Related papers: Testing for change points in time series models an…

When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical…

In this paper we propagate a large deviations approach for proving limit theory for (generally) multivariate time series with heavy tails. We make this notion precise by introducing regularly varying time series. We provide general large…

The object of this paper is to study the asymptotic dependence structure of the linear time series models with infinitely divisible innovations by the use of their characteristic functions. Autoregressive moving-average (ARMA) models and…

A binomial time series describes binary behaviors of individuals within a group, which depend on group behaviors in the past. Binomial time series data is widely applied in fields such as infection tracking and behavior analysis. In this…

In testing of hypothesis the robustness of the tests is an important concern. Generally, the maximum likelihood based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations…

We study a generalization of the Random Energy Model to the case when the number of exponential factors varies at random. Also a relation between REM and the Erd"os-R'enyi limit theorem for maximums of partial sums is considered.

We propose and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth…

For a set of dependent random variables, without stationary or the strong mixing assumptions, we derive the asymptotic independence between their sums and maxima. Then we apply this result to high-dimensional testing problems, where we…

Deep neural network (NN) with millions or billions of parameters can perform really well on unseen data, after being trained from a finite training set. Various prior theories have been developed to explain such excellent ability of NNs,…

Time-reversibility is a crucial feature of many time series models, while time-irreversibility is the rule rather than the exception in real-life data. Testing the null hypothesis of time-reversibilty, therefore, should be an important step…

We describe likelihood-based statistical tests for use in high energy physics for the discovery of new phenomena and for construction of confidence intervals on model parameters. We focus on the properties of the test procedures that allow…

While time series prediction is an important, actively studied problem, the predictive accuracy of time series models is complicated by non-stationarity. We develop a fast and effective approach to allow for non-stationarity in the…

The following note proves that conditional entropy of a sequence is almost time-reversal invariant, specifically they only differ by a small constant factor dependent only upon the forward and backward models that the entropies are being…

We introduce a powerful scan statistic and the corresponding test for detecting the presence and pinpointing the location of a change point within the distribution of a data sequence with the data elements residing in a separable metric…

We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. One salient and distinct feature of…

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…

Data objects taking value in a general metric space have become increasingly common in modern data analysis. In this paper, we study two important statistical inference problems, namely, two-sample testing and change-point detection, for…

We establish a sharp large deviation principle for renewal-reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle…

Permutation entropy has become a standard tool for time series analysis that exploits the temporal properties of these data sets. Many current applications use an approach based on Shannon entropy, which implicitly assumes an underlying…

New inference methods for the multivariate coefficient of variation and its reciprocal, the standardized mean, are presented. While there are various testing procedures for both parameters in the univariate case, it is less known how to do…