Related papers: Approximation of Average Run Length of Moving Sum …
In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal r.v. We approximate a discrete time problem with a continuous time problem allowing us to apply established theory for stationary…
Multi-stream sequential change detection involves simultaneously monitoring many streams of data and trying to detect when their distributions change, if at all. Here, we theoretically study multiple testing issues that arise from detecting…
We propose non-parametric estimators for the average run length (ARL) and average detection delay (ADD) in quickest changepoint detection (QCD) under finite and irregular sequence lengths. Although ARL and ADD are widely used as optimality…
We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the…
We consider the problem of quickest changepoint detection under the Average Run Length (ARL) constraint where the pre-change and post-change laws lie in composite families $\mathscr{P}$ and $\mathscr{Q}$ respectively. In such a problem, a…
We introduce a recursive algorithm of conveniently general form for estimating the coefficient of a moving average model of order one and obtain convergence results for both correct and misspecified MA(1) models. The algorithm encompasses…
Functional time series have become an integral part of both functional data and time series analysis. Important contributions to methodology, theory and application for the prediction of future trajectories and the estimation of functional…
We propose two procedures to detect a change in the mean of high-dimensional online data. One is based on a max-type U-statistic and another is based on a sum-type U-statistic. Theoretical properties of the two procedures are explored in…
We develop a new efficient algorithm for the analysis of large-scale time series data. We firstly define rolling averages, derive their analytical properties, and establish their asymptotic distribution. These theoretical results are…
The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…
We develop a mixture procedure to monitor parallel streams of data for a change-point that affects only a subset of them, without assuming a spatial structure relating the data streams to one another. Observations are assumed initially to…
The problem of quickest change detection (QCD) under transient dynamics is studied, where the change from the initial distribution to the final persistent distribution does not happen instantaneously, but after a series of transient phases.…
Detecting abrupt changes in the community structure of a network from noisy observations is a fundamental problem in statistics and machine learning. This paper presents an online change detection algorithm called Spectral-CUSUM to detect…
After obtaining an accurate approximation for $ARL_0$, we first consider the optimal design of weight parameter for a multivariate EWMA chart that minimizes the stationary average delay detection time (SADDT). Comparisons with moving…
We study sequential change-point detection procedures based on linear sketches of high-dimensional signal vectors using generalized likelihood ratio (GLR) statistics. The GLR statistics allow for an unknown post-change mean that represents…
A method for the detection of changes in the expectation in univariate sequences is provided. Moving sum processes are studied. These rely on the selection of a tuning bandwidth. Here, a framework to overcome bandwidth selection is…
We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities…
In this paper, we study the quickest change detection with mismatched post-change models. A change point is the time instant at which the distribution of a random process changes. The objective of quickest change detection is to minimize…
We consider a popular online change-point problem of detecting a transient change in distributions of i.i.d. random variables. For this change-point problem, several change-point procedures are formulated and some advanced results for a…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…