Change-point Estimation Research Articles

Determination of a Change Point in the Age at Diagnosis of Breast Cancer Using a Survival Model.

Breast cancer, the second cause of cancer-related death after lung cancer and the most common cancer in women after skin cancer, is curable if detected in early stages of clinical presentation. Knowledge as to any age cut-off points which might have significance for prognostic groups is important in screening and treatment planning. Therefore, determining a change-point could improve resource allocation. This study aimed to determine if a change point for survival might exist in the age of breast cancer diagnosis. This study included 568 cases of breast cancer that were registered in Breast Cancer Research Center, Tehran, Iran, during the period 1986-2006 and were followed up to 2012. In the presence of curable cases of breast cancer, a change point in the age of breast cancer diagnosis was estimated using a mixture survival cure model. The data were analyzed using SPSS (versions 20) and R (version 2.15.0) software. The results revealed that a change point in the age of breast cancer diagnosis was at 50 years age. Based on our estimation, 35% of the patients diagnosed with breast cancer at age less than or equal to 50 years of age were cured while the figure was 57% for those diagnosed after 50 years of age. Those in the older age group had better survival compared to their younger counterparts during 12 years of follow up. Our results suggest that it is better to estimate change points in age for cancers which are curable in early stages using survival cure models, and that the cure rate would increase with timely screening for breast cancer.

A variance change point estimation method based on intelligent ensemble model for quality fluctuation analysis

For multivariable production process, knowing the first time of process really changes (change point) will help to accelerate the location of assignable causes and make measures for process adjustment. So effective estimating the change point is an important way to analyse the quality fluctuation of process. In the present study, an intelligent ensemble model for quality fluctuation analysis is proposed to estimate the variance change point in multivariable process. With the method, the process is decomposed based on moving window analysis, then different types of kernel functions are combined together to form the multi-kernel support vector machine model, which has combined the feature mapping capability of each basic kernel in the new feature space. The particle swarm optimisation is considered to search the optimised multi-kernel parameters. After that, each sub-characteristic is regarded as a pattern to be recognised to determine the change point by using the optimised intelligent ensemble model. Finally, a case study is conducted to evaluate the performance of proposed approach. It reveals that the method could estimate the time of variance change point in continuous production process accurately.

Semiparametric test for multiple change-points based on empirical likelihood

In the dynamic financial market, the change of financial asset prices is always described as a certain random events which result in abrupt changes. The random time when the event occurs is called a change point. As the event happens, in order to mitigate property damage the government should increase the macro-control ability. As a result, we need to find a valid statistical model for change point problem to solve it effectively. This paper proposes a semiparametric model for detecting the change points. According to the research of empirical studies and hypothesis testing we acquire the maximum likelihood estimators of change points. We use the loglikelihood ratio to test the multiple change points. We obtain some asymptotic results. The estimated change point is more efficient than the non parametric one through simulation experiments. Real data application illustrates the usage of the model.

Discriminating between Long Memory and Volatility Shifts

We develop a practical implementation of the test proposed in Berkes, Horv´ath, Kokoszka, and Shao (2006) designed to distinguish between a change-point model and a long memory model. Our implementation is calibrated to distinguish between a shift in volatility of returns and long memory in squared returns. It uses a kernel estimator of the long-run variance of squared returns with the maximal lag selected by a data driven procedure which depends on the sample size, the location of the estimated change point and the direction of the apparent volatility shift (increase versus decrease). In a simulations study, we also consider other long-run variance estimators, including the VARHAC estimator, but we find that they lead to tests with inferior performance. Applied to returns on indexes and individual stocks, our test indicates that even for the same asset, a change-point model may be preferable for a certain period of time, whereas there is evidence of long memory in another period of time. Generally there is stronger evidence for long memory in the eight years ending June 2006 than in the eight years starting January 1992. This pattern is most pronounced for US stock indexes and shares in the US financial sector.

A decision theoretic approach to change point estimation for binomial CUSUM control charts

ABSTRACTDetecting when the process has changed is a classical problem in sequential analysis and is an important practical issue in statistical process control. This article is concerned about the binomial cumulative sum (CUSUM) control chart, which is extensively applied to industrial process control, health care, public health surveillance, and other fields. For the binomial CUSUM, a maximum likelihood estimator has been proposed to estimate the change point. In our article, following a decision theoretic approach, we develop a new estimator that aims to improve the existing methods. For interval estimation, we propose a parametric bootstrap procedure to construct the confidence set of the change point. We compare our proposed method with the maximum likelihood estimator and Page's last zero estimator in terms of mean squared error by simulations. We find that the proposed method gives more unbiased and robust results than the existing procedures under various parameter designs. We analyze jewelry manufacturing data for illustration.

Estimation of Change Point in Two-Stage Processes Subject to Step Change and Linear Trend

When a control chart signals, it shows the process parameters have changed due to assignable cause(s). However, control chart signal is not the real time of a change in the process. Knowing the real time of change would simplify the detection and elimination of the assignable causes of variation. In this paper, a two-stage process is considered when the mean values of quality characteristics are changed under step shift and linear drift. First, a control chart based on the discriminant analysis (DA) is utilized to monitor the process. Then, when the out-of-control signal is received, the maximum likelihood estimator (MLE) based on the DA statistics, and clustering approach based on Mahalanobis distance of residuals are developed to estimate the real time of the change. The performances of the proposed estimators under different shifts are evaluated through numerical examples and a real case. The results indicate the better performance of the clustering approach rather than the MLE in most cases under both step shift and drift.

A New Spectrum Sensing Strategy for Dynamic Primary Users in Cognitive Radio

In this letter, a new spectrum sensing strategy is proposed for primary users (PUs), which are dynamic whereby it is assumed that at least one and possibly multiple PU status changes occur in the channel during the sensing period. According to our proposed strategy, the last status change point of the PU is estimated first using maximum likelihood estimation (MLE). Then, any known spectrum sensing method can be applied to the observed samples between this last status change point and the end of the sensing period. By this way, degradation in probability of detection due to PU traffic is lessened. Dynamic programming (DP) is used to accelerate computation of the MLE. We also propose a new cumulative sum (CuSum) based weighting scheme. Simulations indicate that the proposed sensing strategy provides an improvement in terms of probability of detection for all the considered spectrum sensing methods. Furthermore, the proposed CuSum based weighting scheme achieves the best probability of detection when employed together with the last status change point estimation strategy.

Detecting Variance Change-Points for Blocked Time Series and Dependent Panel Data

This article proposes a class of weighted differences of averages (WDA) statistics to test and estimate possible change-points in variance for time series with weakly dependent blocks and dependent panel data without specific distributional assumptions. We derive the asymptotic distributions of the test statistics for testing the existence of a single variance change-point under the null and local alternatives. We also study the consistency of the change-point estimator. Within the proposed class of the WDA test statistics, a standardized WDA test is shown to have the best consistency rate and is recommended for practical use. An iterative binary searching procedure is suggested for estimating the locations of possible multiple change-points in variance, whose consistency is also established. Simulation studies are conducted to compare detection power and number of wrong rejections of the proposed procedure to that of a cumulative sum (CUSUM) based test and a likelihood ratio-based test. Finally, we apply the proposed method to a stock index dataset and an unemployment rate dataset. Supplementary materials for this article are available online.

Adaptive LASSO model selection in a multiphase quantile regression

We propose a general adaptive LASSO method for a quantile regression model. Our method is very interesting when we know nothing about the first two moments of the model error. We first prove that the obtained estimators satisfy the oracle properties, which involves the relevant variable selection without using hypothesis test. Next, we study the proposed method when the (multiphase) model changes to unknown observations called change-points. Convergence rates of the change-points and of the regression parameter estimators in each phase are found. The sparsity of the adaptive LASSO quantile estimators of the regression parameters is not affected by the change-points estimation. If the number of phases is unknown, a consistent criterion is proposed. Numerical studies by Monte Carlo simulations show the performance of the proposed method, compared to other existing methods in the literature, for models with a single phase or for multiphase models. The adaptive LASSO quantile method performs better than known variable selection methods, as the least squared method with adaptive LASSO penalty, -method with LASSO-type penalty and quantile method with SCAD penalty.

A pairwise likelihood-based approach for changepoint detection in multivariate time series models

This paper develops a composite likelihood-based approach for multiple changepoint estimation in multivariate time series. We derive a criterion based on pairwise likelihood and minimum description length for estimating the number and locations of changepoints and for performing model selection in each segment. The number and locations of the changepoints can be consistently estimated under mild conditions and the computation can be conducted efficiently with a pruned dynamic programming algorithm. Simulation studies and real data examples demonstrate the statistical and computational efficiency of the proposed method.

Threshold Responses of Blackside Dace (Chrosomus cumberlandensis) and Kentucky Arrow Darter (Etheostoma spilotum) to Stream Conductivity

Abstract - Chrosomus cumberlandensis (Blackside Dace [BSD]) and Etheostoma spilotum (Kentucky Arrow Darter [KAD]) are fish species of conservation concern due to their fragmented distributions, their low population sizes, and threats from anthropogenic stressors in the southeastern United States. We evaluated the relationship between fish abundance and stream conductivity, an index of environmental quality and potential physiological stressor. We modeled occurrence and abundance of KAD in the upper Kentucky River basin (208 samples) and BSD in the upper Cumberland River basin (294 samples) for sites sampled between 2003 and 2013. Segmented regression indicated a conductivity change-point for BSD abundance at 343 μS/cm (95% CI: 123–563 μS/cm) and for KAD abundance at 261 μS/cm (95% CI: 151–370 μS/cm). In both cases, abundances were negligible above estimated conductivity change-points. Post-hoc randomizations accounted for variance in estimated change points due to unequal sample sizes across the conductiv...

Detection and estimation of structural change in heavy-tailed sequence

ABSTRACTIn this paper, bootstrap detection and ratio estimation are proposed to analysis mean change in heavy-tailed distribution. First, the test statistic is constructed into a ratio form on the CUSUM process. Then, the asymptotic distribution of test statistic is obtained and the consistency of the test is proved. To solve the problem that the null distribution of the test statistic contains unknown tail index, we present a bootstrap approximation method to determine the critical values of the null distribution. We also discuss how to estimate change point based on ratio method. The consistency and rate of convergence for the change-point estimator are established. Finally, the excellent performance of our method is demonstrated through simulations using artificial and real data sets. Especially the simulation results of bootstrap test are better than those of another existing method.

Estimation of Change Point in Poisson Random Variables Using the Maximum Likelihood Method

The point at which a process undergoes a significant shift from its usual course is known as change point. Change point analysis entails testing for the presence of change in a given process, and the location of a single or multiple change points. This study presents a maximum likelihood estimate of a single change point in a sequence of independent and identically distributed Poisson random variables which are dependent on some covariates. A Poisson regression model is used to estimate the mean parameter and the likelihood function. A likelihood ratio test is conducted to check whether change exists with critical values of the test being obtained as in Gombay and Horvath [9]. The procedure is validated for simulated data for cases when there is no change and when there is a predefined change point with special application to incidence of road accidents in Kenya.

Оценка надежности разгонного блока “Фрегат”

The paper presents the operating history of the upper stage “Fregat”. We consider three modifications of the upper stage and their differences. The results of point and interval estimates of the reliability of the upper stage “Fregat”. Estimates were obtained with and without taking into account a priori estimates of reliability in the results 55 starts. Given the dynamics of the change point estimates of reliability depending on the number of starts. Considered the event, which ensured a high level of reliability of the upper stage “Fregat”.

Change Point Inference in Growth Curve Models

In this paper we present statistical procedures to do inference about possible change points based on the p value of the test used to assess the goodness-of-fit of the longitudinal model. The first of these procedures deals with a few statistical tests which check for the existence of any change point in the data set under study and the second one considers the estimation of such change points. In addition, we also provide a statistical test to determine whether a specific time point is a change point or not. The effectiveness of the proposed methods are demonstrated through simulation studies.

Change-point detection for shifts in control charts using fuzzy shift change-point algorithms

Knowing the real time of changes, called change-point, in a process is essential for quickly identifying and removing special causes. Many change-point methods in statistical process control assume the distribution and the in-control parameters of the process known, however, they are rarely known accurately. Small errors accompanied with estimated parameters may lead to unfavorable change-point estimates. In this paper, a new method, called fuzzy shift change-point algorithm, which does not require the knowledge of the distribution nor the parameter of the process, is proposed to detect change-points for shifts in process mean. The fuzzy c-partition concept is embedded into change-point formulation in which any possible collection of change-points is considered as a partitioning of data with a fuzzy membership. These memberships are then transferred into the pseudo memberships of observations belonging to each individual cluster, so the fuzzy c-means clustering can be used to obtain the estimates for shifts. Subsequently, the fuzzy c-means algorithm is used again to obtain new iterates of change-point collection memberships by minimizing an objective function concerning the deviations between observations and the corresponding cluster means. The proposed algorithm is nonparametric and applicable to normal and non-normal processes in both phase I and II. The performance of the proposed fuzzy shift change-point algorithm is discussed in comparison with powerful statistical methods through extensive simulation studies. The results demonstrate the superiority and usefulness of our proposed method.

Estimated phase transition and melting temperature of APTES self-assembled monolayer using surface-enhanced anti-stokes and stokes Raman scattering

A structure's temperature can be determined from the Raman spectrum using the frequency and the ratio of the intensities of the anti-Stokes and Stokes signals (the Ias/Is ratio). In this study, we apply this approach and an equation relating the temperature, Raman frequency, and Ias/Is ratio to in-situ estimation of the phase change point of a (3-aminopropyl)triethoxysilane self-assembled monolayer (APTES SAM). Ag nanoparticles were deposited on APTES to enhance the Raman signals. A time-resolved measurement mode was used to monitor the variation in the Raman spectra in situ. Moreover, the structural change in APTES SAM (from ordered to disordered structure) under heating was discussed in detail, and the phase change point (around 118°C) was calculated.

ASYMPTOTICS FOR CHANGE-POINT MODELS UNDER VARYING DEGREES OF MIS-SPECIFICATION.

Change-point models are widely used by statisticians to model drastic changes in the pattern of observed data. Least squares/maximum likelihood based estimation of change-points leads to curious asymptotic phenomena. When the change-point model is correctly specified, such estimates generally converge at a fast rate (n) and are asymptotically described by minimizers of a jump process. Under complete mis-specification by a smooth curve, i.e. when a change-point model is fitted to data described by a smooth curve, the rate of convergence slows down to n1/3 and the limit distribution changes to that of the minimizer of a continuous Gaussian process. In this paper we provide a bridge between these two extreme scenarios by studying the limit behavior of change-point estimates under varying degrees of model mis-specification by smooth curves, which can be viewed as local alternatives. We find that the limiting regime depends on how quickly the alternatives approach a change-point model. We unravel a family of 'intermediate' limits that can transition, at least qualitatively, to the limits in the two extreme scenarios. The theoretical results are illustrated via a set of carefully designed simulations. We also demonstrate how inference for the change-point parameter can be performed in absence of knowledge of the underlying scenario by resorting to subsampling techniques that involve estimation of the convergence rate.

A changepoint statistic with uniform type I error probabilities

ABSTRACTLikelihood ratio tests for a change in mean in a sequence of independent, normal random variables are based on the maximum two-sample t-statistic, where the maximum is taken over all possible changepoints. The maximum t-statistic has the undesirable characteristic that Type I errors are not uniformly distributed across possible changepoints. False positives occur more frequently near the ends of the sequence and occur less frequently near the middle of the sequence. In this paper we describe an alternative statistic that is based upon a minimum p-value, where the minimum is taken over all possible changepoints. The p-value at any particular changepoint is based upon both the two-sample t-statistic at that changepoint and the probability that the maximum two-sample t-statistic is achieved at that changepoint. The new statistic has a more uniform distribution of Type I errors across potential changepoints and it compares favorably with respect to statistical power, false discovery rates, and the mean square error of changepoint estimates.

A hybrid method for estimating the process change point using support vector machine and fuzzy statistical clustering

Control charts are the most popular process monitoring techniques designed to determine whether a process is in a state of statistical control or not. When a process change occurs, the control chart exhibits an out-of-control signal. In most cases, the signal is followed by a substantial amount of delay. To address this drawback, supplementary techniques have been considered to be employed along with the control charts to identify the exact time of the process change. This paper presents a hybrid method for estimating the change point on x¯ chart when neither the change type nor its magnitude are known. For this purpose, two sets of features with the most discriminatory power between x¯ chart patterns are selected. Then the feature vectors are extracted from the control chart patterns (CCPs) and served as an input to a classification scheme which is comprised of several support vector machine (SVM) classifiers. After parameters tuning, the classifiers are built and used for classifying the CCPs and identifying the change type. Once the change type is determined, the fuzzy statistical clustering (FSC) and the maximum likelihood (ML) estimators are employed to identify the process change point. The performance of selected features, the classification scheme, and the change point estimators are evaluated by conducting several simulation studies. Empirical results show that in identifying the change types, the proposed classification scheme is more accurate than two recent CCP classification methods. The results also confirm that the proposed hybrid method offers an accurate estimate of the process change point, as compared to the most recent methods developed for the change point estimation.