Change-point Estimation Research Articles

Change-point estimators with the weighted objective function when sequentially estimating breaks

Change-point estimators based on a recently proposed weighted objective function are investigated, focusing on models with two structural breaks estimated sequentially. The asymptotic distributions of the first- and second-step estimators are examined under the long-span asymptotic scheme, which applies under large break sizes. It is shown that these distributions are generally unimodal and asymmetric. However, under small break sizes, the limiting distribution under the aforementioned scheme fails to accurately approximate the finite sample distribution. The first-step estimator’s finite sample distribution tends to exhibit two peaks, while the corresponding asymptotic distribution remains unimodal. This finite sample characteristic is better approximated under the in-fill asymptotic scheme.

Detection and localization of changes in a panel of densities

We propose a new methodology for identifying and localizing changes in the Fréchet mean of a multivariate time series of probability densities. The functional data objects we study are random densities fs,t indexed by discrete time t and a vector component s, which can be treated as a broadly understood spatial location. Our main objective is to identify the set of components s, where a change occurs with statistical certainty. A challenge of this analysis is that the densities fs,t are not directly observable and must be estimated from sparse and potentially imbalanced data. Such setups are motivated by the analysis of two data sets that we investigate in this work. First, a hitherto unpublished large data set of Brazilian Covid infections and a second, a financial data set derived from intraday prices of U.S. Exchange Traded Funds. Chief statistical advances are the development of change point tests and estimators of components of change for multivariate time series of densities. We prove the theoretical validity of our methodology and investigate its finite sample performance in a simulation study.

Estimation of change-point in the covariate effects on restricted mean survival time

The restricted mean survival time (RMST) emerges as a crucial summary metric in survival analysis. In some cases, certain covariates may have a varying impact on RMST at one specific change-point. For instance, consider studies focusing on women’s health, where a notable shift in a patient’s lifespan might occur when the age at menopause surpasses a particular cutoff value. To tackle this complex phenomenon, we consider a regression analysis of RMST with change-point in the covariate effects. This involves building a generalized linear model that directly captures the relationship between RMST and associated covariates that may have a change-point. Using the smoothed estimating equation with pseudo-observations, we obtain parameter estimators and establish the large sample properties. Finally, we assess the finite sample performance of the proposed method through simulation studies and apply it to real data examples from primary biliary cirrhosis and rectal cancer studies.

A Distribution-Free Method for Change Point Detection in Non-Sparse High Dimensional Data

We propose a distribution-free distance-based method for high dimensional change points that can address challenging situations when the sample size is very small compared to the dimension as in the so-called HDLSS data or when non-sparse changes may occur due to change in many variables but with small significant magnitudes. Our method can detect changes in mean or variance of high dimensional observations as well as other distributional changes. We present efficient algorithms that can detect single and multiple high dimensional change points. We use nonparametric metrics, including a new dissimilarity measure and some new distance and difference distance matrices, to develop a procedure to estimate change point locations. We also introduce a nonparametric test to determine the significance of estimated change points. We provide theoretical guaranties for our method and demonstrate its empirical performance in comparison with some of the recent methods for high dimensional change points. An R package called HDDchangepoint is developed to implement the proposed method.

Irregular surface temperature monitoring in liver procurement via time-vertex signal processing

The liver viability monitoring during its procurement is critical to guarantee the safe liver transportation. Traditionally, the viability is assessed by taking invasive biopsy on the liver surface. Recently, the noninvasive thermal images of liver surface have been used as an alternative assessment way. Researchers have proposed monitoring and classification approaches based on the thermal images. Existing works have demonstrated the importance of the temporal variation or the spatial variation of the thermal images to the viability monitoring. However, there is no prior work to leverage the graph structure of the spatio-temporal processes for the viability monitoring. In this paper, we propose a time-vertex signal processing framework for the irregular thermal data of the pure liver region monitoring. In particular, we extract features of irregular thermal data based on the joint Fourier transform (JFT), which is an integration of graph Fourier transform (GFT) and discrete Fourier transform (DFT). The extracted JFT features can accurately reconstruct the thermal images with a limited number of features. Then, we use a non-parametric online change-point estimation method, based on online scan B statistics, to monitor the JFT features without a parametric distribution. Our proposed framework is applied to both simulation and the liver procurement data, and achieves good monitoring performance.

Detection of a structural break in intraday volatility pattern

We develop theory leading to testing procedures for the presence of a change point in the intraday volatility pattern. The new theory is developed in the framework of Functional Data Analysis. It is based on a model akin to the stochastic volatility model for scalar point-to-point returns. In our context, we study intraday curves, one curve per trading day. After postulating a suitable model for such functional data, we present three tests focusing, respectively, on changes in the shape, the magnitude and arbitrary changes in the sequences of the curves of interest. We justify the respective procedures by showing that they have asymptotically correct size and by deriving consistency rates for all tests. These rates involve the sample size (the number of trading days) and the grid size (the number of observations per day). We also derive the corresponding change point estimators and their consistency rates. All procedures are additionally validated by a simulation study and an application to US stocks.

The multivariate Bernoulli detector: change point estimation in discrete survival analysis.

Time-to-event data are often recorded on a discrete scale with multiple, competing risks as potential causes for the event. In this context, application of continuous survival analysis methods with a single risk suffers from biased estimation. Therefore, we propose the multivariate Bernoulli detector for competing risks with discrete times involving a multivariate change point model on the cause-specific baseline hazards. Through the prior on the number of change points and their location, we impose dependence between change points across risks, as well as allowing for data-driven learning of their number. Then, conditionally on these change points, a multivariate Bernoulli prior is used to infer which risks are involved. Focus of posterior inference is cause-specific hazard rates and dependence across risks. Such dependence is often present due to subject-specific changes across time that affect all risks. Full posterior inference is performed through a tailored local-global Markov chain Monte Carlo (MCMC) algorithm, which exploits a data augmentation trick and MCMC updates from nonconjugate Bayesian nonparametric methods. We illustrate our model in simulations and on ICU data, comparing its performance with existing approaches.

Modified Block Bootstrap Testing for Persistence Change in Infinite Variance Observations

This paper investigates the properties of the change in persistence detection for observations with infinite variance. The innovations are assumed to be in the domain of attraction of a stable law with index κ∈(0,2]. We provide a new test statistic and show that its asymptotic distribution under the null hypothesis of non-stationary I(1) series is a functional of a stable process. When the change point in persistence is not known, the consistency is always given under the alternative, either from stationary I(0) to non-stationary I(1) or vice versa. The proposed tests can be used to identify the direction of change and do not over-reject against constant I(0) series, even in relatively small samples. Furthermore, we also consider the change point estimator which is consistent and the asymptotic behavior of the test statistic in the case of near-integrated time series. A block bootstrap method is suggested to determine critical values because the null asymptotic distribution contains the unknown tail index, which results in critical values depending on it. The simulation study demonstrates that the block bootstrap-based test is robust against change in persistence for heavy-tailed series with infinite variance. Finally, we apply our methods to the two series of the US inflation rate and USD/CNY exchange rate, and find significant evidence for persistence changes, respectively, from I(0) to I(1) and from I(1) to I(0).

Frailty model with change points for survival analysis.

We propose a novel frailty model with change points applying random effects to a Cox proportional hazard model to adjust the heterogeneity between clusters. In the specially focused eight Empowered Action Group (EAG) states in India, there are problems with different survival curves for children up to the age of five in different states. Therefore, when analyzing the survival times for the eight EAG states, we need to adjust for the effects among states (clusters). Because the frailty model includes random effects, the parameters are estimated using the expectation-maximization (EM) algorithm. Additionally, our model needs to estimate change points; we thus propose a new algorithm extending the conventional estimation algorithm to the frailty model with change points to solve the problem. We show a practical example to demonstrate how to estimate the change point and the parameters of the distribution of random effect. Our proposed model can be easily analyzed using the existing R package. We conducted simulation studies with three scenarios to confirm the performance of our proposed model. We re-analyzed the survival time data of the eight EAG states in India to show the difference in analysis results with and without random effect. In conclusion, we confirmed that the frailty model with change points has a higher accuracy than the model without a random effect. Our proposed model is useful when heterogeneity needs to be taken into account. Additionally, the absence of heterogeneity did not affect the estimation of the regression parameters.

A Composite Likelihood-based Approach for Change-point Detection in Spatio-temporal Processes

This paper develops a unified and computationally efficient method for change-point estimation along the time dimension in a non-stationary spatio-temporal process. By modeling a non-stationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameter estimation. Under the framework of increasing domain asymptotics, theoretical results including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the localization error of change-point estimator is , exact recovery of true change-points is possible in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. In addition, we further establish consistency of the change-point estimator under the infill asymptotics framework where the time domain is increasing while the spatial sampling domain is fixed. A computationally efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Extensive simulation studies and an application to the U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method.

Efficient change point detection and estimation in high-dimensional correlation matrices

Efficient change point detection and estimation in high-dimensional correlation matrices

Strong consistency properties of the variance change point estimator based on strong-mixing samples

<p>In this paper, our primary attention was centered on the issue of detecting the variance change point for strong-mixing samples. We delved into the cumulative sum (CUSUM) estimator of variance change model and established the strong convergence rate of the variance change point estimation. Furthermore, to corroborate the effectiveness of the CUSUM based methodology, we have conducted a series of simulations, the outcomes of which underscored its validity.</p>

A machine learning oracle for parameter estimation

AbstractCompeting procedures, involving data smoothing, weighting, imputation, outlier removal, etc., may be available to prepare data for parametric model estimation. Often, however, little is known about the best choice of preparatory procedure for the planned estimation and the observed data. A machine learning‐based decision rule, an “oracle,” can be constructed in such cases to decide the best procedure from a set of available preparatory procedures. The oracle learns the decision regions associated with based on training data synthesized solely from the given data using model parameters with high posterior probability. An estimator in combination with an oracle to guide data preparation is called an oracle estimator. Oracle estimator performance is studied in two estimation problems: slope estimation in simple linear regression (SLR) and changepoint estimation in continuous two‐linear‐segments regression (CTLSR). In both examples, the regression response is given to be increasing, and the oracle must decide whether to isotonically smooth the response data preparatory to fitting the regression model. A measure of performance called headroom is proposed to assess the oracle's potential for reducing estimation error. Experiments with SLR and CTLSR find for important ranges of problem configurations that the headroom is high, the oracle's empirical performance is near the headroom, and the oracle estimator offers clear benefit.

Multiple change-points estimation in panel data models via SaRa

Multiple change-points estimation in panel data models is one of the popular topics in statistics. In this article, we investigate the multiple change-points estimation in the mean of panel data model based on a screening and ranking algorithm. Firstly, the possible change-points are initially screened based on local statistics. Secondly, the threshold is used to further screen the change-points. Finally, the final change-points are screened out using the information criterion. Furthermore, the consistency of the change-point estimators is proved. The Monte Carlo simulation results show that the proposed method can estimate the number and locations of change-points accurately even if the error terms are serially correlated or cross-sectionally correlated, and finally the method is used to analyze the annual GDP growth rate data of 47 countries in the word from 1971 to 2019 to illustrate the effectiveness of the method.

Change point estimation of service rate in M/M/1/m queues: A Bayesian approach

This article presents a novel approach for detecting a change point in the service rate of an M/M/1/m queue. The change point is identified by detecting a change in the probability distribution of a stochastic process. To achieve this, the article proposes a likelihood function that is constructed based on the observed number of customers left in the system at departures. Bayesian estimators are then derived using this likelihood function. The effectiveness of the proposed methods is evaluated through extensive Monte Carlo simulations. Overall, the results demonstrate the effectiveness of the proposed approach for detecting change points in service rates.

Change-point models for identifying behavioral transitions in wild animals

Animal behavior can be difficult, time-consuming, and costly to observe in the field directly. Innovative modeling methods, such as hidden Markov models (HMMs), allow researchers to infer unobserved animal behaviors from movement data, and implementations often assume that transitions between states occur multiple times. However, some behavioral shifts of interest, such as parturition, migration initiation, and juvenile dispersal, may only occur once during an observation period, and HMMs may not be the best approach to identify these changes. We present two change-point models for identifying single transitions in movement behavior: a location-based change-point model and a movement metric-based change-point model. We first conducted a simulation study to determine the ability of these models to detect a behavioral transition given different amounts of data and the degree of behavioral shifts. We then applied our models to two ungulate species in central Pennsylvania that were fitted with global positioning system collars and vaginal implant transmitters to test hypotheses related to parturition behavior. We fit these models in a Bayesian framework and directly compared the ability of each model to describe the parturition behavior across species. Our simulation study demonstrated that successful change point estimation using either model was possible given at least 12 h of post-change observations and 15 min fix interval. However, our models received mixed support among deer and elk in Pennsylvania due to behavioral variation between species and among individuals. Our results demonstrate that when the behavior follows the dynamics proposed by the two models, researchers can identify the timing of a behavioral change. Although we refer to detecting parturition events, our results can be applied to any behavior that results in a single change in time.

A note on online change point detection

We investigate sequential change point estimation and detection in univariate nonparametric settings, where a stream of independent observations from sub-Gaussian distributions with a common variance factor and piecewise-constant but otherwise unknown means are collected. We develop a simple CUSUM-based methodology that provably control the probability of false alarms or the average run length while minimizing, in a minimax sense, the detection delay. We allow for all the model parameters to vary in order to capture a broad range of levels of statistical hardness for the problem at hand. We further show how our methodology is applicable to the case in which multiple change points are to be estimated sequentially.

Real-Time Leak Location of Long-Distance Pipeline Using Adaptive Dynamic Programming.

In traditional leak location methods, the position of the leak point is located through the time difference of pressure change points of both ends of the pipeline. The inaccurate estimation of pressure change points leads to the wrong leak location result. To address it, adaptive dynamic programming is proposed to solve the pipeline leak location problem in this article. First, a pipeline model is proposed to describe the pressure change along pipeline, which is utilized to reflect the iterative situation of the logarithmic form of pressure change. Then, under the Bellman optimality principle, a value iteration (VI) scheme is proposed to provide the optimal sequence of the nominal parameter and obtain the pipeline leak point. Furthermore, neural networks are built as the VI scheme structure to ensure the iterative performance of the proposed method. By transforming into the dynamic optimization problem, the proposed method adopts the estimation of the logarithmic form of pressure changes of both ends of the pipeline to locate the leak point, which avoids the wrong results caused by unclear pressure change points. Thus, it could be applied for real-time leak location of long-distance pipeline. Finally, the experiment cases are given to illustrate the effectiveness of the proposed method.

Change Point Detection in Dynamic Networks via Regularized Tensor Decomposition

Dynamic network captures time-varying interactions among multiple entities at different time points, and detecting its structural change points is of central interest. This article proposes a novel method for detecting change points in dynamic networks by fully exploiting the latent network structure. The proposed method builds upon a tensor-based embedding model, which models the time-varying network heterogeneity through an embedding matrix. A fused lasso penalty is equipped with the tensor decomposition formulation to estimate the embedding matrix and a power update algorithm is developed to tackle the resultant optimization task. The error bound of the obtained estimated embedding matrices is established without incurring the computational-statistical gap. The proposed method also produces a set of estimated change points, which, coupled with a simple screening procedure, assures asymptotic consistency in change point detection under much milder assumptions. Various numerical experiments on both synthetic and real datasets also support its advantage. Supplementary materials for this article are available online.

A Least Squares Estimator for Gradual Change-Point in Time Series with m-Asymptotically Almost Negatively Associated Errors

As a new member of the NA (negative associated) family, the m-AANA (m-asymptotically almost negatively associated) sequence has many statistical properties that have not been developed. This paper mainly studies its properties in the gradual change point model. Firstly, we propose a least squares type change point estimator, then derive the convergence rates and consistency of the estimator, and provide the limit distributions of the estimator. It is interesting that the convergence rates of the estimator are the same as that of the change point estimator for independent identically distributed observations. Finally, the effectiveness of the estimator in limited samples can be verified through several sets of simulation experiments and an actual hydrological example.