Asymptotics of M-estimators in two-phase linear regression models

Stochastic Processes and their Applications

Volumn 103, Issue 1, 2003, Pages 123-154

  Koul, Hira L ^a   Qian, Lianfen ^b   Surgailis, Donatas ^c  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b FLORIDA ATLANTIC UNIVERSITY   (United States)

^c VILNIUS UNIVERSITY   (Lithuania)

Author keywords

Change point estimator; Compound Poisson process; Fixed jump size

Indexed keywords

EID: 0037211063     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(02)00185-0     Document Type: Article

References (33)

1. Anderson, R.L., Nelson, L.A., 1975. A family of models involving intersecting straight lines and concomitant experimental designs useful in evaluating response to fertilizer nutrients. Biometrics 31, 303-318.
2. Bai, J., Perron, P., 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66, 47-78.
3. Barrodale, I., Roberts, F.D.K., 1973. An improved algorithm for discrete L1 linear approximations. SIAM J. Numer. Anal. 10, 839-848.
4. Bhattacharya, P.K., 1990. Weak convergence ofthe log-likelihood process in the two-phase linear regression problem. In: Bahadur, R.R. (Ed.), Probability, Statistics and Design of Experiments. Wiley Eastern, New Delhi, pp. 145-156.
5. Bhattacharya, P.K., 1994. Some aspects of change-point analysis. IMS Lecture Notes-Monograph Series, Vol. 23. Hayward, CA, pp. 28-56.
6. Billingsley, P., 1968. Convergence of Probability Measures. Wiley, New York.
7. Conte, S.D., Dunsmore, H.E., Shen, V.Y., 1986. Software Engineering Metrics and Models. Benjamin Cummings, Menlo Park, CA.
8. Csörgo, M., Horváth, L., 1997. Limit Theorems in Change-Point Analysis. Wiley, New York.
9. Eubank, R.L., 1984. Approximate regression models and splines. Comm. Statist.-Theory Methods Ser. A 13, 433-484.
10. Feder, P.I., 1975a. On asymptotic distribution theory in segmented regression problems-identified case. Ann. Statist. 3, 49-83.
11. Feder, P.I., 1975b. The log likelihood ratio in segmented regression. Ann. Statist. 3, 84-97.
12. Gikhman, I.I., Skorokhod, A.V., 1975. Theory of Stochastic Processes, Vol. 2. W.B. Saunders Company, Philadelphia.
13. Heiler, S., Willers, R., 1988. Asymptotic normality of R-estimates in the linear model. Statistics 19, 173-184.
14. Henderson, H.V., Velleman, P.F., 1981. Building multiple regression models interactively. Biometrics 37, 391-411.
15. Hinkley, D.V., 1969. Inference about the intersection in two-phase regression. Biometrika 56, 495-504.
16. Hinkley, D.V., 1971. Inference in two-phase regression. J. Amer. Statist. Assoc. 66, 736-743.
17. Hogg, R.V., Ledolter, J., 1992. Applied Statistics for Engineers and Physical Scientists, 2nd ed. Macmillan Publishing Company, New York.
18. Huber, P.J., 1967. The behavior of maximum likelihood estimates under nonstandard conditions. Proceedings of the Fifth Berkeley Symposium on Mathematics Statistic & Probability, Vol. 1. University California Press, Berkeley, pp. 221-234.
19. Hudson, D.J., 1966. Fitting segmented curves whose join points have to be estimated. J. Amer. Statist. Assoc. 61, 1097-1129.
20. Ibragimov, I.A., Has'minskii, R.Z., 1981. Statistical Estimation: Asymptotic Theory. Springer, New York.
21. Koul, H.L., 2002. Weighted empirical processes in nonlinear dynamic models. In: Lecture Notes in Statistics, Vol. 166. Springer, New York.
22. Koul, H.L., Qian, L., 2002. Asymptotics of maximum likelihood estimator in a two-phase linear regression model. Technical Report, RM-582, J. Statist. Plann. Inference 108, 99-119.
23. Loader, C.R., 1996. Change-point estimation using nonparametric regression. Ann. Statist. 24, 1667-1678.
24. Müller, H.G., 1992. Change-point in nonparametric regression analysis. Ann. Statist. 20, 737-761.
25. Müller, H.G., Song, K.S., 1997. Two-stage change-point estimators in smooth regression models. Statist. Probab. Lett. 34, 323-335.
26. Müller, H.G., Stadtmüller, U., 1999. Discontinuous versus smooth regression. Ann. Statist. 27, 299-337.
27. Quandt, R.E., 1958. The estimation of the parameters of a linear regression system obeying two separate regimes. J. Amer. Statist. Assoc. 53, 873-880.
28. Rukhin, A.L., Vajda, I., 1997. Change-point estimation as a nonlinear regression problem. Statistics 30, 181-200.
29. Schulze, U., 1987. Multiphase regression: stability testing, estimation, hypothesis testing. Akademie Berlin, ISBN 3-05-500224-5.
30. Sprent, P., 1961. Some hypotheses concerning two-phase regression lines. Biometrics 17, 634-645.
31. van de Geer, S., 1988. Regression analysis and empirical processes. CWI Tract. 45.
32. Whitt, W., 1980. Some useful functions for functional limit theorems. Math. Oper. Res. 5, 67-85.
33. Wu, J.S., Chu, C.K., 1993. Kernel-type estimators of jump points and values of a regression function. Ann. Statist. 21 (3), 1545-1566.