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Register a new userA novel change point approach for the detection of gas emission sources using remotely contained concentration data
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Added by
Claudia Kirch
Publication date
2020
fields
Mathematical Statistics
and research's language is
English
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Motivated by an example from remote sensing of gas emission sources, we derive two novel change point procedures for multivariate time series where, in contrast to classical change point literature, the changes are not required to be aligned in the different components of the time series. Instead the change points are described by a functional relationship where the precise shape depends on unknown parameters of interest such as the source of the gas emission in the above example. Two different types of tests and the corresponding estimators for the unknown parameters describing the change locations are proposed. We derive the null asymptotics for both tests under weak assumptions on the error time series and show asymptotic consistency under alternatives. Furthermore, we prove consistency for the corresponding estimators of the parameters of interest. The small sample behavior of the methodology is assessed by means of a simulation study and the above remote sensing example analyzed in detail.
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Changepoint detection is the problem of finding abrupt or gradual changes in time series data when the distribution of the time series changes significantly. There are many sophisticated statistical algorithms for solving changepoint detection problem, although there is not much work devoted towards gradual changepoints as compared to abrupt ones. Here we present a new approach to solve changepoint detection problem using fuzzy rough set theory which is able to detect such gradual changepoints. An expression for the rough-fuzzy estimate of changepoints is derived along with its mathematical properties concerning fast computation. In a statistical hypothesis testing framework, asymptotic distribution of the proposed statistic on both single and multiple changepoints is derived under null hypothesis enabling multiple changepoint detection. Extensive simulation studies have been performed to investigate how simple crude statistical measures of disparity can be subjected to improve their efficiency in estimation of gradual changepoints. Also, the said rough-fuzzy estimate is robust to signal-to-noise ratio, high degree of fuzziness in true changepoints and also to hyper parameter values. Simulation studies reveal that the proposed method beats other fuzzy methods and also popular crisp methods like WBS, PELT and BOCD in detecting gradual changepoints. The applicability of the estimate is demonstrated using multiple real-life datasets including Covid-19. We have developed the python package roufcp for broader dissemination of the methods.
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 popular 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.
Topological Data Analysis (TDA) is a rapidly growing field, which studies methods for learning underlying topological structures present in complex data representations. TDA methods have found recent success in extracting useful geometric structures for a wide range of applications, including protein classification, neuroscience, and time-series analysis. However, in many such applications, one is also interested in sequentially detecting changes in this topological structure. We propose a new method called Persistence Diagram based Change-Point (PD-CP), which tackles this problem by integrating the widely-used persistence diagrams in TDA with recent developments in nonparametric change-point detection. The key novelty in PD-CP is that it leverages the distribution of points on persistence diagrams for online detection of topological changes. We demonstrate the effectiveness of PD-CP in an application to solar flare monitoring.
This paper investigates the (in)-consistency of various bootstrap methods for making inference on a change-point in time in the Cox model with right censored survival data. A criterion is established for the consistency of any bootstrap method. It is shown that the usual nonparametric bootstrap is inconsistent for the maximum partial likelihood estimation of the change-point. A new model-based bootstrap approach is proposed and its consistency established. Simulation studies are carried out to assess the performance of various bootstrap schemes.
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when at most one change point occurs and generalize them to multiple change points settings. The proposed statistics leverage edge weight information in the graphs, exhibiting substantial improvements in testing power and localization accuracy in simulations. We derive the null limiting distribution, provide accurate analytic approximations to control type I error, and establish theoretical guarantees on the power consistency under contiguous alternatives for the one change point setting, as well as the minimax localization rate. In the multiple change points setting, the asymptotic correctness of the number and location of change points are also guaranteed. The methods are illustrated on the MIT proximity network data.
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