Abstract Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis. We develop a structural subsampling procedure such that the observations are encoded into multiple sequences of Bernoulli variables. A maximum likelihood approach in conjunction with a newly developed searching algorithm is implemented to detect change points on each Bernoulli process separately. Then, aggregation statistics are proposed to collectively synthesize change-point results from all individual univariate time series into consistent and stable location estimations. We also study a weighting strategy to measure the degree of relevance for different subsampled groups. Simulation studies are conducted and shown that the proposed change-point methodology for multivariate time series has favorable performance comparing with currently available state-of-the-art nonparametric methods under various settings with different degrees of complexity. Real data analyses are finally performed on categorical, ordinal, and continuous time series taken from fields of genetics, climate, and finance.
more »
« less
Application of Change Point Analysis of Response Time Data to Detect Test Speededness
Computer-based and web-based testing have become increasingly popular in recent years. Their popularity has dramatically expanded the availability of response time data. Compared to the conventional item response data that are often dichotomous or polytomous, response time has the advantage of being continuous and can be collected in an unobstrusive manner. It therefore has great potential to improve many measurement activities. In this paper, we propose a change point analysis (CPA) procedure to detect test speededness using response time data. Specifically, two test statistics based on CPA, the likelihood ratio test and Wald test, are proposed to detect test speededness. A simulation study has been conducted to evaluate the performance of the proposed CPA procedure, as well as the use of asymptotic and empirical critical values. Results indicate that the proposed procedure leads to high power in detecting test speededness, while keeping the false positive rate under control, even when simplistic and liberal critical values are used. Accuracy of the estimation of the actual change point, however, is highly dependent on the true change point. A real data example is also provided to illustrate the utility of the proposed procedure and its contrast to the response-only procedure. Implications of the findings are discussed at the end.
more »
« less
- Award ID(s):
- 1853166
- PAR ID:
- 10351765
- Date Published:
- Journal Name:
- Educational and psychological measurement
- Volume:
- 82
- Issue:
- 5
- ISSN:
- 0013-1644
- Page Range / eLocation ID:
- 1031-1062
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Change point detection is widely used for finding transitions between states of data generation within a time series. Methods for change point detection currently assume this transition is instantaneous and therefore focus on finding a single point of data to classify as a change point. However, this assumption is flawed because many time series actually display short periods of transitions between different states of data generation. Previous work has shown Bayesian Online Change Point Detection (BOCPD) to be the most effective method for change point detection on a wide range of different time series. This paper explores adapting the change point detection algorithms to detect abrupt changes over short periods of time. We design a segment-based mechanism to examine a window of data points within a time series, rather than a single data point, to determine if the window captures abrupt change. We test our segment-based Bayesian change detection algorithm on 36 different time series and compare it to the original BOCPD algorithm. Our results show that, for some of these 36 time series, the segment-based approach for detecting abrupt changes can much more accurately identify change points based on standard metrics.more » « less
-
The use of video-imaging data for in-line process monitoring applications has become popular in industry. In this framework, spatio-temporal statistical process monitoring methods are needed to capture the relevant information content and signal possible out-of-control states. Video-imaging data are characterized by a spatio-temporal variability structure that depends on the underlying phenomenon, and typical out-of-control patterns are related to events that are localized both in time and space. In this article, we propose an integrated spatio-temporal decomposition and regression approach for anomaly detection in video-imaging data. Out-of-control events are typically sparse, spatially clustered and temporally consistent. The goal is not only to detect the anomaly as quickly as possible (“when”) but also to locate it in space (“where”). The proposed approach works by decomposing the original spatio-temporal data into random natural events, sparse spatially clustered and temporally consistent anomalous events, and random noise. Recursive estimation procedures for spatio-temporal regression are presented to enable the real-time implementation of the proposed methodology. Finally, a likelihood ratio test procedure is proposed to detect when and where the anomaly happens. The proposed approach was applied to the analysis of high-sped video-imaging data to detect and locate local hot-spots during a metal additive manufacturing process.more » « less
-
Abstract Cumulative sum (CUSUM) statistics are widely used in the change point inference and identification. For the problem of testing for existence of a change point in an independent sample generated from the mean-shift model, we introduce a Gaussian multiplier bootstrap to calibrate critical values of the CUSUM test statistics in high dimensions. The proposed bootstrap CUSUM test is fully data dependent and it has strong theoretical guarantees under arbitrary dependence structures and mild moment conditions. Specifically, we show that with a boundary removal parameter the bootstrap CUSUM test enjoys the uniform validity in size under the null and it achieves the minimax separation rate under the sparse alternatives when the dimension p can be larger than the sample size n. Once a change point is detected, we estimate the change point location by maximising the ℓ∞-norm of the generalised CUSUM statistics at two different weighting scales corresponding to covariance stationary and non-stationary CUSUM statistics. For both estimators, we derive their rates of convergence and show that dimension impacts the rates only through logarithmic factors, which implies that consistency of the CUSUM estimators is possible when p is much larger than n. In the presence of multiple change points, we propose a principled bootstrap-assisted binary segmentation (BABS) algorithm to dynamically adjust the change point detection rule and recursively estimate their locations. We derive its rate of convergence under suitable signal separation and strength conditions. The results derived in this paper are non-asymptotic and we provide extensive simulation studies to assess the finite sample performance. The empirical evidence shows an encouraging agreement with our theoretical results.more » « less
-
Due to limited amplitude and controlled phase of current supplied by inverter-interfaced renewable power plants (IIRPPs), the IIRPP-side distance protection of lines connected to IIRPPs fails to detect the fault location accurately, so it may malfunction. The composite sequence network of a line connected to an IIRPP during asymmetrical faults is analyzed, and an adaptive distance protection based on the analytical model of additional impedance is proposed in this study. Based on open circuit property of negative-sequence network at the IIRPP-side, the equivalent impedance of power grid and current flowing through fault point are calculated in real-time using local measurements, which are substituted into the analytical model of additional impedance to calculate fault location. In the case of negative-sequence reactive current injection from IIRPPs during asymmetrical faults, the error of calculating fault point current from local measurements is analyzed and corrected to ensure reliability of the proposed protection. The proposed protection alleviates the effect of fault resistance in a system with weak sources. In addition, the proposed protection can adapt to different grid codes (GCs), the operation mode change of the power grid, and the capacity change of the IIRPP. PSCAD/EMTDC test results verify the effectiveness of the proposed protection.more » « less
An official website of the United States government

