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Statistical inference for multiple change‐point models
dc.contributor.authorWang, Wu
dc.contributor.authorHe, Xuming
dc.contributor.authorZhu, Zhongyi
dc.date.accessioned2020-12-02T14:36:32Z
dc.date.availableWITHHELD_13_MONTHS
dc.date.available2020-12-02T14:36:32Z
dc.date.issued2020-12
dc.identifier.citationWang, Wu ; He, Xuming; Zhu, Zhongyi (2020). "Statistical inference for multiple change‐point models." Scandinavian Journal of Statistics 47(4): 1149-1170.
dc.identifier.issn0303-6898
dc.identifier.issn1467-9469
dc.identifier.urihttps://hdl.handle.net/2027.42/163546
dc.description.abstractIn this article, we propose a new technique for constructing confidence intervals for the mean of a noisy sequence with multiple change‐points. We use the weighted bootstrap to generalize the bootstrap aggregating or bagging estimator. A standard deviation formula for the bagging estimator is introduced, based on which smoothed confidence intervals are constructed. To further improve the performance of the smoothed interval for weak signals, we suggest a strategy of adaptively choosing between the percentile intervals and the smoothed intervals. A new intensity plot is proposed to visualize the pattern of the change‐points. We also propose a new change‐point estimator based on the intensity plot, which has superior performance in comparison with the state‐of‐the‐art segmentation methods. The finite sample performance of the confidence intervals and the change‐point estimator are evaluated through Monte Carlo studies and illustrated with a real data example.
dc.publisherCambridge University Press
dc.publisherWiley Periodicals, Inc.
dc.subject.othercopy number variation
dc.subject.othermultiple change‐points
dc.subject.otherbootstrap
dc.subject.otherbinary segmentation
dc.subject.otherbagging estimator
dc.titleStatistical inference for multiple change‐point models
dc.typeArticle
dc.rights.robotsIndexNoFollow
dc.subject.hlbsecondlevelStatistics (Mathematical)
dc.subject.hlbtoplevelScience
dc.description.peerreviewedPeer Reviewed
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/163546/3/sjos12456.pdfen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/163546/2/sjos12456_am.pdfen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/163546/1/SJOS_12456_supplement.pdfen_US
dc.identifier.doi10.1111/sjos.12456
dc.identifier.sourceScandinavian Journal of Statistics
dc.identifier.citedreferencePerron, P. ( 2006 ). Dealing with structural breaks. In K. Patterson & T. Mills (Eds.), Palgrave handbook of econometrics (Vol. 1, pp. 278 – 352 ). New York, NY: Palgrave‐Macmillan.
dc.identifier.citedreferenceKillick, R., Fearnhead, P., & Eckley, I. ( 2012 ). Optimal detection of changepoints with a linear computational cost. Journal of the American Statistical Association, 107 ( 500 ), 1590 – 1598.
dc.identifier.citedreferenceKillick, R., Haynes, K. & Eckley, I. A. ( 2016 ). Changepoint: An R package for changepoint analysis. R package version 2.2.2. https://CRAN.R‐project.org/package=changepoint.
dc.identifier.citedreferenceKim, C., Suh, M.‐S., & Hong, K.‐O. ( 2009 ). Bayesian changepoint analysis of the annual maximum of daily and subdaily precipitation over South Korea. Journal of Climate, 22 ( 24 ), 6741 – 6757.
dc.identifier.citedreferenceKirch, C. ( 2007 ). Block permutation principles for the change analysis of dependent data. Journal of Statistical Planning and Inference, 137 ( 7 ), 2453 – 2474.
dc.identifier.citedreferenceKunsch, H. R. ( 1989 ). The jackknife and the bootstrap for general stationary observations. The Annals of Statistics, 17 ( 3 ), 1217 – 1241.
dc.identifier.citedreferenceMuggeo, V. M. ( 2012 ). Cumseg: Change point detection in genomic sequences. R package version 1.1. https://CRAN.R‐project.org/package=cumSeg.
dc.identifier.citedreferenceMuggeo, V. M., & Adelfio, G. ( 2011 ). Efficient change point detection for genomic sequences of continuous measurements. Bioinformatics, 27 ( 2 ), 161 – 166.
dc.identifier.citedreferenceNiu, Y. S., & Zhang, H. ( 2012 ). The screening and ranking algorithm to detect DNA copy number variations. The Annals of Applied Statistics, 6 ( 3 ), 1306 – 1326.
dc.identifier.citedreferenceOlshen, A. B., Venkatraman, E., Lucito, R., & Wigler, M. ( 2004 ). Circular binary segmentation for the analysis of array‐based DNA copy number data. Biostatistics, 5 ( 4 ), 557 – 572.
dc.identifier.citedreferencePein, F., Hotz, T., Sieling, H. & Aspelmeier, T. ( 2017 ). Stepr: Multiscale change‐point inference. R package version 2.0‐1. https://CRAN.R‐project.org/package=stepR.
dc.identifier.citedreferencePein, F., Sieling, H., & Munk, A. ( 2017 ). Heterogeneous change point inference. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79 ( 4 ), 1207 – 1227.
dc.identifier.citedreferenceR Core Team ( 2019 ). R: A language and environment for statistical computing. R foundation for statistical computing. Vienna, Austria. https://www.R‐project.org/.
dc.identifier.citedreferenceRozenholc, Y., & Nuel, G. ( 2013 ). Fast estimation of posterior probabilities in change‐point analysis through a constrained hidden Markov model. Computational Statistics & Data Analysis, 68, 129 – 140.
dc.identifier.citedreferenceShiryaev, A. N. ( 1963 ). On optimum methods in quickest detection problems. Theory of Probability & Its Applications, 8 ( 1 ), 22 – 46.
dc.identifier.citedreferenceSiegmund, D. ( 1988 ). Confidence sets in change‐point problems. International Statistical Review/Revue Internationale de Statistique, 56 ( 1 ), 31 – 48.
dc.identifier.citedreferenceSnijders, A. M., Nowak, N., Segraves, R., Blackwood, S., Brown, N., Conroy, J., … Kimura, K. ( 2001 ). Assembly of microarrays for genome‐wide measurement of DNA copy number. Nature Genetics, 29 ( 3 ), 263 – 264.
dc.identifier.citedreferenceSpokoiny, V., & Zhilova, M. ( 2015 ). Bootstrap confidence sets under model misspecification. The Annals of Statistics, 43 ( 6 ), 2653 – 2675.
dc.identifier.citedreferenceVander Vaart, A. W. ( 2000 ). Asymptotic Statistics. Cambridge, MA: Cambridge University Press.
dc.identifier.citedreferencevander Vaart, A. W., & Weller, J. A. ( 1996 ). Weak convergence and empirical processes: With applications to statistics. New York, NY: Springer‐Verlag.
dc.identifier.citedreferenceVostrikova, L. J. ( 1981 ). Detecting ’disorder’ in multidimensional random process. Soviet Mathematics Doklady, 24, 55 – 59.
dc.identifier.citedreferenceWager, S., Hastie, T., & Efron, B. ( 2014 ). Confidence intervals for random forests: The jackknife and the infinitesimal jackknife. The Journal of Machine Learning Research, 15 ( 1 ), 1625 – 1651.
dc.identifier.citedreferenceYao, Y.‐C. ( 1988 ). Estimating the number of change‐points via Schwarz’criterion. Statistics & Probability Letters, 6 ( 3 ), 181 – 189.
dc.identifier.citedreferenceArnold, T. B. & Tibshirani, R. J. ( 2014 ). Genlasso: Path algorithm for generalized lasso problems. R package version 1.3. https://CRAN.R‐project.org/package=genlasso.
dc.identifier.citedreferenceBai, J. ( 1997 ). Estimating multiple breaks one at a time. Econometric Theory, 13 ( 3 ), 315 – 352.
dc.identifier.citedreferenceBaranowski, R. & Fryzlewicz, P. ( 2015 ). Wbs: wild binary segmentation for multiple change‐point detection. R package version 1.3. https://CRAN.R‐project.org/package=wbs
dc.identifier.citedreferenceCarlstein, E. ( 1986 ). The use of subseries values for estimating the variance of a general statistic from a stationary sequence. The Annals of Statistics, 14 ( 3 ), 1171 – 1179.
dc.identifier.citedreferenceChatterjee, S., & Bose, A. ( 2005 ). Generalized bootstrap for estimating equations. The Annals of Statistics, 33 ( 1 ), 414 – 436.
dc.identifier.citedreferenceChernoff, H., & Zacks, S. ( 1964 ). Estimating the current mean of a normal distribution which is subjected to changes in time. The Annals of Mathematical Statistics, 35 ( 3 ), 999 – 1018.
dc.identifier.citedreferenceChernozhukov, V., Chetverikov, D., & Kato, K. ( 2013 ). Gaussian approximations and multiplier bootstrap for maxima of sums of high‐dimensional random vectors. The Annals of Statistics, 41 ( 6 ), 2786 – 2819.
dc.identifier.citedreferenceChib, S. ( 1998 ). Estimation and comparison of multiple change‐point models, J. Econometrics, 86 ( 2 ), 221 – 241.
dc.identifier.citedreferenceCleynen, A., Rigaill, G. & Koskas, M. ( 2016 ). Segmentor3IsBack: a fast segmentation algorithm. R package version. 2. https://CRAN.R‐project.org/package=Segmentor3IsBack.
dc.identifier.citedreferenceDavison, A. C., & Hinkley, D. V. ( 1997 ). Bootstrap Methods and Their Application. Cambridge, MA: Cambridge University Press.
dc.identifier.citedreferenceDu, C., Kao, C.‐L. M., & Kou, S. ( 2016 ). Stepwise signal extraction via marginal likelihood. Journal of the American Statistical Association, 111 ( 513 ), 314 – 330.
dc.identifier.citedreferenceEfron, B. ( 1982 ). The jackknife, the bootstrap, and other resampling plans. Philadelphia, PA: Siam.
dc.identifier.citedreferenceEfron, B. ( 1992 ). Jackknife‐after‐bootstrap standard errors and influence functions. Journal of the Royal Statistical Society: Series B (Methodological), 54 ( 1 ), 83 – 111.
dc.identifier.citedreferenceEfron, B. ( 2014 ). Estimation and accuracy after model selection. Journal of the American Statistical Association, 109 ( 507 ), 991 – 1007.
dc.identifier.citedreferenceFreedman, D. ( 1984 ). On bootstrapping two‐stage least‐squares estimates in stationary linear models. The Annals of Statistics, 12 ( 3 ), 827 – 842.
dc.identifier.citedreferenceFrick, K., Axel, M., & Hannes, S. ( 2014 ). Multiscale change point inference. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76 ( 3 ), 495 – 580.
dc.identifier.citedreferenceFryzlewicz, P. ( 2014 ). Wild binary segmentation for multiple change‐point detection. The Annals of Statistics, 42 ( 6 ), 2243 – 2281.
dc.identifier.citedreferenceGiordano, R., Stephenson, W., Liu, R., Jordan, M. & Broderick, T. ( 2019 ). A swiss army infinitesimal jackknife, Paper presented at the 22nd International Conference on Artificial Intelligence and Statistics 89, 1139–1147.
dc.identifier.citedreferenceHarchaoui, Z., & Lévy‐Leduc, C. ( 2010 ). Multiple change‐point estimation with a total variation penalty. Journal of the American Statistical Association, 105 ( 492 ), 1480 – 1493.
dc.identifier.citedreferenceHastings, P., Lupski, J. R., Rosenberg, S. M., & Ira, G. ( 2009 ). Mechanisms of change in gene copy number. Nature Reviews Genetics, 10 ( 8 ), 551 – 564.
dc.identifier.citedreferenceHlávka, Z., Hušková, M., Kirch, C., & Meintanis, S. G. ( 2016 ). Bootstrap procedures for online monitoring of changes in autoregressive models. Communications in Statistics‐Simulation and Computation, 45 ( 7 ), 2471 – 2490.
dc.identifier.citedreferenceHorowitz, J. L. ( 2019 ). Bootstrap methods in econometrics. Annual Review of Economics, 11, 193 – 224.
dc.identifier.citedreferenceHušková, M., & Kirch, C. ( 2010 ). A note on studentized confidence intervals for the change‐point. Economic Record, 25 ( 2 ), 269 – 289.
dc.identifier.citedreferenceJaeckel, L. ( 1972 ). The infinitesimal jackknife Memorandum MM72‐1215‐11. Murray Hill: Bell Laboratories.
dc.owningcollnameInterdisciplinary and Peer-Reviewed


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