paper we propose and examine gap statistics for assessing uniform distribution hypotheses. We provide examples relevant to data integrity testing for which max-gap statistics provide greater sensitivity than chi-square ($\chi^2$),…

Pearson's chi-squared test is widely used to test the goodness of fit between categorical data and a given discrete distribution function. When the number of sets of the categorical data, say $k$, is a fixed integer, Pearson's chi-squared…

A test of the null hypothesis that a hazard rate is monotone nondecreasing, versus the alternative that it is not, is proposed. Both the test statistic and the means of calibrating it are new. Unlike previous approaches, neither is based on…

A minimax estimator has the minimum possible error ("risk") in the worst case. We construct the first minimax estimators for quantum state tomography with relative entropy risk. The minimax risk of non-adaptive tomography scales as…

Motivated by real-world machine learning applications, we analyze approximations to the non-asymptotic fundamental limits of statistical classification. In the binary version of this problem, given two training sequences generated according…

Two main concepts studied in machine learning theory are generalization gap (difference between train and test error) and excess risk (difference between test error and the minimum possible error). While information-theoretic tools have…

We consider the problem of empirical Bayes estimation for (multivariate) Poisson means. Existing solutions that have been shown theoretically optimal for minimizing the regret (excess risk over the Bayesian oracle that knows the prior) have…

We study quantum algorithms for verifying properties of the output probability distribution of a classical or quantum circuit, given access to the source code that generates the distribution. We consider the basic task of uniformity…

We study the scaling of classification error rates with respect to the size of the training dataset. In contrast to classical results where rates are minimax optimal for a problem class, this work starts with the empirical observation that,…

This paper considers the problem of testing many moment inequalities, where the number of moment inequalities ($p$) is possibly larger than the sample size ($n$). Chernozhukov et al. (2019) proposed asymptotic tests for this problem using…

We consider random-design linear prediction and related questions on the lower tail of random matrices. It is known that, under boundedness constraints, the minimax risk is of order $d/n$ in dimension $d$ with $n$ samples. Here, we study…

The issue addressed in this paper is that of testing for common breaks across or within equations of a multivariate system. Our framework is very general and allows integrated regressors and trends as well as stationary regressors. The null…

Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…