Change-point detection in a shape-restricted regression model

Statistics

Volumn 48, Issue 3, 2014, Pages 641-656

  Nosek, Konrad ^a   Szkutnik, Zbigniew ^a  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

change point; likelihood ratio test; linear regression model with inequality constraints

Indexed keywords

EID: 84898907876     PISSN: 02331888     EISSN: 10294910     Source Type: Journal    
DOI: 10.1080/02331888.2012.760094     Document Type: Article

References (33)

1. J A Żoła̧dź, Z Szkutnik, J Majerczak and K Duda, Detection of change point in oxygen uptake during an incremental exercise test using recursive residuals: relationship to the plasma lactate accumulation and blood acid base balance. Eur. J. Appl. Physiol78 (1998), pp. 369-377
2. M Frisén, E Andersson and K Pettersson, Semiparametric estimation of outbreak regression, Statistics 44 (2010), pp. 107-117 (doi:10.1080/02331880903021484). doi: 10.1080/02331880903021484
3. R L Brown, J Durbin and J M Evans, Techniques for testing the constancy of regression relationships over time (with discussion), J. Roy. Stat. Soc. B 37 (1975), pp. 149-192
4. T Schweder, Some 'optimal' methods to detect structural shift or outliers in regression, J. Amer. Statist. Assoc. 71 (1976), pp. 491-501
5. H- J Kim, B Yu and E J Feuer, Selecting the number of change-points in segmented line regression, Statist. Sinica 19 (2009), pp. 597-609
6. H- J Kim and D Siegmund, The likelihood ratio tests for a change-point in simple linear regression, Biometrika 76 (1989), pp. 409-423 (doi:10.1093/biomet/76.3.409). doi: 10.1093/biomet/76.3.409
7. L Horváth, Detecting changes in linear regressions, Statistics 26 (1995), pp. 189-208 (doi:10.1080/02331889508802489). doi: 10.1080/02331889508802489
8. J Chen and A K Gupta, Parametric statistical change point analysis, Birkhaeuser, Boston (MA), 2000.
9. D V Hinkley, Inference in two-phase regression, J. Amer. Statist. Assoc. 66 (1971), pp. 736-743 (doi:10.1080/01621459.1971.10482337). doi: 10.1080/01621459.1971.10482337
10. S A Julious, Inference and estimation in changepoint regression problem, The Statistician 50 (2001), pp. 51-61
11. H- J Kim and L Cai, Robustness of the likelihood ratio test for a change in simple linear regression, J. Amer. Statist. Assoc. 88 (1993), pp. 864-871 (doi:10.1080/01621459.1993.10476351). doi: 10.1080/01621459.1993.10476351
12. W Ploberger and W Krämer, The CUSUM test with OLS residuals, Econometrica 60 (1992), pp. 271-285 (doi:10.2307/2951597). doi: 10.2307/2951597
13. Y Wu, Inference for change-point and post-change means after a CUSUM test, Springer, New York, 2005.
14. L Horváth, Z Horváth and M Hušková, Ratio tests for change point detection. IMS Collect1 (2008), pp. 293-304
15. Y Ninomiya, Information criterion for Gaussian change-point model, Statist. Probab. Lett. 72 (2005), pp. 237-247 (doi:10.1016/j.spl.2004.10.037). doi: 10.1016/j.spl.2004.10.037
16. K Nosek, Schwarz information criterion based tests for a change-point in regression models, Statist. Papers 51 (2010), pp. 915-929 (doi:10.1007/s00362-008-0186-4). doi: 10.1007/s00362-008-0186-4
17. G Shen and J K Ghosh, Developing a new BIC for detecting change-points, J. Statist. Plann. Inference 141 (2011), pp. 1436-1447 (doi:10.1016/j.jspi.2010.10.017). doi: 10.1016/j.jspi.2010.10.017
18. M Hušková and C Kirch, A note on studentized confidence intervals for the change-point, Comput. Statist. 25 (2010), pp. 269-289 (doi:10.1007/s00180-009-0175-7). doi: 10.1007/s00180-009-0175-7
19. B E Brodsky and B S Darkhovsky, Nonparametric methods in change-point problems, Kluwer Academic Publishers, Dordrecht, 1993.
20. K Nosek and Z Szkutnik, A power study of k-linear-r-ahead recursive residuals test for change-point in finite sequences, J. Stat. Comput. Simul. 78 (2008), pp. 1201-1213 (doi:10.1080/00949650701588473). doi: 10.1080/00949650701588473
21. H Mukerjee and R Tu, Order-restricted inferences in linear regression, J. Amer. Statist. Assoc. 90 (1995), pp. 717-728 (doi:10.1080/01621459.1995.10476565). doi: 10.1080/01621459.1995.10476565
22. T Robertson, F T Wright and R L Dykstra, snaOrder restricted statistical inference, Wiley, New York, 1988.
23. G H Hillier, Joint tests for zero restrictions on nonnegative regression coefficients, Biometrika 73 (1986), pp. 657-669 (doi:10.1093/biomet/73.3.657). doi: 10.1093/biomet/73.3.657
24. C Gourieroux, A Holly and A Monfort, Likelihood ratio test, Wald test, and Kuhn-Tucker test in linear models with inequality constraints on the regression parameters, Econometrica 50 (1982), pp. 63-80 (doi:10.2307/1912529). doi: 10.2307/1912529
25. M J Silvapulle and P K Sen, Constrained statistical inferenceWiley, New York, 2005.
26. M C Meyer, A test for linear versus convex regression function using shape-restricted regression, Biometrika 90 (2003), pp. 223-232 (doi:10.1093/biomet/90.1.223). doi: 10.1093/biomet/90.1.223
27. M D Perlman, One-side testing problem in multivariate analysis, Ann. Math. Statist. 40 (1969), pp. 549-567 (doi:10.1214/aoms/1177697723). doi: 10.1214/aoms/1177697723
28. P E Gill, W Murray and M H Wright, Practical optimization, Academic Press, New York, 1981.
29. D.AS Fraser and H Massam, A mixed primal-dual bases algorithm for regression under inequality constraints. Application to convex regression, Scand. J. Statist. 16 (1989), pp. 65-74
30. R F Raubertas, CI C Lee and E V Nordheim, Hypothesis tests for normal means constrained by linear inequalities. Comm. Statist, Theory Methods 15 (1986), pp. 2809-2833(doi:10.1080/03610928608829280). doi: 10.1080/03610928608829280
31. W H Press, B P Flannery, S A Teukolsky and W T Vetterling, Numerical recipes in C: the art of scientific computing, Cambridge University Press, Cambridge, 1988.
32. H Akaike, Information theory and an extension of the maximum likelihood principle In: Petrov B N, Csaki F, editors. Second international symposium on information theory. Budapest: Akademiai Kiado; 1973; p. 267-281.
33. R M Kuiper, H Hoijtink and M J Silvapulle, An Akaike-type information criterion for model selection under inequality constraints, Biometrika 98 (2011), pp. 495-501 (doi:10.1093/biomet/asr002). doi: 10.1093/biomet/asr002