Change-point estimator in gradually changing sequences

Daniela Jarušková

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 3, page 551-561
  • ISSN: 0010-2628

Abstract

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Recently Hušková (1998) has studied the least squares estimator of a change-point in gradually changing sequence supposing that the sequence increases (or decreases) linearly after the change-point. The present paper shows that the limit behavior of the change-point estimator for more complicated gradual changes is similar. The limit variance of the estimator can be easily calculated from the covariance function of a limit process.

How to cite

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Jarušková, Daniela. "Change-point estimator in gradually changing sequences." Commentationes Mathematicae Universitatis Carolinae 39.3 (1998): 551-561. <http://eudml.org/doc/248232>.

@article{Jarušková1998,
abstract = {Recently Hušková (1998) has studied the least squares estimator of a change-point in gradually changing sequence supposing that the sequence increases (or decreases) linearly after the change-point. The present paper shows that the limit behavior of the change-point estimator for more complicated gradual changes is similar. The limit variance of the estimator can be easily calculated from the covariance function of a limit process.},
author = {Jarušková, Daniela},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {gradual type of change; polynomial regression; estimator; limit distribution; change-point problem; gradual change; polynomial regression},
language = {eng},
number = {3},
pages = {551-561},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Change-point estimator in gradually changing sequences},
url = {http://eudml.org/doc/248232},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Jarušková, Daniela
TI - Change-point estimator in gradually changing sequences
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 3
SP - 551
EP - 561
AB - Recently Hušková (1998) has studied the least squares estimator of a change-point in gradually changing sequence supposing that the sequence increases (or decreases) linearly after the change-point. The present paper shows that the limit behavior of the change-point estimator for more complicated gradual changes is similar. The limit variance of the estimator can be easily calculated from the covariance function of a limit process.
LA - eng
KW - gradual type of change; polynomial regression; estimator; limit distribution; change-point problem; gradual change; polynomial regression
UR - http://eudml.org/doc/248232
ER -

References

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  1. Anderson T.W., The Statistical Analysis of Time Series, John Wiley New York (1971). (1971) Zbl0225.62108MR0283939
  2. Billingsley P., Convergence of Probability Measures, John Wiley New York (1968). (1968) Zbl0172.21201MR0233396
  3. Davies R.B., Hypothesis testing when a nuisance parameter is present only under the alternative, Biometrika 74 33-43 (1987). (1987) Zbl0612.62023MR0885917
  4. Hinkley D., Inference about the intersection in two-phase regression, Biometrika 56 495-504 (1969). (1969) Zbl0183.48505
  5. Hušková M., Estimation in location model with gradual changes, Comment. Math. Univ. Carolinae 39 (1998), 147-157. (1998) MR1623002
  6. Knowles M., Siegmund D., Zhang H., Confidence regions in semilinear regression, Biometrika 78 15-31 (1991). (1991) Zbl0728.62063MR1118227
  7. Petrov V.V., Predel'nyje teoremy dlja sum nezavisimych slucajnych velicin, Nauka Moskva (1987). (1987) MR0896036
  8. Siegmund D., Zhang H., Confidence region in broken line regression, Change-point problems IMS Lecture Notes - Monograph Series 23 292-316. (1994) MR1477932

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