Change-point Estimation Research Articles

Identifying multiple changes for a functional data sequence with application to freeway traffic segmentation

Motivated by the study of road segmentation partitioned by shifts in traffic conditions along a freeway, we introduce a two-stage procedure, Dynamic Segmentation and Backward Elimination (DSBE), for identifying multiple changes in the mean functions for a sequence of functional data. The Dynamic Segmentation procedure searches for all possible changepoints using the derived global optimality criterion coupled with the local strategy of at-most-one-changepoint by dividing the entire sequence into individual subsequences that are recursively adjusted until convergence. Then, the Backward Elimination procedure verifies these changepoints by iteratively testing the unlikely changes to ensure their significance until no more changepoints can be removed. By combining the local strategy with the global optimal changepoint criterion, the DSBE algorithm is conceptually simple and easy to implement and performs better than the binary segmentation-based approach at detecting small multiple changes. The consistency property of the changepoint estimators and the convergence of the algorithm are proved. We apply DSBE to detect changes in traffic streams through real freeway traffic data. The practical performance of DSBE is also investigated through intensive simulation studies for various scenarios.

Detection of multiple change points for linear processes under negatively super-additive dependence

This paper focuses on the issue of detecting the multiple change points for linear processes under negatively super-additive dependence (NSD). We propose a CUSUM-type method in the multiple variance change model and establish the weak convergence rate of the change points estimation. To carry out this method, we give a multiple variance-change iterative (MVCI) algorithm. Additionally, some simulations are implemented to substantiate the validity of the CUSUM-type method. Comparison with some best methods indicates that the CUSUM-type change point estimation is computationally competitive and superior in terms of the mean squared error (MSE).

Applying a change-point control chart based on likelihood ratio to supply chain network monitoring

In this paper, a supply chain network system is viewed as a serial-parallel multistage process; and the application of a change point control chart based on likelihood ratio is explored to monitor this system. Firstly, state-space modeling is used to characterize complexity of the supply chain network system. Then, a change point control chart based on likelihood ratio is built to trigger potential tardy orders in the system. A case study is illustrated to indicate that the change point control charts can effectively signal process mean shift, and accurately estimate the change point and the out-of-control stage in term of power of detection and the accuracy of estimation of change point. We also investigate the effect of misspecified parameters of state space equations on the performance of the change point control chart. The results show that the performance of the change point control chart is relatively stable.

Robust change point estimation in two-phase linear regression models: An application to metabolic pathway data

In this study, we develop robust versions of the change point estimation methods given by Hudson (1966) and Muggeo (2003) in the two-phase linear regression model. We use a modified maximum likelihood (MML) methodology originated by Tiku (1967, 1968) when the error terms of a two-phase linear regression model are independently and identically distributed as long-tailed symmetric. Proposed estimators are shown to be more efficient and robust using the Monte-Carlo simulation. Julious’s (Julious, 2001) metabolic pathway data is analyzed in the application part of the study. It is shown that for this data using a LS estimator is inappropriate since there is an outlying observation. We therefore use proposed robust estimators instead of LS estimators and obtain more reliable results.

Homogeneity tests of covariance matrices with high-dimensional longitudinal data.

This paper deals with the detection and identification of changepoints among covariances of high-dimensional longitudinal data, where the number of features is greater than both the sample size and the number of repeated measurements. The proposed methods are applicable under general temporal-spatial dependence. A new test statistic is introduced for changepoint detection, and its asymptotic distribution is established. If a changepoint is detected, an estimate of the location is provided. The rate of convergence of the estimator is shown to depend on the data dimension, sample size, and signal-to-noise ratio. Binary segmentation is used to estimate the locations of possibly multiple changepoints, and the corresponding estimator is shown to be consistent under mild conditions. Simulation studies provide the empirical size and power of the proposed test and the accuracy of the changepoint estimator. An application to a time-course microarray dataset identifies gene sets with significant gene interaction changes over time.

Nuisance-parameter-free changepoint detection in non-stationary series

Many changepoint detection procedures rely on the estimation of nuisance parameters (like long-run variance). If a change has occurred, estimators might be biased and data adaptive rules for the choice of tuning parameters might not work as expected. If the data are not stationary, this becomes more challenging. The aim of this paper is to present two changepoint tests, which involve neither nuisance nor tuning parameters. This is achieved by combing self-normalization and wild bootstrap. We investigate the asymptotic behavior and show the consistency of the bootstrap under the hypothesis as well as under the alternative, assuming mild conditions on the weak dependence of the time series. As a by-product, a changepoint estimator is introduced and its consistency is proved. The results are illustrated through a simulation study. The new completely data-driven tests are applied to real data examples from finance and hydrology.

Change Point Estimation of the Stationary State in Auto Regressive Moving Average Models, Using Maximum Likelihood Estimation and Singular Value Decomposition-based Filtering

In this paper, for the first time, the subject of change point estimation has been utilized in the stationary state of auto regressive moving average (ARMA) (1, 1). In the monitoring phase, in case the features of the question pursue a time series, i.e., ARMA(1,1), on the basis of the maximum likelihood technique, an approach will be developed for the estimation of the stationary state’s change point. To estimate unidentified parameters following the change point, the dynamic linear model’s filtering was utilized on the basis of the singular decomposition of values. The proposed model has wide applications in several fields such as finance, stock exchange marks and rapid production. The results of simulation showed the suggested estimator’s effectiveness. In addition, a real example on stock exchange market is offered to delineate the application.

Phase‐I monitoring of log‐linear model‐based processes (a case study in health care: Kidney patients)

AbstractProcesses with multiple correlated categorical quality characteristics are called multivariate categorical processes. These processes are usually shown by contingency tables and are characterized by log‐linear models. In this paper, two monitoring approaches including likelihood ratio test (LRT) and F test are developed to monitor multivariate categorical processes based on the contingency table in Phase I. In addition, a change point estimator for multivariate categorical processes is developed in Phase I. The performances of the two proposed approaches are evaluated in terms of probability of signal, while the performance of the proposed change point estimator is evaluated in terms of accuracy and precision criteria through simulation experiments. Meanwhile, we compare the performance of the two proposed control charts with an existing control chart called “−2LRT” control chart for multivariate categorical processes. In the end, a typical application of the proposed methods is illustrated in a real‐world health care system.

Changepoint analysis of Klementinum temperature series

AbstractThis paper presents a statistical analysis of the stationarity of the Prague–Klementinum temperature series. In the first part, the stationarity of annual means is rejected, and several nonstationary models are suggested to assess the increase in temperature in the most recent decades. The analysis shows that positions of the changepoint estimates depend largely on our decision as to whether we apply a discontinuous or a continuous piecewise linear model. In the second part, we study the stationarity of the seasonal behavior of the series, particularly the stationarity of the mean annual profiles. The analysis of the seasonal cycle shows that the increase in temperature has not the same character throughout the calendar year. Rather, an increase in temperature in winter days is larger than an increase in summer days, and the temperature difference between summer and winter days decreases.

LDJump: Estimating variable recombination rates from population genetic data.

As recombination plays an important role in evolution, its estimation and the identification of hotspot positions is of considerable interest. We propose a novel approach for estimating population recombination rates based on genotyping or sequence data that involves a sequential multiscale change point estimator. Our method also permits demography to be taken into account. It uses several summary statistics within a regression model fitted on suitable scenarios. Our proposed method is accurate, computationally fast, and provides a parsimonious solution by ensuring a type I error control against too many changes in the recombination rate. An application to human genome data suggests a good congruence between our estimated and experimentally identified hotspots. Our method is implemented in the R‐package LDJump, which is freely available at https://github.com/PhHermann/LDJump.

Rank-based multiple change-point detection

A nonparametric procedure is proposed to estimate multiple change-points of location changes in a univariate data sequence by using ranks instead of the raw data. While existing rank-based multiple change-point detection methods are mostly based on sequential tests, we treat it as a model selection problem. We derive the corresponding Schwarz’s information criterion for rank-statistics, theoretically prove the consistency of the change-point estimator and use a pruned dynamic programing algorithm to achieve the change-point estimator. Simulation studies show our method’s robustness, effectiveness and efficiency in detecting mean-changes. We also apply the method to a gene dataset as an illustration.

On residual CUSUM statistic for PINAR(1) model in statistical design and diagnostic of control chart

This paper studies the residual-based CUSUM test statistic in first-order Poisson integer-valued autoregressive (PINAR(1)) models. The residuals are calculated with squared difference (SD) estimates, and a retrospective phase (Phase I) analysis is conducted. Moreover, the upper one-sided CUSUM-type chart (RCUSUMV chart) is considered for effectively detecting abnormal shifts in a monitoring phase (Phase II) situation. Numerical experiments show that our method can be good alternative to conventional CUSUM charts when an effective detection and accurate change point estimation for small shifts are primary concerns.

Bayes and Non-Bayes Estimation of Change Point in Nonstandard Mixture Inverse Weibull Distribution

We consider a sequence of independent random variables X1, X2,… , Xm, …,Xn (n ≥ 3) exhibiting a change in the probability distribution of the data generating mechanism. We suppose that the distribution changes at some point, called a change point, to a second distribution for the remaining observations. We propose Bayes estimators of change point under symmetric loss functions and asymmetric loss functions. The sensitivity analysis of Bayes estimators are carried out by simulation and numerical comparisons with R-programming.

A Hybrid Lower Bound for Parameter Estimation of Signals With Multiple Change-Points

Change-point estimation has received much attention in the literature as it plays a significant role in several signal processing applications. However, the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters, namely the parameters associated with the noise distribution and the change-point locations. In this paper, we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters. Specifically, we propose a hybrid Cramer–Rao–Weiss-Weinstein bound and derive its associated closed-form expressions. Numerical simulations assess the tightness of the proposed bound in the case of Gaussian and Poisson observations.

Evaluation of Socioeconomic Status Indicators for Confounding Adjustment in Observational Studies of Medication Use.

Methodologic research evaluating confounding due to socioeconomic status (SES) in observational studies of medications is limited. We identified 7,109 patients who initiated brand or generic atorvastatin from Medicare claims (2011-2013) linked to electronic medical records and census data. We created a propensity score (PS) containing only claims-based covariates and augmented it with additional claims-based proxies for SES, ZIP code, and block group level SES. Cox models with PS fine-stratification and weighting were used to compare rates of a cardiovascular end point and emergency department visits. Adjustment with only claims-based variables substantially improved balance on all SES variables compared with the unadjusted. Although inclusion of SES in PS models further improved balance on SES variables compared with models with claims-based covariates only, it did not materially change point estimates for either outcome. Inclusion of claims-based proxies may mitigate confounding by SES when aggregate-level SES information is unavailable.

Poisson source localization on the plane: change-point case

We present a detection problem where several spatially distributed sensors observe Poisson signals emitted from a single radioactive source of unknown position. The measurements at each sensor are modeled by independent inhomogeneous Poisson processes. A method based on Bayesian change-point estimation is proposed to identify the location of the source’s coordinates. The asymptotic behavior of the Bayesian estimator is studied. In particular, the consistency and the asymptotic efficiency of the estimator are analyzed. The limit distribution and the convergence of the moments are also described. The similar statistical model could be used in GPS localization problems.

A fast algorithm for short term electric load forecasting by a hidden semi-markov process

ABSTRACTThe paper proposes an alternative algorithm to implement the current manual choosing mechanism of energy companies whose dedicated department has a library of electric load models and one best model is chosen manually everyday for daily forecast. The proposed algorithm is a combination of an estimation of change point, and a fast ECM algorithm based on the empirical probability function, as well as methods of a hidden markov chain. We train parameters of the proposed algorithm based on a historical dataset consisting of loads, exogenous information such as temperature, and the daily recommended best model which is unavailable sometimes. Simulations and a test on a real-world dataset show that compared with other state-of-art algorithms, the proposed algorithm is fast and efficient for short-term electric load forecasting. An implement to the proposed algorithm written in Matlab is provided in supplement file.

Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data

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 among observations, which can be applied to various data types as long as an informative similarity measure on the sample space can be defined. The existing approach along this line has low power and/or biased estimates for change-points under some common scenarios. We address these problems by considering new tests based on similarity information. Simulation studies show that the new approaches exhibit substantial improvements in detecting and estimating change-points. In addition, under some mild conditions, the new test statistics are asymptotically distribution-free under the null hypothesis of no change. Analytic $p$-value approximations to the significance of the new test statistics for the single change-point alternative and changed interval alternative are derived, making the new approaches easy off-the-shelf tools for large datasets. The new approaches are illustrated in an analysis of New York taxi data.

Assessing health care interventions via an interrupted time series model: Study power and design considerations.

The delivery and assessment of quality health care is complex with many interacting and interdependent components. In terms of research design and statistical analysis, this complexity and interdependency makes it difficult to assess the true impact of interventions designed to improve patient health care outcomes. Interrupted time series (ITS) is a quasi-experimental design developed for inferring the effectiveness of a health policy intervention while accounting for temporal dependence within a single system or unit. Current standardized ITS methods do not simultaneously analyze data for several units nor are there methods to test for the existence of a change point and to assess statistical power for study planning purposes in this context. To address this limitation, we propose the "Robust Multiple ITS" (R-MITS) model, appropriate for multiunit ITS data, that allows for inference regarding the estimation of a global change point across units in the presence of a potentially lagged (or anticipatory) treatment effect. Under the R-MITS model, one can formally test for the existence of a change point and estimate the time delay between the formal intervention implementation and the over-all-unit intervention effect. We conducted empirical simulation studies to assess the type one error rate of the testing procedure, power for detecting specified change-point alternatives, and accuracy of the proposed estimating methodology. R-MITS is illustrated by analyzing patient satisfaction data from a hospital that implemented and evaluated a new care delivery model in multiple units.

Beyond Cumulative Sum Charting in Non-Stationarity Detection and Estimation

In computer science, stochastic processes, and industrial engineering, stationarity is often taken to imply a stable, predictable flow of events and non-stationarity, consequently, a departure from such a flow. Efficient detection and accurate estimation of non-stationarity are crucial in understanding the evolution of the governing dynamics. Pragmatic considerations include protecting human lives and property in the context of devastating processes such as earthquakes or hurricanes. Cumulative Sum (CUSUM) charting, the prevalent technique to weed out such non-stationarities, suffers from assumptions on a priori knowledge of the pre and post-change process parameters and constructs such as time discretization. In this paper, we have proposed two new ways in which non-stationarity may enter an evolving system - an easily detectable way, which we term strong corruption, where the post-change probability distribution is deterministically governed, and an imperceptible way which we term hard detection, where the post-change distribution is a probabilistic mixture of several densities. In addition, by combining the ordinary and switched trend of incoming observations, we develop a new trend ratio statistic in order to detect whether a stationary environment has changed. Surveying a variety of distance metrics, we examine several parametric and non-parametric options in addition to the established CUSUM and find that the trend ratio statistic performs better under the especially difficult scenarios of hard detection. Simulations (both from deterministic and mixed inter-event time densities), sensitivity-specificity type analyses, and estimated time of change distributions enable us to track the ideal detection candidate under various non-stationarities. Applications on two real data sets sampled from volcanology and weather science demonstrate how the estimated change points are in agreement with those obtained in some of our previous works, using different methods. Incidentally, this study sheds light on the inverse nature of dependence between the Hawaiian volcanoes Kilauea and Mauna Loa and demonstrates how inhabitants of the now-restless Kilauea may be relocated to Mauna Loa to minimize the loss of lives and moving costs.