Related papers: Error Exponents of Mismatched Likelihood Ratio Tes…

We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…

A decision must often be made between heavy-tailed and Gaussian errors for a regression or a time series model, and the t-distribution is frequently used when it is assumed that the errors are heavy-tailed distributed. The performance of…

Positive and negative likelihood ratios are parameters which are used to assess and compare the effectiveness of binary diagnostic tests. Both parameters only depend on the sensitivity and specificity of the diagnostic test and are…

This paper tackles the challenge of detecting unreliable behavior in regression algorithms, which may arise from intrinsic variability (e.g., aleatoric uncertainty) or modeling errors (e.g., model uncertainty). First, we formally introduce…

Statistical tests of pseudorandom number generators (PRNGs) are applicable to any type of random number generators and are indispensable for evaluation. While several practical packages for statistical tests of randomness exist, they may…

Testing for regime switching when the regime switching probabilities are specified either as constants (`mixture models') or are governed by a finite-state Markov chain (`Markov switching models') are long-standing problems that have also…

We consider the problem of guessing the realization of a random variable but under more general Tsallis' non-extensive entropic framework rather than the classical Maxwell-Boltzman-Gibbs-Shannon framework. We consider both the conditional…

Composite likelihoods are a class of alternatives to the full likelihood which are widely used in many situations in which the likelihood itself is intractable. A composite likelihood may be computed without the need to specify the full…

We employ a general Monte Carlo method to test composite hypotheses of goodness-of-fit for several popular multivariate models that can accommodate both asymmetry and heavy tails. Specifically, we consider weighted L2-type tests based on a…

We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…

Many scientific applications involve testing theories that are only partially specified. This task often amounts to testing the goodness-of-fit of a candidate distribution while allowing for reasonable deviations from it. The tolerant…

In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…

Within the machine learning community, the widely-used uniform convergence framework has been used to answer the question of how complex, over-parameterized models can generalize well to new data. This approach bounds the test error of the…

We study the properties of several likelihood-based statistics commonly used in testing for the presence of a known signal under a mixture model with known background, but unknown signal fraction. Under the null hypothesis of no signal, all…

In this paper we develop a novel bootstrap test for the comparison of two multinomial distributions. The two distributions are called {\it equivalent} or {\it similar} if a norm of the difference between the class probabilities is smaller…

Recently, there has been significant interest in linear regression in the situation where predictors and responses are not observed in matching pairs corresponding to the same statistical unit as a consequence of separate data collection…

Relative error approaches are more of concern compared to absolute error ones such as the least square and least absolute deviation, when it needs scale invariant of output variable, for example with analyzing stock and survival data. An…

We investigate a state discrimination problem which interpolates minimum-error and unambiguous discrimination by introducing a margin for the probability of error. We closely analyze discrimination of two pure states with general occurrence…

Exact lower and upper bounds on the best possible misclassification probability for a finite number of classes are obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. These…

Particle physics experiments use likelihood ratio tests extensively to compare hypotheses and to construct confidence intervals. Often, the null distribution of the likelihood ratio test statistic is approximated by a $\chi^2$ distribution,…