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Keywords:
gradual type of change; polynomial regression; estimator; limit distribution
gradual type of change; polynomial regression; estimator; limit distribution
Summary:
Recently Hu\v{s}ková (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.
References:
[1] Anderson T.W.: The Statistical Analysis of Time Series. John Wiley New York (1971). MR 0283939 | Zbl 0225.62108
[2] Billingsley P.: Convergence of Probability Measures. John Wiley New York (1968). MR 0233396 | Zbl 0172.21201
[3] Davies R.B.: Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74 33-43 (1987). MR 0885917 | Zbl 0612.62023
[4] Hinkley D.: Inference about the intersection in two-phase regression. Biometrika 56 495-504 (1969). Zbl 0183.48505
[5] Hušková M.: Estimation in location model with gradual changes. Comment. Math. Univ. Carolinae 39 (1998), 147-157. MR 1623002
[6] Knowles M., Siegmund D., Zhang H.: Confidence regions in semilinear regression. Biometrika 78 15-31 (1991). MR 1118227 | Zbl 0728.62063
[7] Petrov V.V.: Predel'nyje teoremy dlja sum nezavisimych slucajnych velicin. Nauka Moskva (1987). MR 0896036
[8] Siegmund D., Zhang H.: Confidence region in broken line regression. Change-point problems IMS Lecture Notes - Monograph Series 23 292-316. MR 1477932
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