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This paper presents the derivation of an expression for computing the exact distribution of the change-point maximum likelihood estimate (MLE) in the context of a mean shift within a sequence of time-ordered independent multivariate normal random vectors. The study assumes knowledge of nuisance parameters, including the covariance matrix and the magnitude of the mean change. The derived distribution is then utilized as an approximation for the change-point estimate distribution when the magnitude of the mean change is unknown. Its efficiency is evaluated through simulation studies, revealing that the exact distribution outperforms the asymptotic distribution. Notably, even in the absence of a change, the exact distribution maintains its efficiency, a feature not shared by the asymptotic distribution. To demonstrate the practical application of the developed methodology, the monthly averages of water discharges from the Nacetinsky creek in Germany are analyzed, and a comparison with the analysis conducted using the asymptotic distribution is presented. [ABSTRACT FROM AUTHOR]

We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This allows results from the frequentist and Bayesian paradigms to be bridged together. Thanks to this link, one can rely on the consistency of the number and locations of the estimated CPs and the computational efficiency of frequentist methods, and obtain a probability of observing a CP at a given time, compute model posterior probabilities, and select or combine CP methods via Bayesian posteriors. Furthermore, we adapt several CP methods to take advantage of the MDL probabilistic representation. Based on simulated data, we show that the adapted CP methods can improve structural break detection compared to state-of-the-art approaches. Finally, we empirically illustrate the usefulness of combining CP detection methods when dealing with long time series and forecasting. [ABSTRACT FROM AUTHOR]

AbstractThe 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. [ABSTRACT FROM AUTHOR]

Understanding wildfire spread in Canada is critical to promoting forest health and protecting human life and infrastructure. Quantifying fire spread from noisy images, where change-point boundaries separate regions of fire, is critical to accurately estimating fire spread rates. The challenge lies in denoising the fire images and accurately identifying highly non-linear fire lines without smoothing over boundaries. In this paper, we develop an iterative smoothing algorithm for change-point data that utilizes oversmoothed estimates of the underlying data generating process to inform re-smoothing. We demonstrate its effectiveness on simulated one- and two-dimensional change-point data, and robustness to response outliers. Then, we apply the methodology to fire spread images from laboratory micro-fire experiments and show that the regions fuel, burning and burnt-out are smoothed while boundaries are preserved. [ABSTRACT FROM AUTHOR]

Exponential random graph models (ERGM) are known as one of the most flexible models for profile monitoring of the complex structure of dynamic social networks, especially for networks with a large number of nodes. Usually, only one realization of a network is available instead of a random sample and the correlations between nodes increase the computational cost. Parametrizing via ERGM, the parameters of the model corresponding to the features of the network (namely, edges, k -star, and triangles) are then monitored using Hotelling's T 2 and likelihood ratio test control charts in Phase I for two general scenarios in both the directed and undirected edges cases. The results show that the presented control charts efficiently characterize the profile consisting of a network at each sampling time. The power of each method at a constant nominal Type I error probability is numerically reported for different shifts in the parameters. The results are also employed in the analysis of Gnutella Internet Peer-to-Peer Networks. [ABSTRACT FROM AUTHOR]

This research focuses on the role of advertising expenditure in determining the success of a product and its impact on the rate of product sales. We introduce the concept of change-point, which considers fluctuations in the adoption rate due to shifts in advertising strategies and competitor dynamics. The product diffusion models incorporating advertising expenditure and change-points are proposed and validated using two real-world product advertising and sales datasets. The models's accuracy and applicability has been assessed through R 2 (coefficient of determination) and mean square error (MSE). By investigating the relationship between advertising expenditure, change-point, and product sales, this study provides valuable insights for marketing and advertising strategies, aiding in better decision-making processes. [ABSTRACT FROM AUTHOR]

Accurately predicting the growth curve of technological innovations during their product life cycle is essential for a firm's strategic planning and survival in an ever-increasing competitive environment. The dissemination of innovation among prospective customers is commonly measured using the diffusion process. Despite considerable research on modeling the diffusion dynamics of innovation, no sustainable model focuses on repurchasing behavior under the effect of price change and time-varying adoption rate. Consequently, the present study develops a new sales forecast model to analyze the propagation of technological products using the two-dimensional framework that integrates the effect of price change and its continuation time in the market. A Cobb–Douglas function has been utilized to mathematically relate the dynamic price and goodwill of the innovation to the product's value. The dynamic behavior of the adoption rate is described using the concept of change-point. A control chart (or c-chart) is utilized to identify the change-point location in the diffusion process of the technological products. The proposed model is fitted to the historical data from two industries, Electronics and Automobiles, using a non-linear least square (NLS) estimation procedure to demonstrate its practical applicability. The empirical analysis shows that the proposed model fits better than well-established diffusion models. [ABSTRACT FROM AUTHOR]

We derive a Cramér–von Mises test for testing a class of time dependent coefficients Coditional Heteroscedastic AutoRegressive Non Linear (CHARN) models. The test statistic is based on the log-likelihood ratio process whose weak convergence in a suitable Fréchet space is studied under the null hypothesis and under the sequence of local alternatives considered. This study makes use of the locally asymptotically normal (LAN) result previously established. Using the Karhunen–Loève expansion of the limiting process of the log-likelihood ratio process, the asymptotic null distribution and the power of the test statistic are accurately approximated. These results are applied to change-point analysis. An empirical study is done for evaluating the performance of the methodology proposed. [ABSTRACT FROM AUTHOR]

AbstractThe standard Brownian motion (Bm) with a linear drift is a convenient statistical structure for monitoring ongoing clinical trials in practice for more than four decades (Lan and DeMets). Under this model, the most current one-point statistic is sufficient. However, in our experience, the sponsor and the data monitoring committee often would like to make decision or recommendation based on the “trend” observed from the history of data, not just a one-point snapshot. In this article, we introduce and advance the fractional Brownian motion (fBm) with drift model to formally accommodate this need. The possible dependence and/or the nonlinear trend (e.g., piecewise linear drift with change-point) of observations in clinical trials may come from uncontrollable factors such as patient entry processes may have seasonal patterns over time, patient survival time may depend on the practices of clinical centers, physicians or censoring time (Lai et al.). The violations of the standard Bm and the need for the fBm are discussed with illustrative examples. The common methods including conditional power and sample size re-estimation used for monitoring clinical trials are derived and implemented in the Dynamic Data Monitoring (DDM) system for practitioners under the fBm. [ABSTRACT FROM AUTHOR]

Among various quality assurance activities, process capability indices (PCIs) are recognized as the most effective tools to quantify and evaluate process performance. The one-sided capability index $${C_{pu}}$$ C p u can adequately measure the process capability for processes with a smaller-is-better (S-type) quality characteristic. While focusing on the index $${C_{pu}}$$ C p u , this study constructs a capability control chart to monitor the short-term capability based on the exponentially weighted moving average (EWMA). Simulations have shown that the EWMA capability control chart is adaptive regarding average run length. Further, this study applies change-point analysis to determine whether and when the short-term capability-level changes. Using these two proposed methods, engineers can realize a variety of short-term process capabilities in good time and implement control measures efficiently against a poor long-term process capability. [ABSTRACT FROM AUTHOR]

• A multi-stage degradation model based on nonlinear Wiener process is established. • The stage-varying noises is considered to depict the multi-stage degradation process. • The nonlinear parameter is determined by COLA to simplify the parameter estimation. • A real-time adaptive detection method is proposed to better identify change points. • Simulation study and real case studies show the superiority of the proposed method. For multi-stage degradation processes, the degradation modeling and change-point detection play vital roles in the reliability assessment. The linear Wiener process with identical noise is mainly used to fit multi-stage degradation processes, which is often no consistent with practices, since many degradation processes are nonlinear and their noises are different in different stages. Furthermore, the maximum likelihood estimation method was often used to detect change-points from the entire process data, and it cannot detect the change-point timely. Therefore, considering the stage-varying noises, a degradation model based on the nonlinear Wiener process is proposed to characterize the multi-stage degradation process. Then, its nonlinear parameter is determined using the constrained optimization by linear approximations, and other parameters are estimated by the maximum likelihood estimation method. Note that under the same distribution, the Bayesian information criterion value of the observation data decreases with sample size, and a real-time adaptive change-point detection method is proposed by monitoring the change of Bayesian information criterion value. Finally, degradation processes of the battery and the wheel tread are analyzed to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Because of the "curse of dimensionality," high-dimensional processes present challenges to traditional multivariate statistical process monitoring (SPM) techniques. In addition, the unknown underlying distribution of and complicated dependency among variables such as heteroscedasticity increase the uncertainty of estimated parameters and decrease the effectiveness of control charts. In addition, the requirement of sufficient reference samples limits the application of traditional charts in high-dimension, low-sample-size scenarios (small n, large p). More difficulties appear when detecting and diagnosing abnormal behaviors caused by a small set of variables (i.e., sparse changes). In this article, we propose two change-point–based control charts to detect sparse shifts in the mean vector of high-dimensional heteroscedastic processes. Our proposed methods can start monitoring when the number of observations is a lot smaller than the dimensionality. The simulation results show that the proposed methods are robust to nonnormality and heteroscedasticity. Two real data examples are used to illustrate the effectiveness of the proposed control charts in high-dimensional applications. The R codes are provided online. [ABSTRACT FROM AUTHOR]

Two problems concerning detecting change-points in linear regression models are considered. One involves discontinuous jumps in a regression model and the other involves regression lines connected at unknown places. Significant literature has been developed for estimating piecewise regression models because of their broad range of applications. The segmented (SEG) regression method with an R package has been employed by many researchers since it is easy to use, converges fast, and produces sufficient estimates. The SEG method allows for multiple change-points but is restricted to continuous models. Such a restriction really limits the practical applications of SEG when it comes to discontinuous jumps encountered in real change-point problems very often. In this paper, we propose a piecewise regression model, allowing for discontinuous jumps, connected lines, or the occurrences of jumps and connected change-points in a single model. The proposed segmentation approach can derive the estimates of jump points, connected change-points, and regression parameters simultaneously, allowing for multiple change-points. The initializations of the proposed algorithm and the decision on the number of segments are discussed. Experimental results and comparisons demonstrate the effectiveness and superiority of the proposed method. Several real examples from diverse areas illustrate the practicability of the new method. [ABSTRACT FROM AUTHOR]

Estimating thresholds when a threshold effect exists has important applications in biomedical research. However, models/methods commonly used in the biomedical literature may lead to a biased estimate. For patients undergoing coronary artery bypass grafting (CABG), it is thought that exposure to low oxygen delivery (DO2) contributes to an increased risk of avoidable acute kidney injury. This research is motivated by estimating the threshold of nadir DO2 for CABG patients to help develop an evidence-based guideline for improving cardiac surgery practices. We review several models (sudden-jump model, broken-stick model, and the constrained broken-stick model) that can be adopted to estimate the threshold and discuss modeling assumptions, scientific plausibility, and implications in estimating the threshold. Under each model, various estimation methods are studied and compared. In particular, under a constrained broken-stick model, a modified two-step Newton–Raphson algorithm is introduced. Through comprehensive simulation studies and an application to data on CABG patients from the University of Michigan, we show that the constrained broken-stick model is flexible, more robust, and able to incorporate scientific knowledge to improve efficiency. The two-step Newton–Raphson algorithm has good computational performances relative to existing methods. [ABSTRACT FROM AUTHOR]

The quality of some products or processes can be characterised by the functional relationship referred to as a profile. Profile monitoring aims to check the stability of this relationship over time. In some applications, the response variable of interest in profiles follows a Poisson distribution and the observations within each profile are autocorrelated. Besides, the design points and/or the number of measurements are not the same for different profiles. However, most existing studies on monitoring Poisson profiles have not incorporated the correlation, and the design points within a profile are fixed. It has been shown in many studies that ignoring correlations may lead to poor performance or even misleading results in profile monitoring. Therefore, this article proposes a Phase I scheme to detect and estimate the change-point of autocorrelated Poisson profiles with random or unbalanced design points. The proposed method uses the generalised estimating equation (GEE) approach to model the within-profile correlation and then integrates the change-point algorithm with the modified score test to detect the change-point. Numerical simulations are conducted to investigate the detection effectiveness and diagnostic accuracy of the proposed scheme. Finally, an application to warranty claims is presented to illustrate the implementation of the proposed method. [ABSTRACT FROM AUTHOR]

Multiple change-points estimation for functional time series is studied in this paper. The change-point problem is first transformed into a high-dimensional sparse estimation problem via basis functions. Group least absolute shrinkage and selection operator (LASSO) is then applied to estimate the number and the locations of possible change points. However, the group LASSO (GLASSO) always overestimate the true points. To circumvent this problem, a further Information Criterion (IC) is applied to eliminate the redundant estimated points. It is shown that the proposed two-step procedure estimates the number and the locations of the change-points consistently. Simulations and two temperature data examples are also provided to illustrate the finite sample performance of the proposed method. [ABSTRACT FROM AUTHOR]

This research work focuses on Bayesian inference in this study to detect a change in the rate of a Maxwell distribution model with independent random variables. The paper specifically analyzes a single rate shift and demonstrates how the Bayesian framework can be used to efficiently solve this problem. To produce samples from Maxwell distribution and evaluate the datasets, simulation techniques were used, and the R programming language was used. Although the model looks to be simple, no analytical solutions are available for parameter inference, necessitating the use of approximations. The study emphasizes the Gibbs sampler's applicability for change-point analysis using a Markovian updating approach. The simulation research findings show that the predicted rate is near to the true value, confirming the consistency and stability of the Bayesian estimator. [ABSTRACT FROM AUTHOR]

Abstract We study a likelihood ratio test for detecting multiple weak changes in the mean of a class of CHARN models. The locally asymptotically normal (LAN) structure of the family of likelihoods under study is established. It results that the test is asymptotically optimal, and an explicit form of its asymptotic local power is given as a function of the candidates change locations and change magnitudes. Strategies for weak change-points detection and their locations estimates are described. The estimates are obtained as the time indices maximizing an estimate of the local power. A simulation study shows the good performance of our methods compared to some existing approaches. These methods are also applied to three sets of real data. [ABSTRACT FROM AUTHOR]

Selecting the number of change points in segmented line regression is an important problem in trend analysis, and there have been various approaches proposed in the literature. We first study the empirical properties of several model selection procedures and propose a new method based on two Schwarz type criteria, a classical Bayes Information Criterion (BIC) and the one with a harsher penalty than BIC ( BIC 3 ). The proposed rule is designed to use the former when effect sizes are small and the latter when the effect sizes are large and employs the partial R 2 to determine the weight between BIC and BIC 3 . The proposed method is computationally much more efficient than the permutation test procedure that has been the default method of Joinpoint software developed for cancer trend analysis, and its satisfactory performance is observed in our simulation study. Simulations indicate that the proposed method performs well in keeping the probability of correct selection at least as large as that of BIC 3 , whose performance is comparable to that of the permutation test procedure, and improves BIC 3 when it performs worse than BIC. The proposed method is applied to the U.S. prostate cancer incidence and mortality rates. [ABSTRACT FROM AUTHOR]

Dealing with structural breaks is an essential step in most empirical economic research. This is particularly true in panel data comprised of many cross-sectional units, which are all affected by major events. The COVID-19 pandemic has affected most sectors of the global economy; however, its impact on stock markets is still unclear. Most markets seem to have recovered while the pandemic is ongoing, suggesting that the relationship between stock returns and COVID-19 has been subject to structural break. It is therefore important to know if a structural break has occurred and, if it has, to infer the date of the break. Motivated by this last observation, the present article develops a new break detection toolbox that is applicable to different sized panels, easy to implement and robust to general forms of unobserved heterogeneity. The toolbox, which is the first of its kind, includes a structural change test, a break date estimator, and a break date confidence interval. Application to a panel covering 61 countries from January 3 to September 25, 2020, leads to the detection of a structural break that is dated to the first week of April. The effect of COVID-19 is negative before the break and zero thereafter, implying that while markets did react, the reaction was short-lived. A possible explanation is the quantitative easing programs announced by central banks all over the world in the second half of March. [ABSTRACT FROM AUTHOR]

Abstract Most of studies on change-point at a regional or global scale have only examined a single hydrometeorological variable and have been unable to identify any underlying explanations. In this study, we identified change-points and long-term trends of six wildfire-related variables and attempted to explain the cause of change-point from atmospheric–oceanic indices. As a result, we discovered that the main change-point dates for the precipitation, temperature, and drought codes, as well as the duff moisture code, fine fuel moisture code, and fire weather index, were 1995–2000 and 2000–2005, respectively. Furthermore, the relationship between the change-point of six variables and atmospheric–oceanic indices was discussed through the correlation coefficient. For example, the Atlantic Multidecadal Oscillation was found to dominate the precipitation in West Africa. In addition, we divided the globe into eight homogenous wildfire weather zones based on the change-point dates and long-term trends of the six variables.

【Objective】 Phosphorus (P) leaching from soils is not only an environmental concern but also a financial loss to farmers. Understanding the mechanisms underlying mobility of P in different soils is essential to alleviating its loss to surface runoff and leaching to groundwater. 【Method】 We studied the physical and chemical properties of typical soils in Shanxi province, including chestnut-cinnamon soil, regosol soil, loessial soil and fluvo-aquic soil, which combine to cover 88.51% of the land surface across the province. For each soil, we measured its organic matter, particle size in the range of >0.002 mm, 0.002~0.05 mm and 0.05~2 mm, texture, active Fe (Al), Olsen-P and CaCl2-P. Soluble P at different concentrations was added to each soil, and it was allowed to reach equilibrium. The contents of Olsen-P and CaCl2-P were then determined using NaHCO3 and CaCl2, and the threshold that resulted in P starting to leach was calculated from the relationship between Olsen-P and CaCl2-P. 【Result】 The critical P content beyond which P leached is 73.50 mg/kg for cinnamon soil, 7.0 mg/kg for chestnut-cinnamon soil, 23.30 mg/kg for neutral regosols soil, 39.4 mg/kg for loessial soil and 61.36 mg/kg for fluvo-aquic soil. The critical Olsen-P content in all soils increased with the increase in organic matter content but not significantly (p>0.05). Logarithm of the critical Olsen-P content is significantly correlated to the logarithm of clay and active Fe content (p0.05). 【Conclusion】 Vulnerability of the main five soils to P leaching is ranked in the order of neutral regosol soil>loessial soil>fluvo-aquic soil>chestnut-cinnamon soil>cinnamon soil. Clay and active Fe contents are the edaphic factors affecting P leaching the most.

Abstract Volatility is one of the most important features of financial time series data. There are often structural changes in volatility over time, and an accurate estimation of the volatility of financial time series requires careful identification of change-points. A common approach to modeling the volatility of time series data is based on the well-known GARCH model. Although the problem of change-point estimation of volatility dynamics derived from the GARCH model has been considered in the literature, these approaches rely on parametric assumptions of the conditional error distribution, which are often violated in financial time series. This may lead to inaccuracies in change-point detection, resulting in unreliable GARCH volatility estimates. This article introduces a novel change-point detection algorithm based on a semiparametric GARCH model. The proposed method retains the structural advantages of the GARCH process while incorporating the flexibility of nonparametric conditional error distribution. The approach utilizes a penalized likelihood derived from a semiparametric GARCH model and an efficient binary segmentation algorithm. The results show that in terms of change-point estimation and detection accuracy, the semiparametric method outperforms the commonly used Quasi-MLE (QMLE) and other variations of the GARCH models in wide-ranging scenarios. [ABSTRACT FROM AUTHOR]

Abstract Existing monitoring tools for multivariate data are often asymptotically distribution-free, computationally intensive, or require a large stretch of stable data. Many of these methods are not applicable to ‘high-dimension, low sample size’ scenarios. With rapid technological advancement, high-dimensional data has become omnipresent in industrial applications. We propose a distribution-free change-point monitoring method applicable to high-dimensional data. Through an extensive simulation study, performance comparison has been done for different parameter values, under different multivariate distributions with complex dependence structures. The proposed method is robust and efficient in detecting change points under a wide range of shifts in the process distribution. A real-life application is illustrated with the help of a high-dimensional image surveillance dataset. [ABSTRACT FROM AUTHOR]

Graph-based change-point detection methods are often applied due to their advantages for using high-dimensional data. Most applications focus on extracting effective information of objects while ignoring their main features. However, in some applications, one may be interested in detecting objects with different features, such as color. Therefore, we propose a general graph-based change-point detection method under the multi-way tensor framework, aimed at detecting objects with different features that change in the distribution of one or more slices. Furthermore, considering that recorded tensor sequences may be vulnerable to natural disturbances, such as lighting in images or videos, we propose an improved method incorporating histogram equalization techniques to improve detection efficiency. Finally, through simulations and real data analysis, we show that the proposed methods achieve higher efficiency in detecting change-points. [ABSTRACT FROM AUTHOR]

In the era of big data, high-dimensional data always arrive in streams, making timely and accurate decision necessary. It has become particularly important to rapidly and sequentially identify individuals whose behavior deviates from the norm. Aiming at identifying as many irregular behavioral patterns as possible, the authors develop a large-scale dynamic testing system in the framework of false discovery rate (FDR) control. By fully exploiting the sequential feature of datastreams, the authors propose a screening-assisted procedure that filters streams and then only tests streams that pass the filter at each time point. A data-driven optimal screening threshold is derived, giving the new method an edge over existing methods. Under some mild conditions on the dependence structure of datastreams, the FDR is shown to be strongly controlled and the suggested approach for determining screening thresholds is asymptotically optimal. Simulation studies show that the proposed method is both accurate and powerful, and a real-data example is used for illustrative purpose. [ABSTRACT FROM AUTHOR]

The linear spline model is able to accommodate nonlinear effects while allowing for an easy interpretation. It has significant applications in studying threshold effects and change-points. However, its application in practice has been limited by the lack of both rigorously studied and computationally convenient method for estimating knots. A key difficulty in estimating knots lies in the nondifferentiability. In this article, we study influence functions of regular and asymptotically linear estimators for linear spline models using the semiparametric theory. Based on the theoretical development, we propose a simple semismooth estimating equation approach to circumvent the nondifferentiability issue using modified derivatives, in contrast to the previous smoothing-based methods. Without relying on any smoothing parameters, the proposed method is computationally convenient. To further improve numerical stability, a two-step algorithm taking advantage of the analytic solution available when knots are known is developed to solve the proposed estimating equation. Consistency and asymptotic normality are rigorously derived using the empirical process theory. Simulation studies have shown that the two-step algorithm performs well in terms of both statistical and computational properties and improves over existing methods. for this article are available online. [ABSTRACT FROM AUTHOR]

We consider the change-point detection in a general class of time series models, including multivariate continuous and integer- valued time series. We propose a Wald-type statistic based on the estimator performed by a general contrast function, which can be constructed from the likelihood, a quasi-likelihood, a least squares method, etc. Sufficient conditions are provided to ensure that the test statistic convergences to a well-known distribution under the null hypothesis (of no change) and diverges to infinity under the alternative, which establishes the consistency of the procedure. Some examples of models are detailed to illustrate the scope of application of the proposed change-point detection tool. The procedure is applied to simulated and real data examples for numerical illustration. [ABSTRACT FROM AUTHOR]

Two problems concerning detecting change-points in linear regression models are considered. One involves discontinuous jumps in a regression model and the other involves regression lines connected at unknown places. Significant literature has been developed for estimating piecewise regression models because of their broad range of applications. The segmented (SEG) regression method with an R package has been employed by many researchers since it is easy to use, converges fast, and produces sufficient estimates. The SEG method allows for multiple change-points but is restricted to continuous models. Such a restriction really limits the practical applications of SEG when it comes to discontinuous jumps encountered in real change-point problems very often. In this paper, we propose a piecewise regression model, allowing for discontinuous jumps, connected lines, or the occurrences of jumps and connected change-points in a single model. The proposed segmentation approach can derive the estimates of jump points, connected change-points, and regression parameters simultaneously, allowing for multiple change-points. The initializations of the proposed algorithm and the decision on the number of segments are discussed. Experimental results and comparisons demonstrate the effectiveness and superiority of the proposed method. Several real examples from diverse areas illustrate the practicability of the new method.

The usual mean change-point detecting method based on normal linear regression is not robust to heavy-tailed data with potential outlying points. We propose a robust change-point estimation procedure based on a quantile regression model with asymmetric Laplace error distribution and develop a non-iterative sampling algorithm from a Bayesian perspective. The algorithm can generate independently and identically distributed samples approximately from the posterior distribution of the position of the change-point, which can be used for statistical inferences straightforwardly. The procedure combines the robustness of quantile regression and the computational efficiency of the non-iterative sampling algorithm. A simulation study is conducted to illustrate the performance of the procedure with satisfying findings, and finally, real data is analyzed to show the usefulness of the algorithm by comparison with the usual change-point detection method based on normal regression. [ABSTRACT FROM AUTHOR]

Time-series data often have an abrupt structure change at an unknown location. This paper proposes a new statistic to test the existence of a change-point in a multinomial sequence, where the number of categories is comparable with the sample size as it tends to infinity. To construct this statistic, the pre-classification is implemented first; then, it is given based on the mutual information between the data and the locations from the pre-classification. Note that this statistic can also be used to estimate the position of the change-point. Under certain conditions, the proposed statistic is asymptotically normally distributed under the null hypothesis and consistent under the alternative hypothesis. Simulation results show the high power of the test based on the proposed statistic and the high accuracy of the estimate. The proposed method is also illustrated with a real example of physical examination data. [ABSTRACT FROM AUTHOR]

Most of studies on change-point at a regional or global scale have only examined a single hydrometeorological variable and have been unable to identify any underlying explanations. In this study, we identified change-points and long-term trends of six wildfire-related variables and attempted to explain the cause of change-point from atmospheric–oceanic indices. As a result, we discovered that the main change-point dates for the precipitation, temperature, and drought codes, as well as the duff moisture code, fine fuel moisture code, and fire weather index, were 1995–2000 and 2000–2005, respectively. Furthermore, the relationship between the change-point of six variables and atmospheric–oceanic indices was discussed through the correlation coefficient. For example, the Atlantic Multidecadal Oscillation was found to dominate the precipitation in West Africa. In addition, we divided the globe into eight homogenous wildfire weather zones based on the change-point dates and long-term trends of the six variables. [ABSTRACT FROM AUTHOR]

We propose and investigate a new test of model instability in the mean. The test is based on p-variation of stepwise CUSUM process. We establish a limiting distribution of the test statistics under null as well as under contiguous alternative. [ABSTRACT FROM AUTHOR]

The Cox proportional hazards regression model is commonly used to measure relative associations between independent variables and time until a well‐defined event in the presence of censored event times. A requisite assumption of this model is that the relative hazards are constant over time. That is, it is assumes that for two different specifications of covariates, the relative ratio of the hazard rates is constant over the time of interest. Although this assumption is generally robust to deviations, interpretation of model results may be misleading and invalid when this assumption is substantially violated. A single point in time where the relative hazard ratios change significantly is known as a change‐point. Estimating the change‐point may be clinically or scientifically important and can be used for stratified analysis. This paper describes common methods for testing the proportional hazards assumption, estimating the change‐point, and conducting a stratified analysis. Methods are illustrated through an analysis on time‐to‐decannulation among paediatric tracheostomy patients. [ABSTRACT FROM AUTHOR]

This article presents skewed multifractal cross-correlations between price and volumes on the carbon emissions trading markets in China and Europe. The BEAST algorithm is first used to detect change points in financial time series and to divide series into two adjacent intervals. The study performs a skewed multifractal detrended cross-correlations analysis and further investigates the impact of the COVID-19 pandemic on multifractality and risk between price and volumes on both markets, from 30 April 2014 to 25 July 2023. The results demonstrate that the multifractality of cross-correlations in both markets underwent significant changes before and after the change points, indicating skewed multifractality. In both markets, the price-volume nexus exhibited increased anti-persistence, higher multifractal risks, and reduced market efficiency after the outbreak of the pandemic. This may be attributed to the pandemic-induced shifts in carbon emissions trading market trends and heightened volatility. In conclusion, the outbreak of the pandemic had increased the instability of the carbon markets and the Hubei market exhibited higher levels of multifractality and multifractal risk. • Skewed multifractal cross-correlations of Hubei and EU carbon markets is investigated. • The BEAST algorithm is first used to detect change points and MF-DCCA is used. • The outbreak of the pandemic has impacted multifractality of the two carbon markets. • The Hubei market exhibited higher levels of multifractality and multifractal risk. [ABSTRACT FROM AUTHOR]

IntroductionIdentifying at what point atrophy rates first change in Alzheimer's disease is important for informing design of presymptomatic trials.MethodsSerial T1-weighted magnetic resonance imaging scans of 94 participants (28 noncarriers, 66 carriers) from the Dominantly Inherited Alzheimer Network were used to measure brain, ventricular, and hippocampal atrophy rates. For each structure, nonlinear mixed-effects models estimated the change-points when atrophy rates deviate from normal and the rates of change before and after this point.ResultsAtrophy increased after the change-point, which occurred 1-1.5 years (assuming a single step change in atrophy rate) or 3-8 years (assuming gradual acceleration of atrophy) before expected symptom onset. At expected symptom onset, estimated atrophy rates were at least 3.6 times than those before the change-point.DiscussionAtrophy rates are pathologically increased up to seven years before "expected onset". During this period, atrophy rates may be useful for inclusion and tracking of disease progression.

The next best thing to be able to peep into the future is to be able to predict it accurately. With enterprises increasingly relying upon innovation. they wish to predict how their new products and services will be absorbed and accepted in the market. Several mathematical models help in predicting innovation diffusion in the market so that sound decisions on production, quantities and finance could be taken. Continuing that effort to predict innovation diffusion more accurately, we have developed and analyzed a stochastic model of innovation diffusion by depicting a dynamic potential market. Whenever the potential adopter population is substantial and the products considered are durable. the adoption process assumes a stochastic form. Here. we suggest a stochastic innovation-diffusion model assuming the potential market to be dynamic in nature. The stochastic model is solved analytically by applying the stochastic differential equation. The change point concept is also incorporated in the model by assuming that adoption rate of product per remaining potential adopter might change due to shift in marketing strategy. Estimation of parameters in the model is illustrated for applicability and accuracy. Predictive validity and MSE have been employed to examine the effectiveness of the proposed model and the values are compared with other existing models to demonstrate its efficiency. [ABSTRACT FROM AUTHOR]

We consider an integer-valued time series (Y t) t ∈ Z where the model after a time k ∗ is Poisson autoregressive with the conditional mean that depends on a parameter θ ∗ ∈ Θ ⊂ R d . The structure of the process before k ∗ is unknown; it could be any other integer-valued process, that is, (Y t) t ∈ Z could be nonstationary. It is established that the maximum likelihood estimator of θ ∗ computed on the nonstationary observations is consistent and asymptotically normal. Subsequently, we carry out the sequential change-point detection in a large class of Poisson autoregressive models, and propose a monitoring scheme for detecting change. The procedure is based on an updated estimator, which is computed without the historical observations. The above results of inference in a nonstationary setting are applied to prove the consistency of the proposed procedure. A simulation study as well as a real data application are provided. [ABSTRACT FROM AUTHOR]

Since its release of Version 1.0 in 1998, Joinpoint software developed for cancer trend analysis by a team at the US National Cancer Institute has received a considerable attention in the trend analysis community and it became one of most widely used software for trend analysis. The paper published in Statistics in Medicine in 2000 (a previous study) describes the permutation test procedure to select the number of joinpoints, and Joinpoint Version 1.0 implemented the permutation procedure as the default model selection method and employed parametric methods for the asymptotic inference of the model parameters. Since then, various updates and extensions have been made in Joinpoint software. In this paper, we review basic features of Joinpoint, summarize important updates of Joinpoint software since its first release in 1998, and provide more information on two major enhancements. More specifically, these enhancements overcome prior limitations in both the accuracy and computational efficiency of previously used methods. The enhancements include: (i) data driven model selection methods which are generally more accurate under a broad range of data settings and more computationally efficient than the permutation test and (ii) the use of the empirical quantile method for construction of confidence intervals for the slope parameters and the location of the joinpoints, which generally provides more accurate coverage than the prior parametric methods used. We show the impact of these changes in cancer trend analysis published by the US National Cancer Institute. [ABSTRACT FROM AUTHOR]

A bent line expectile regression model can describe the effect of a covariate on the response variable with two different straight lines, which intersect at an unknown change-point. Due to the existence of the change-point, the objective function of the model is not differentiable with respect to the change-point, so it cannot be solved by the method of the traditional linear expectile regression model. For this model, a new estimation method is proposed by a smoothing technique, that is, using Gaussian kernel function to approximate the indicator function in the objective function. It can not only estimate the regression coefficients and change-point location simultaneously, but also have better estimation effect, which compensates for the insufficiency of the previous estimation methods. Under the given regularity conditions, the theoretical proofs of the consistency and asymptotic normality of the proposed estimators are derived. There are two parts of numerical simulations in this paper. Simulation 1 discusses various error distributions at different expectile levels under different conditions, the results show that the mean values of the biases of the estimation method in this paper, and other indicators, are very small, which indicates the robust property of the new method. Simulation 2 considers the symmetric and asymmetric bent lien expectile regression models, the results show that the estimated values of the estimation method in this paper are similar to the true values, which indicates the estimation effect and large sample performance of the proposed method are excellent. In the application research, the method in this paper is applied to the Arctic annual average temperature data and the Nile annual average flow data. The research shows that the standard errors of the estimation method in this paper are very similar to 0, indicating that the parameter estimation accuracy of the new method is very high, and the location of the change-point can be accurately estimated, which further confirms that the new method is effective and feasible. [ABSTRACT FROM AUTHOR]

Due to the continuous dependence of society on technology and the fast growth of Open Source Software (OSS), there is a need for the software industry to shift to multi‐release software development. To include the revisions in user demands and testing environment, factors that affect OSS reliability have to be considered. Here, we propose a quantitative method for assessing the reliability of multi‐release OSS by using Software Reliability Growth Models based on the Non‐Homogenous Poisson Process. Various factors like imperfect debugging, error generation, change‐point have been considered. The model has been estimated on Statistical Package for Social Sciences using three releases of the Apache dataset. It is concluded that the results obtained are improved than the existing ones. [ABSTRACT FROM AUTHOR]

Kerosene is known to be one of the useful substances in crude oil. It is considered to be a useful household substance. It is a combustible hydrocarbon liquid widely used as fuel in industry and households. Over the years, it has been shown that there is an upward trend in the price of kerosene which has affected its use negatively. It would be of interest to investigate the change points in the price of kerosene in the six states of the southwestern region of Nigeria between 2015 and 2021. Mann Kendall trend test was used to determine the trends in the data. The Mann Kendall trend analysis showed a significant upward trend with their pvalues less than 0.05 for all the States. Furthermore, Bayesian and Pettitt approaches were employed to detect change points in the price of Kerosene in the six states (Ekiti, Lagos, Ogun, Ondo, Osun and Oyo) of the southwestern region of Nigeria. The Pettitt method showed a single shift in each of the States while the Bayesian approach showed multiple shifts in each State. Both methods give the change point with dates while the Bayesian also provides the posterior means for the change points. [ABSTRACT FROM AUTHOR]

The aim of this paper is to infer the effects that change on human mobility had on the transmission dynamics during the first four months of the SARS-CoV-2 pandemic in Costa Rica, which could have played a role in delaying community transmission in the country. First, by using parametric and non-parametric change-point detection techniques, we were able to identify two different periods when the trend of daily new cases significantly changed. Second, we explored the association of these changes with data on population mobility. This also allowed us to estimate the lag between changes in human mobility and rates of daily new cases. The information was then used to establish an association between changes in population mobility and the sanitary measures adopted during the study period. Results showed that during the initial two months of the pandemic in Costa Rica, the implementation of sanitary measures and their impact on reducing human mobility translated to a mean reduction of 54% in the number of daily cases from the projected number, delaying community transmission.