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We consider change-point tests based on rank statistics to test for structural changes in long-range dependent observations. Under the hypothesis of stationary time series and under the assumption of a change with decreasing change-point…

Statistics Theory · Mathematics 2020-10-01 Annika Betken , Martin Wendler

I propose two U-statistics to test coefficients in generalized linear models. One of them is used to deal with global hypothesis and the other one to test with the nuisance parameter. Both the statistics proposed are within high-dimensional…

Applications · Statistics 2013-12-03 Gong Zi Jiang Nan

We investigate the power of the CUSUM test and the Wilcoxon change-point test for a shift in the mean of a process with long-range dependent noise. We derive analytiv formulas for the power of these tests under local alternatives. These…

Statistics Theory · Mathematics 2013-03-21 Herold Dehling , Aeneas Rooch , Murad S. Taqqu

Simultaneous tests of superiority and non-inferiority hypotheses on multiple endpoints are often performed in clinical trials to demonstrate that a new treatment is superior over a control on at least one endpoint and non-inferior on the…

Methodology · Statistics 2023-10-02 Wenfeng Chen , Naiqing Zhao , Guoyou Qin , Jie Chen

We present a new way of testing ordered hypotheses against all alternatives which overpowers the classical approach both in simplicity and statistical power. Our new method tests the constrained likelihood ratio statistic against the…

Methodology · Statistics 2018-06-26 Diaa Al Mohamad , Jelle J. Goeman , Erik W. van Zwet , Eric A. Cator

This paper describes and compares several prominent single and multiple changepoint techniques for time series data. Due to their importance in inferential matters, changepoint research on correlated data has accelerated recently.…

Methodology · Statistics 2021-01-07 Xueheng Shi , Colin Gallagher , Robert Lund , Rebecca Killick

In this paper, we consider a change-point problem for a centered, stationary and $m$-dependent multivariate random field. Under the distribution free assumption, a change-point test using CUSUM statistic is proposed to detect anomalies…

Statistics Theory · Mathematics 2024-06-28 Vitalii Makogin , Duc Nguyen

An important assumption in the work on testing for structural breaks in time series consists in the fact that the model is formulated such that the stochastic process under the null hypothesis of "no change-point" is stationary. This…

Methodology · Statistics 2015-03-31 Holger Dette , Weichi Wu , Zhou Zhou

We study the detection of change-points in time series. The classical CUSUM statistic for detection of jumps in the mean is known to be sensitive to outliers. We thus propose a robust test based on the Wilcoxon two-sample test statistic.…

Statistics Theory · Mathematics 2013-04-10 Herold Dehling , Roland Fried , Isabel García , Martin Wendler

In this paper new tests for the independence of two high-dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type…

Statistics Theory · Mathematics 2023-04-19 Taras Bodnar , Holger Dette , Nestor Parolya

In this paper, a novel test for testing whether data are Missing Completely at Random is proposed. Asymptotic properties of the test are derived utilizing the theory of non-degenerate U-statistics. It is shown that the novel test statistic…

Statistics Theory · Mathematics 2023-10-31 Danijel Aleksić

Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a…

Statistics Theory · Mathematics 2021-01-05 Mengjia Yu , Xiaohui Chen

In this article, we propose a class of test statistics for a change point in the mean of high-dimensional independent data. Our test integrates the U-statistic based approach in a recent work by \cite{hdcp} and the $L_q$-norm based…

Methodology · Statistics 2021-02-01 Yangfan Zhang , Runmin Wang , Xiaofeng Shao

We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini's mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic,…

Statistics Theory · Mathematics 2021-05-24 Sara Kristin Schmidt , Max Wornowizki , Roland Fried , Herold Dehling

We consider the testing and estimation of change-points, locations where the distribution abruptly changes, in a sequence of multivariate or non-Euclidean observations. We study a nonparametric framework that utilizes similarity information…

Methodology · Statistics 2018-02-23 Lynna Chu , Hao Chen

This article considers change point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on $U$-statistic in Chen…

Statistics Theory · Mathematics 2021-08-10 Runmin Wang , Changbo Zhu , Stanislav Volgushev , Xiaofeng Shao

For a bivariate time series $((X_i,Y_i))_{i=1,...,n}$ we want to detect whether the correlation between $X_i$ and $Y_i$ stays constant for all $i = 1,...,n$. We propose a nonparametric change-point test statistic based on Kendall's tau and…

Statistics Theory · Mathematics 2022-04-12 Herold Dehling , Daniel Vogel , Martin Wendler , Dominik Wied

We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly…

Statistics Theory · Mathematics 2016-08-16 István Berkes , Lajos Horváth , Piotr Kokoszka , Qi-Man Shao

In this paper, change-point problems for long memory stochastic volatility models are considered. A general testing problem which includes various alternative hypotheses is discussed. Under the hypothesis of stationarity the limiting…

Statistics Theory · Mathematics 2017-06-21 Annika Betken , Rafał Kulik

We propose a new asymptotic test to assess the stationarity of a time series' mean that is applicable in the presence of both heteroscedasticity and short-range dependence. Our test statistic is composed of Gini's mean difference of local…

Statistics Theory · Mathematics 2021-08-23 Sara Kristin Schmidt