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Permutation tests are a distribution free way of performing hypothesis tests. These tests rely on the condition that the observed data are exchangeable among the groups being tested under the null hypothesis. This assumption is easily…

Methodology · Statistics 2017-12-14 Daniell Toth

We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…

Statistics Theory · Mathematics 2026-01-23 Hirofumi Ota , Masaaki Imaizumi

Functional data often arise as sequential temporal observations over a continuous state-space. A set of functional data with a possible change in its structure may lead to a wrong conclusion if it is not taken in to account. So, sometimes,…

Methodology · Statistics 2015-03-18 Buddhananda Banerjee , Satyaki Mazumder

We consider the problem of sequentially testing for changes in the mean parameter of a time series, compared to a benchmark period. Most tests in the literature focus on the null hypothesis of a constant mean versus the alternative of a…

Methodology · Statistics 2025-09-23 Patrick Bastian , Tim Kutta , Rupsa Basu , Holger Dette

There has been much interest in the nonparametric testing of conditional independence in the econometric and statistical literature, but the simplest and potentially most useful method, based on the sample partial correlation, seems to have…

Statistics Theory · Mathematics 2020-05-27 Wicher Bergsma

New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and…

Methodology · Statistics 2018-08-01 Dominik Liebl , Stefan Rameseder

We propose nonparametric open-end sequential testing procedures that can detect all types of changes in the contemporary distribution function of possibly multivariate observations. Their asymptotic properties are theoretically investigated…

Methodology · Statistics 2022-11-15 Mark Holmes , Ivan Kojadinovic , Alex Verhoijsen

For a spatiotemporal process $\{X_j(s,t) | ~s \in S~,~t \in T \}_{j =1, \ldots , n} $, where $S$ denotes the set of spatial locations and $T$ the time domain, we consider the problem of testing for a change in the sequence of mean…

Statistics Theory · Mathematics 2022-03-10 Holger Dette , Pascal Quanz

We propose statistical procedures for detecting changes in the mean of spatial random fields observed on regular grids. The proposed framework provides a general approach to change detection in spatial processes. Extending a block-based…

Methodology · Statistics 2025-12-15 Sheila T. Görz , Roland Fried

Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…

Statistics Theory · Mathematics 2019-11-19 Rok Blagus , Jakob Peterlin , Janez Stare

A common problem in machine learning is determining if a variable significantly contributes to a model's prediction performance. This problem is aggravated for datasets, such as gene expression datasets, that suffer the worst case of…

Methodology · Statistics 2023-10-13 Yue Wu , Ted Spaide , Kenji Nakamichi , Russell Van Gelder , Aaron Lee

Classical and more recent tests for detecting distributional changes in multivariate time series often lack power against alternatives that involve changes in the cross-sectional dependence structure. To be able to detect such changes…

Statistics Theory · Mathematics 2014-09-16 Axel Bücher , Ivan Kojadinovic , Tom Rohmer , Johan Segers

Permutation tests enable testing statistical hypotheses in situations when the distribution of the test statistic is complicated or not available. In some situations, the test statistic under investigation is multivariate, with the multiple…

Methodology · Statistics 2023-11-08 Zdeněk Hlávka , Daniel Hlubinka , Šárka Hudecová

Classical change point analysis aims at (1) detecting abrupt changes in the mean of a possibly non-stationary time series and at (2) identifying regions where the mean exhibits a piecewise constant behavior. In many applications however, it…

Statistics Theory · Mathematics 2020-02-17 Axel Bücher , Holger Dette , Florian Heinrichs

In the common time series model $X_{i,n} = \mu (i/n) + \varepsilon_{i,n}$ with non-stationary errors we consider the problem of detecting a significant deviation of the mean function $\mu$ from a benchmark $g (\mu )$ (such as the initial…

Statistics Theory · Mathematics 2020-05-25 Holger Dette , Florian Heinrichs

It is of importance to investigate the significance of a subset of covariates $W$ for the response $Y$ given covariates $Z$ in regression modeling. To this end, we propose a significance test for the partial mean independence problem based…

Methodology · Statistics 2024-06-06 Leheng Cai , Xu Guo , Wei Zhong

In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…

Methodology · Statistics 2021-12-21 Yafei Wang , Tingyu Lai , Bei Jiang , Linglong Kong , Zhongzhan Zhang

Most existing methods for testing equality of means of functional data from multiple populations rely on assumptions of equal covariance and/or Gaussianity. In this work we provide a new testing method based on a statistic that is…

Methodology · Statistics 2025-09-30 Chuang Xu , Andrew T. A. Wood , Yanrong Yang

We propose using a permutation test to detect discontinuities in an underlying economic model at a known cutoff point. Relative to the existing literature, we show that this test is well suited for event studies based on time-series data.…

Econometrics · Economics 2022-07-12 Federico A. Bugni , Jia Li , Qiyuan Li

Anomaly detection when observing a large number of data streams is essential in a variety of applications, ranging from epidemiological studies to monitoring of complex systems. High-dimensional scenarios are usually tackled with…

Methodology · Statistics 2025-12-18 Ivo V. Stoepker , Rui M. Castro , Ery Arias-Castro , Edwin van den Heuvel
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