Related papers: Learning Optimal Test Statistics in the Presence o…

We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…

Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…

The mission of statistics is to provide adequate statistical hypotheses (models) for observed data. But what is an "adequate" model? To answer this question, one needs to use the notions of algorithmic information theory. It turns out that…

We consider the problem of parametric statistical inference when likelihood computations are prohibitively expensive but sampling from the model is possible. Several so-called likelihood-free methods have been developed to perform inference…

Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…

This paper considers estimation of a quantized constant in noise when using uniform and nonuniform quantizers. Estimators based on simple arithmetic averages, on sample statistical moments and on the maximum-likelihood procedure are…

Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…

We consider the problem of designing experiments for the estimation of a target in regression analysis if there is uncertainty about the parametric form of the regression function. A new optimality criterion is proposed, which minimizes the…

In nested simulation literature, a common assumption is that the experimenter can choose the number of outer scenarios to sample. This paper considers the case when the experimenter is given a fixed set of outer scenarios from an external…

It is well understood that Bayesian decision theory and average case analysis are essentially identical. However, if one is interested in performing uncertainty quantification for a numerical task, it can be argued that standard approaches…

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

We investigate the performance of the scan (maximum likelihood ratio statistic) and of the average likelihood ratio statistic in the problem of detecting a deterministic signal with unknown spatial extent in the prototypical univariate…

Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data…

When faced with a small sample from a large universe of possible outcomes, scientists often turn to the venerable Good--Turing estimator. Despite its pedigree, however, this estimator comes with considerable drawbacks, such as the need to…

Profile likelihood is the key tool for dealing with nuisance parameters in likelihood theory. It is often asserted, however, that profile likelihood is not a 'true' likelihood. One implication is that likelihood theory lacks the generality…

We establish a fundamental connection between optimal structure learning and optimal conditional independence testing by showing that the minimax optimal rate for structure learning problems is determined by the minimax rate for conditional…

Several interesting generative learning algorithms involve a complex probability distribution over many random variables, involving intractable normalization constants or latent variable normalization. Some of them may even not have an…

When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…

In this letter, the optimality of the likelihood ratio test (LRT) is investigated for binary hypothesis testing problems in the presence of a behavioral decision-maker. By utilizing prospect theory, a behavioral decision-maker is modeled to…