Related papers: Asymptotically Minimax Robust Likelihood Ratio Tes…

Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing…

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…

We introduce fully nonparametric two-sample tests for testing the null hypothesis that the samples come from the same distribution if the values are only indirectly given via current status censoring. The tests are based on the likelihood…

We propose a novel kernel-based nonparametric two-sample test, employing the combined use of kernel mean and kernel covariance embedding. Our test builds on recent results showing how such combined embeddings map distinct probability…

Health data are often not symmetric to be adequately modeled through the usual normal distributions; most of them exhibit skewed patterns. They can indeed be modeled better through the larger family of skew-normal distributions covering…

We consider the problem of sequentially testing a simple null hypothesis versus a composite alternative hypothesis that consists of a finite set of densities. We study sequential tests that are based on thresholding of mixture-based…

Empirical likelihood serves as a powerful tool for constructing confidence intervals in nonparametric regression and regression discontinuity designs (RDD). The original empirical likelihood framework can be naturally extended to these…

This paper develops a theory of distribution- and time-uniform asymptotics, culminating in the first large-sample anytime-valid inference procedures that are shown to be uniformly valid in a rich class of distributions. Historically,…

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited…

We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and our focus is on establishing the exact…

This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions…

The problem of quickest detection of a change in the distribution of a sequence of independent observations is considered. It is assumed that the pre-change distribution is known (accurately estimated), while the only information about the…

We revisit the outlier hypothesis testing framework of Li \emph{et al.} (TIT 2014) and derive fundamental limits for the optimal test under the generalized Neyman-Pearson criterion. In outlier hypothesis testing, one is given multiple…

The semi-parametric Cox proportional hazards regression model has been widely used for many years in several applied sciences. However, a fully parametric proportional hazards model, if appropriately assumed, can often lead to more…

Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…

Based on the convex least-squares estimator, we propose two different procedures for testing convexity of a probability mass function supported on N with an unknown finite support. The procedures are shown to be asymptotically calibrated.

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

We propose a novel data-driven method to learn a mixture of multiple kernels with random features that is certifiabaly robust against adverserial inputs. Specifically, we consider a distributionally robust optimization of the kernel-target…

We develop a near-optimal testing procedure under the framework of Gaussian differential privacy for simple as well as one- and two-sided tests under monotone likelihood ratio conditions. Our mechanism is based on a private mean estimator…

Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing,…