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Estimator of a change point in single index models

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Science China Mathematics 2014年第8期57卷 1701-1712页

作者： JIN BaiSuo DONG CuiLing TAN ChangChun MIAO BaiQi Department of Statistics and Finance University of Science and Technology of China School of Mathematical Sciences Xinjiang Normal University School of Mathematics Hefei University of Technology

This paper considers the problem of change point in single index *** order to obtain asymptotically valid confidence intervals for the estimation of the change point,the convergence rate and asymptotic distribution of the change point estimate is *** simulation results are presented which show that the numerical performance of our estimator is satisfactory.

关键词： single index model change point convergence rate asymptotic distribution

Consistency of the <i>φ</i>-Divergence Based change point Estimator

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Open Journal of Statistics 2020年第5期10卷 832-849页

作者： Mwelu Susan Anthony G. Waititu Peter N. Mwita Charity Wamwea Pan-African University Institute of Basic Sciences Technology and Innovation Nairobi Kenya Department of Statistics and Actuarial Sciences JKUAT Nairobi Kenya Department of Mathematics Statistics and Actuarial Sciences Machakos University Machakos Kenya

This paper utilizes a change-point estimator based on the φ-divergence. Since we seek a near perfect translation to reality, then locations of parameter change within a finite set of data have to be accounted for since the assumption of stationary model is too restrictive especially for long time series. The estimator is shown to be consistent through asymptotic theory and finally proven through simulations. The estimator is applied to the generalized Pareto distribution to estimate changes in the scale and shape parameters.

关键词： change point Consistency φ-Divergence Kullback-Leibler Generalized Pareto Distribution

Limit Distribution of the φ-Divergence Based change point Estimator

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维普期刊数据库

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Open Journal of Statistics 2021年第3期11卷 337-350页

作者： Mwelu Susan Anthony G. Waititu Peter N. Mwita Charity Wamwea Pan African University Institute for Basic Sciences Technology and Innovation Nairobi Kenya Department of Statistics and Actuarial Sciences JKUAT Nairobi Kenya Department of Mathematics Statistics and Actuarial Sciences Machakos University Machakos Kenya

The assumption of stationarity is too restrictive especially for long time series. This paper studies the change point problem through a change point estimator based on the φ-divergence which provides a rich set of distance like measures between pairs of distributions. The change point problem is considered in the following sub-fields: the problem of divergence estimation, testing for the homogeneity between two samples as well as estimating the time of change. The asymptotic distribution of the change point estimator is estimated by the limiting distribution of a stochastic process within given bounds through asymptotic theory surrounding the likelihood theory. The distribution is found to converge to that of a standardized Brownian bridge process.

关键词： change point φ-Divergence Estimator Test Statistic Distribution Wald

Non-Stationary Trend change point Pattern Using 24-Hourly Annual Maximum Series (AMS) Precipitation Data

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维普期刊数据库

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Journal of Water Resource and Protection 2022年第8期14卷 592-609页

作者： Masi G. Sam Ify L. Nwaogazie Chiedozie Ikebude Department of Civil and Environmental Engineering University of Port Harcourt Rivers State Nigeria

This paper mainly investigated the basic information about non-stationary trend change point patterns. After performing the investigation, the corresponding results show the existence of a trend, its magnitude, and change points in 24-hourly annual maximum series (AMS) extracted from monthly maximum series (MMS) data for thirty years (1986-2015) rainfall data for Uyo metropolis. Trend analysis was performed using Mann-Kendall (MK) test and Sen’s slope estimator (SSE) used to obtain the trend magnitude, while the trend change point analysis was conducted using the distribution-free cumulative sum test (CUSUM) and the sequential Mann-Kendall test (SQMK). A free CUSUM plot date of change point of rainfall trend as 2002 at 90% confidence interval was obtained from where the increasing trend started and became more pronounced in the year 2011, another change point year from the SQMK plot with the trend intensifying. The SSE gave an average rate of change in rainfall as 2.1288 and 2.16 mm/year for AMS and MMS time series data respectively. Invariably, the condition for Non-stationary concept application is met for intensity-duration-frequency modeling.

关键词： Precipitation Data Series Trend Analysis Mann-Kendall Test change point

Nonparametric Inference in a Simple change-point Model

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维普期刊数据库

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Acta Mathematica Sinica,English Series 2008年第9期24卷 1483-1496页

作者： Zhan Feng Wang Yao Hua Wu and Lin Cheng Zhao Department of Statistics and Finance University of Science and Technology of China Hefei 230026 P. R. China

In this paper, we consider a change point model allowing at most one change, X($\tfrac{i}{n}$\tfrac{i}{n}) = f($\tfrac{i}{n}$\tfrac{i}{n}) + e($\tfrac{i}{n}$\tfrac{i}{n}), where f(t) = α + θ $I_{(t_0 ,1)} $I_{(t_0 ,1)} (t), 0 ≤ t ≤ 1, {e($\tfracchange point{n}$\tfracchange point{n}), ..., e($\tfrac{n}{n}$\tfrac{n}{n})} is a sequence of i.i.d. random variables distributed as e with 0 being the median of e. For this change point model, hypothesis test problem about the change-point t0 is studied and a test statistic is constructed. Furthermore, a nonparametric estimator of t0 is proposed and shown to be strongly consistent. Finally, we give an estimator of jump θ and obtain it’s asymptotic property. Performance of the proposed approach is investigated by extensive simulation studies.

关键词： sample median change point extreme distribution Bahadur representation

Discrete Software Reliability Growth Modeling for Errors of Different Severity Incorporating change-point Concept

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International Journal of Automation and computing 2007年第4期4卷 396-405页

作者： D.N.Goswami Sunil K.Khatri Reecha Kapur School of Studies in Computer Science and Applications Jiwaji UniversityGwalior 474011India Mother Teresa Institute of Management Guru Gobind Singh Indraprastha UniversityDelhi110092India Department of Mathematics and Computer Applications Bundelkhand UniversityJhansi 284128India

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

关键词： Discrete software reliability growth model non-homogeneous Poisson process fault severity change point probability generating function.

Inference of change-point in single index models

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Science China Mathematics 2008年第10期51卷 1855-1870页

作者： CAO GuanQun WANG ZhanFeng WU YaoHua ZHAO LinCheng Department of Statistics and Finance University of Science and Technology of ChinaHefei 230026China

Single index models are widely used in medicine, econometrics and some other fields. In this paper, we consider the inference of a change point problem in single index models. Based on density-weighted average derivative estimation (ADE) method, we propose a statistic to test whether a change point exists or not. The null distribution of the test statistic is obtained using a permutation technique. The permuted statistic is rigorously shown to have the same distribution in the limiting sense under both null and alternative hypotheses. After the null hypothesis of no change point is rejected, an ADE-based estimate of the change point is proposed under assumption that the change point is unique. A simulation study confirms the theoretical results.

关键词： change point single index models density weighted average derivatives U-statistic Brownian bridges 62F05 62G05

change-point Estimation of a Mean Shift in Moving-average Processes Under Dependence Assumptions

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Acta Mathematicae Applicatae Sinica 2006年第4期22卷 615-626页

作者： Yun-xia Li Zhejiang University of Finance and Economics Hangzhou 310018 China

In this paper we discuss the least-square estimator of the unknown change point in a mean shift for moving-average processes of ALNQD sequence. The consistency and the rate of convergence for the estimated change point are established. The asymptotic distribution for the change point estimator is obtained. The results are also true for ρ-mixing, φ-mixing, α-mixing sequences under suitable conditions. These results extend those of Bai, who studied the mean shift point of a linear process of i.i.d, variables, and the condition ∑j=0^∞j｜aj｜〈 ∞ in Bai is weakened to ∑j=0^∞｜aj｜〈∞.

关键词： Mean shift moving-average process change point ALNQD rate of convergence

change-point detection for expected shortfall in time series

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Journal of Management Science and Engineering 2021年第3期6卷 324-335页

作者： Lingyu Sun Dong Li Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China Center for Statistical Science Department of Industrial EngineeringTsinghua UniversityBejing 100084China

Expected shortfall(ES)is a popular risk measure and plays an important role in risk and portfolio ***,change-point detection of risk measures has been attracting much attention in *** on the self-normalized CUSUM statistic in Fan,Glynn and Pelger(2018)and the Wild Binary Segmentation(WBS)algorithm in Fryzlewicz(2014),this paper proposes a variant WBS procedure to detect and estimate change points of ES in time *** strengthened Schwarz information criterion is also introduced to determine the number of change *** Carlo simulation studies are conducted to assess the finite-sample performance of our variant WBS procedure about ES in time *** empirical application is given to illustrate the usefulness of our procedure.

关键词： change point Expected shortfall Risk measure