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For general repeated measures designs the Wald-type statistic (WTS) is an asymptotically valid procedure allowing for unequal covariance matrices and possibly non-normal multivariate observations. The drawback of this procedure is the poor…

Estimating the strength of dependency between two variables is fundamental for exploratory analysis and many other applications in data mining. For example: non-linear dependencies between two continuous variables can be explored with the…

In this paper, we investigate local permutation tests for testing conditional independence between two random vectors $X$ and $Y$ given $Z$. The local permutation test determines the significance of a test statistic by locally shuffling…

Modern data acquisition based on high-throughput technology is often facing the problem of missing data. Algorithms commonly used in the analysis of such large-scale data often depend on a complete set. Missing value imputation offers a…

Random forests have been widely used for their ability to provide so-called importance measures, which give insight at a global (per dataset) level on the relevance of input variables to predict a certain output. On the other hand, methods…

Recently, invariant risk minimization (IRM) was proposed as a promising solution to address out-of-distribution (OOD) generalization. However, it is unclear when IRM should be preferred over the widely-employed empirical risk minimization…

We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…

The problem of detecting changes in covariance for a single pair of features has been studied in some detail, but may be limited in importance or general applicability. In contrast, testing equality of covariance matrices of a {\it set} of…

We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…

Statistical significance testing is used in natural language processing (NLP) to determine whether the results of a study or experiment are likely to be due to chance or if they reflect a genuine relationship. A key step in significance…

Random Forests (RFs) are widely used Machine Learning models in low-power embedded devices, due to their hardware friendly operation and high accuracy on practically relevant tasks. The accuracy of a RF often increases with the number of…

Randomized benchmarking (RB) protocols are standard tools for characterizing quantum devices. Prior analyses of RB protocols have not provided a complete method for analyzing realistic data, resulting in a variety of ad-hoc methods. The…

Sequential estimation of the success probability $p$ in inverse binomial sampling is considered in this paper. For any estimator $\hat p$, its quality is measured by the risk associated with normalized loss functions of linear-linear or…

We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically…

Valid uncertainty quantification after model selection remains challenging in high-dimensional linear regression, especially within the possibilistic inferential model (PIM) framework. We develop possibilistic inferential models for…

Recent work on reinforcement learning with verifiable rewards (RLVR) has shown that large language models (LLMs) can be substantially improved using outcome-level verification signals, such as unit tests for code or exact-match checks for…

The infinitesimal jackknife (IJ) has recently been applied to the random forest to estimate its prediction variance. These theorems were verified under a traditional random forest framework which uses classification and regression trees…

Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are…

The issue of estimating residual variance in regression models has experienced relatively little attention in the machine learning community. However, the estimate is of primary interest in many practical applications, e.g. as a primary…

While many statistical procedures rely on a fixed sample size, sequential methods allow a decision-maker to adapt the sample size to achieve a given precision. In this way, sequential tests reduce the average number of observations required…