The paper deals with the asymptotic distribution of the least squares estimator of a change point in a regression model where the regression function has two phases --- the first linear and the second quadratic. In the case when the linear coefficient after change is non-zero the limit distribution of the change point estimator is normal whereas it is non-normal if the linear coefficient is zero.
@article{119289,
author = {Daniela Jaru\v skov\'a},
title = {Change-point estimator in continuous quadratic regression},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {42},
year = {2001},
pages = {741-752},
zbl = {1091.62506},
mrnumber = {1883382},
language = {en},
url = {http://dml.mathdoc.fr/item/119289}
}
Jarušková, Daniela. Change-point estimator in continuous quadratic regression. Commentationes Mathematicae Universitatis Carolinae, Tome 42 (2001) pp. 741-752. http://gdmltest.u-ga.fr/item/119289/
Weak convergence of the log-likelihood process in two-phase linear regression problem, Proceedings of the R.C. Bose Symposium on Probability, Statistics and Design of Experiments 145-156 (1990). (1990)
On asymptotic distribution theory in segmented regression problems - identified case, The Annals of Statistics 3 49-83 (1975). (1975) | MR 0378267 | Zbl 0324.62014
Inference about the intersection in two-phase regression, Biometrika 56 495-504 (1969). (1969) | Zbl 0183.48505
Estimation in location model with gradual changes, Comment. Math. Univ. Carolinae 39 147-157 (1998). (1998) | MR 1623002
Gradual changes versus abrupt changes, Journal of Statistical Planning and Inference 76 109-125 (1999). (1999) | MR 1673343
Change-point estimator in gradually changing sequences, Comment. Math. Univ. Carolinae 39 551-561 (1998). (1998) | MR 1666790
Nonlinear Regression, John Wiley New York (1989). (1989) | MR 0986070 | Zbl 0721.62062