Nonparametric adaptive change point estimation and on line detection

References

• Baron , M and Rukhin , A. L . 1997 . Asymptotic behavior of confidence regions in the change point problem . J. Statist. Planning Inference , 58 : 263 – 282 .
   Google Scholar
• Basseville , M and Nikiforov , I. V . 1993 . Detection of Abrupt Changes: Theory and Application . PTR Prentice Hall, Inc ,
   Google Scholar
• Bhattacharya , P. K and Zhou , H . 1996 . A generalized cusum procedure for sequential detection of change point in a parametric family when the initial parameter is unknown . Sequential Anal , 15 : 311 – 325 .
   Google Scholar
• Brown , L. D . 1986 . Fundamentals of Statistical Exponential Families with Applications in Statistical Decision Theory . Institute of Mathematical Stastics, Lecture Notes Monograph Series , 9
   Google Scholar
• Carlstein , E . 1988 . Nonparametric estimation of a change point . Ann. Statist , 16 : 188 – 197 .
   Web of Science ®Google Scholar
• Cobb , G. W . 1978 . The problem of the Nile: conditional solution to a change point problem . Biometrika , 62 : 243 – 251 .
   Web of Science ®Google Scholar
• Combay , E . 1995 . Nonparametric truncated sequential change point detection . Statistics & Decisions , 13 : 71 – 82 .
   Google Scholar
• Devroye , L and Györfi , L . 1985 . Nonparametric density estimation . The L₁ view ,
   Google Scholar
• Duembgen , L . 1991 . The asymptotic behavior of some nonparametric change point estimators . Ann. Statist , 19 : 1471 – 1495 .
   Google Scholar
• Ferger , D . 1991 . Nonparametric change point detection based on U stastics . PhD thesis, University of Giessen ,
   Google Scholar
• Ghosh , M , Mukhopadhyay , N and Sen , P. K . 1997 . Sequential Estimation .
   Google Scholar
• Gordon , L and Pollak , M . 1994 . An efficient sequential nonparametric scheme for detecting a change of distribution . Ann. Statist , 22 : 763 – 804 .
   Web of Science ®Google Scholar
• Gordon , L and Pollak , M . 1997 . Average run length to false alarm for surveilance schemes designed with partially specified pre change distribution . Ann. Statist , 25 : 1284 – 1310 .
   Web of Science ®Google Scholar
• Hinkley , D. V . 1970 . Inference about the change point in a sequence of random variables . Biometrika , 57 : 1 – 17 .
   Web of Science ®Google Scholar
• Hu , I and Rukhin , A. L . 1995 . A lower bound for error probability in change point estimation . Statistica Sinica , 5 : 319 – 331 .
   Web of Science ®Google Scholar
• Incl´n , C and Tiao , G. C . 1994 . Use of sums of squares for retrospective detection of changes in variances . J. Amer. Stat. Assoc , 89 : 913 – 923 .
   Web of Science ®Google Scholar
• Jouzel , J , Lorius , C , Petit , J. R , Genton , C , Barkov , N. I , Koatlyakov , M and Petrov , M . 1987 . Vostok ice core: a continuous isotope temperature record over the last climatic cycle . Nature , 329 : 403 – 408 . 160,000 years
   Web of Science ®Google Scholar
• Lai , T. L . 1995 . Sequential changepoint detection in quality control and dynamical systems . J. R. Statist. Soc. B , 57 : 613 – 658 .
   Google Scholar
• Manley , G . 1974 . Central England Temperatures: monthly means 1659 to 1973 . Q.J.R. Meteorol. Soc , 100 : 389 – 405 .
   Web of Science ®Google Scholar
• Moustakides , G. V . 1986 . Optimal stopping times for detecting a change in distribution . Ann. Statist , 14 : 1379 – 1388 .
   Web of Science ®Google Scholar
• Page , E. S . 1954 . Continuous inspection schemes . Biometrika , 41 : 100 – 115 .
   Web of Science ®Google Scholar
• Parker , D. E , Legg , T. P and Folland , C. K . 1992 . A new daily central england temperature series, 1772-1991 . Int. J. Clim , 12 : 317 – 342 .
   Web of Science ®Google Scholar
• Ritov , Y . 1990 . Decision theoretic optimality of CUSUM procedure . Ann. Statist , 18 : 1464 – 1469 .
   Web of Science ®Google Scholar
• Siegmund , D . 1988 . Confidence sets in change point problems . International Statistical Review , 56 : 31 – 48 .
   Web of Science ®Google Scholar
• Yakir , B . 1996 . Dynamic sampling policy for detecting a change in distribution, with a probability bound on false alarm . Ann. Statist , 5 : 2199 – 2214 .
   Google Scholar