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 under stationarity and under alternatives to stationarity. Monte Carlo experiments reveal their good finite-sample behavior in the case of continuous univariate, bivariate and trivariate observations. A short data example concludes the work.
A multivariate dispersion control chart monitors changes in the process variability of multiple correlated quality characteristics. In this article, we investigate and compare the performance of charts designed to monitor variability based on individual and grouped multivariate observations. We compare one of the most well-known methods for monitoring individual observations -- a multivariate EWMA chart proposed by Huwang et al -- to various charts based on grouped observations. In addition, we compare charts based on monitoring with overlapping and nonoverlapping subgroups. We recommend using…
We provide an online framework for analyzing data recorded by smart watches during running activities. In particular, we focus on identifying variations in the behavior of one or more measurements caused by changes in physical condition, such as physical discomfort, periods of prolonged de-training, or even the malfunction of measuring devices. Our framework considers data as a sequence of running activities represented by multivariate time series of physical and biometric data. We combine classical changepoint detection models with an unknown number of components with Gaussian state space mod…
Near real time change detection is important for a variety of Earth monitoring applications and remains a high priority for remote sensing science. Data sparsity, subtle changes, seasonal trends, and the presence of outliers make detecting actual landscape changes challenging. Adams and MacKay (2007) introduced Bayesian Online Changepoint Detection (BOCPD), a computationally efficient, exact Bayesian method for change detection. Incorporation of prior information allows for relaxed dependence on dense data and an extensive stable period, making this method applicable to relatively short time s…
This paper introduces the multivariate tail-inflated normal (MTIN) distribution, an elliptical heavy-tails generalization of the multivariate normal (MN). The MTIN belongs to the family of MN scale mixtures by choosing a convenient continuous uniform as mixing distribution. Moreover, it has a closed-form for the probability density function characterized by only one additional ``inflation'' parameter, with respect to the nested MN, governing the tail-weight. The first four moments are also computed; interestingly, they always exist and the excess kurtosis can assume any positive value. The met…
Flexible regression methods where interest centres on the way that the whole distribution of a response vector changes with covariates are very useful in some applications. A recently developed technique in this regard uses the matrix-variate Dirichlet process as a prior for a mixing distribution on a coefficient in a multivariate linear regression model. The method is attractive, particularly in the multivariate setting, for the convenient way that it allows for borrowing strength across different component regressions and for its computational simplicity and tractability. The purpose of the …
Monitoring several correlated quality characteristics of a process is common in modern manufacturing and service industries. Although a lot of attention has been paid to monitoring the multivariate process mean, not many control charts are available for monitoring the covariance matrix. This paper presents a comprehensive overview of the literature on control charts for monitoring the covariance matrix in a multivariate statistical process monitoring (MSPM) framework. It classifies the research that has previously appeared in the literature. We highlight the challenging areas for research and …
Dynamic statistical process monitoring methods have been widely studied and applied in modern industrial processes. These methods aim to extract the most predictable temporal information and develop the corresponding dynamic monitoring schemes. However, measurement noise is widespread in real-world industrial processes, and ignoring its effect will lead to sub-optimal modeling and monitoring performance. In this article, a probabilistic predictable feature analysis (PPFA) is proposed for multivariate time series modeling, and a multi-step dynamic predictive monitoring scheme is developed. The …
In the context of a motivating study of dynamic network flow data on a large-scale e-commerce web site, we develop Bayesian models for on-line/sequential analysis for monitoring and adapting to changes reflected in node-node traffic. For large-scale networks, we customize core Bayesian time series analysis methods using dynamic generalized linear models (DGLMs). These are integrated into the context of multivariate networks using the concept of decouple/recouple that was recently introduced in multivariate time series. This method enables flexible dynamic modeling of flows on large-scale netwo…
We consider the situation where multivariate functional data has been collected over time at each of a set of sites. Our illustrative setting is bivariate, monitoring ozone and PM$_{10}$ levels as a function of time over the course of a year at a set of monitoring sites. The data we work with is from 24 monitoring sites in Mexico City which record hourly ozone and PM$_{10}$ levels. We use the data for the year 2017. Hence, we have 48 functions to work with. Our objective is to implement model-based clustering of the functions across the sites. Using our example, such clustering can be consider…
A multivariate control chart is designed to monitor process parameters of multiple correlated quality characteristics. Often data on multivariate processes are collected as individual observations, i.e. as vectors one at the time. Various control charts have been proposed in the literature to monitor the covariance matrix of a process when individual observations are collected. In this study, we review this literature; we find 30 relevant articles from the period 1987-2019. We group the articles into five categories. We observe that less research has been done on CUSUM, high-dimensional and no…
Multivariate Exponentially Weighted Moving Average, MEWMA, charts are popular, handy and effective procedures to detect distributional changes in a stream of multivariate data. For doing appropriate performance analysis, dealing with the steady-state behavior of the MEWMA statistic is essential. Going beyond early papers, we derive quite accurate approximations of the respective steady-state densities of the MEWMA statistic. It turns out that these densities could be rewritten as the product of two functions depending on one argument only which allows feasible calculation. For proving the rela…
A sequential multiple assignment randomized trial (SMART) facilitates comparison of multiple adaptive treatment strategies (ATSs) simultaneously. Previous studies have established a framework to test the homogeneity of multiple ATSs by a global Wald test through inverse probability weighting. SMARTs are generally lengthier than classical clinical trials due to the sequential nature of treatment randomization in multiple stages. Thus, it would be beneficial to add interim analyses allowing for early stop if overwhelming efficacy is observed. We introduce group sequential methods to SMARTs to fa…
Appropriate preprocessing is a fundamental prerequisite for analyzing a noisy dataset. The purpose of this paper is to apply a nonparametric preprocessing method, called Singular Spectrum Analysis (SSA), to a variety of datasets which are subsequently analyzed by means of multiple statistical hypothesis tests. SSA is a nonparametric preprocessing method which has recently been utilized in the context of many life science problems. In the present work, SSA is compared with three other state-of-the-art preprocessing methods in terms of goodness of denoising and in terms of the statistical power …
Statistical modeling of multivariate and spatial extreme events has attracted broad attention in various areas of science. Max-stable distributions and processes are the natural class of models for this purpose, and many parametric families have been developed and successfully applied. Due to complicated likelihoods, the efficient statistical inference is still an active area of research, and usually composite likelihood methods based on bivariate densities only are used. Thibaud et al. (2016, Ann. Appl. Stat., to appear) use a Bayesian approach to fit a Brown--Resnick process to extreme tempe…
The aim of sequential change-point detection is to issue an alarm when it is thought that certain probabilistic properties of the monitored observations have changed. This work is concerned with nonparametric, closed-end testing procedures based on differences of empirical distribution functions that are designed to be particularly sensitive to changes in the comtemporary distribution of multivariate time series. The proposed detectors are adaptations of statistics used in a posteriori (offline) change-point testing and involve a weighting allowing to give more importance to recent observation…
Modern data collecting methods and computation tools have made it possible to monitor high-dimensional processes. In this article, Phase II monitoring of high-dimensional processes is investigated when the available number of samples collected in Phase I is limitted in comparison to the number of variables. A new charting statistic for high-dimensional multivariate processes based on the diagonal elements of the underlying covariance matrix is introduced and a unified procedure for Phase I and II by employing a self-starting control chart is proposed. To remedy the effect of outliers, we adopt…
It is well known that the conventional cumulative sum (CUSUM) test suffers from low power and large detection delay. In order to improve the power of the test, we propose two alternative statistics. The backward CUSUM detector considers the recursive residuals in reverse chronological order, whereas the stacked backward CUSUM detector sequentially cumulates a triangular array of backwardly cumulated residuals. A multivariate invariance principle for partial sums of recursive residuals is given, and the limiting distributions of the test statistics are derived under local alternatives. In the r…
Hydroclimatic processes are characterized by heterogeneous spatiotemporal correlation structures and marginal distributions that can be continuous, mixed-type, discrete or even binary. Simulating exactly such processes can greatly improve hydrological analysis and design. Yet this challenging task is accomplished often by ad hoc and approximate methodologies that are devised for specific variables and purposes. In this study, a single framework is proposed allowing the exact simulation of processes with any marginal and any correlation structure. We unify, extent, and improve of a general-purp…
We propose a new sequential monitoring scheme for changes in the parameters of a multivariate time series. In contrast to procedures proposed in the literature which compare an estimator from the training sample with an estimator calculated from the remaining data, we suggest to divide the sample at each time point after the training sample. Estimators from the sample before and after all separation points are then continuously compared calculating a maximum of norms of their differences. For open-end scenarios our approach yields an asymptotic level $α$ procedure, which is consistent under th…
