On detecting jumps in time series: nonparametric setting

References

• Bahadur , RR . (1966) . A note on quantiles in large samples . Annals of Mathematical Statistics , 37 : 577 – 580 .
   Google Scholar
• Brodsky BE Darkhovsky BS (1993) Nonparametric Methods in Change-Point Problems Mathematics and its applications, 243 Kluwer Academic Publishers Dordrecht
   Google Scholar
• Brodsky BE Darkhovsky BS (2000) Non-Parametric Statistical Diagnosis Problems and Methods Mathematics and its applications, 509 Kluwer Academic Publishers Dordrecht
   Google Scholar
• Chiu , CK , Godtliebsen , F and Marron , JS . (1998) . Edge-preserving smoothers for image processing . Journal of the American Statistical Association , 93 : 526 – 556 .
   Web of Science ®Google Scholar
• Girshick , MA and Rubin , H . (1952) . A Bayes approach to a quality control model . Annals of Mathematical Statistics , 23 ( 1 ) : 114 – 125 .
   Google Scholar
• Hesse , CH . (1990) . A Bahadur-type representation for empirical quantiles of a large class of stationary, possibly infinite-variance, linear processes . Annals of Statistics , 18 : 1188 – 1202 .
   Web of Science ®Google Scholar
• Kiefer , J . (1967) . On Bahadur's representation of sample quantiles . Annals of Mathematical Statistics , 38 : 1323 – 1342 .
   Google Scholar
• Kryzak , A , Rafajłowicz , E and Skubalska-RafajRafajłowicz , E . (2001) . Clipped median and space-filling curves in image filtering . Nonlinear Analysis , 47 : 303 – 314 .
   Google Scholar
• Lee , JS . (1983) . Digital image smoothing and the sigma filter . Computer Vision, Graphics, and Image Processing , 24 : 255 – 269 .
   Google Scholar
• Moustakides , GV . (1986) . Optimal stopping times for detecting changes in distributions . Annals of Statistics , 14 : 1379 – 1387 .
   Web of Science ®Google Scholar
• Page , ES . (1954) . Continuous inspection schemes . Biometrika , 1 : 100 – 115 .
   Web of Science ®Google Scholar
• Page , ES . (1955) . A test for a change in a parameter occurring at an unknown point . Biometrika , 42 : 523 – 526 .
   Web of Science ®Google Scholar
• Pawlak , M and Rafajłowicz , E . (2000) . Vertically weighted regression–a tool for nonlinear data analysis and constructing control charts . Journal of the German Statistical Association , 84 : 367 – 388 .
   Google Scholar
• Pawlak , M and Rafajłowicz , E . (2001a) . Jump preserving signal reconstruction using vertical weighting . Nonlinear Analysis , 47 : 327 – 338 .
   Google Scholar
• Pawlak M Rafajłowicz E (2001b) On a nonlinear method of function recovering: The vertical regression approach Presented at Workshop on Nonlinear Estimation & Classification, University of California Berkeley
   Google Scholar
• Pollak , M . (1985) . Optimal detection of a change in distribution . Annals of Statistics , 13 : 206 – 227 .
   Web of Science ®Google Scholar
• Rafajłowicz E (1996) Model free control charts for continuous time production processes Polytechnika Wroclaw, Technical Report No. 56/96
   Google Scholar
• Ritov , Y . (1990) . Decision theoretic optimality of the CUSUM procedure . Annals of Statistics , 18 : 1464 – 1469 .
   Web of Science ®Google Scholar
• Roberts , SW . (1959) . Control chart tests based on geometric moving averages . Technometrics , 1 : 239 – 250 .
   Google Scholar
• Rue , H , Chu , CK , Godtliebsen , F and Marron , JS . (2002) . M-smoother with local linear fit . Journal of Nonparametric Statistics , 14 : 155 – 168 .
   Web of Science ®Google Scholar
• Schmid , W and Schöne , A . (1997) . Some properties of the EWMA control chart in the presence of autocorrelation . Annals of Statistics , 25 ( 3 ) : 1277 – 1283 .
   Google Scholar
• Schmid , W and Steland , A . (2000) . Sequential control of non-stationary processes by nonparametric kernel control charts . AStA , 84 ( 3 ) : 315 – 336 .
   Google Scholar
• Serfling RJ (1980) Approximation Theorems in Mathematical Statistics, Wiley New York
   Google Scholar
• Shiryaev AN (1963) On optimal methods in the quickiest detection problems Teor. Veroyatn., Primen. 8 26 51 (Russian)
   Google Scholar
• Steland , A . (2002a) . Nonparametric monitoring of financial time series by jump-preserving estimators . Statistical Papers , 43 : 361 – 377 .
   Google Scholar
• Steland A (2002b) Sequential credit risk: Can we benefit from sequential nonparametric control? Selected Papers Operation Research Proceedings 2002 pp. 337–344
   Google Scholar
• Steland A (2003a) Optimal sequential kernel smoothers for dependent processes Journal of Statistical Planning and Inference (to appear)
   Google Scholar
• Steland A (2003b) Sequential control of time series by functionals of kernel-weighted empirical processes under local alternatives Metrika (to appear)
   Google Scholar
• Steland A (2003c) NP-optimal kernels for nonparametric sequential detection rules Economic Quality Control (to appear)
   Google Scholar
• Vasipoulos , AV and Stamboulis , AP . (1978) . Modification of control chart limits in the presence of data correlation . Journal of Quality Control , 10 : 20 – 30 .
   Google Scholar
• Yakir , B . (1996) . A lower bound on the ARL to detection with a probability constraint on false alarm . Annals of Statistics , 24 : 431 – 435 .
   Google Scholar
• Yakir , B . (1997) . A note on optimal detection of a change in distribution . Annal of Statistics , 25 : 2117 – 2126 .
   Web of Science ®Google Scholar