Estimation of multiple-regime regressions with least absolutes deviation

Journal of Statistical Planning and Inference

Volumn 74, Issue 1, 1998, Pages 103-134

  Bai, Jushan ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Asymptotic distribution; Least absolute deviation; Multiple change points; Multiple regime regressions; Primary 62F12; Secondary 60J05, 62F35

Indexed keywords

EID: 0013019044     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0378-3758(98)00082-2     Document Type: Article

References (29)

1. Babu G.J. Strong representations for LAD estimators in linear models. Probab. Theory Related Fields. 83:1989;547-558.
2. Bai J. Least squares estimation of a shift in linear processes. J. Time Ser. Anal. 15:1994;453-472.
3. Bai J. Least absolute deviation estimation of a shift. Econometric Theory. 11:1995;403-436.
4. Bai, J., Perron, P., 1998. Estimating and testing linear models with multiple structural changes. Econometrica 66, 47-78.
5. 1 norm. Comm. ACM 17, 319-320.
6. Bassett G., Koenker K. Asymptotic theory of least absolute error regression. J. Amer. Statist. Assoc. 73:1978;618-622.
7. Bhattacharya P.K. Maximum likelihood estimation of a change-point in the distribution of independent random variables, General multiparameter case. J. Multi. Anal. 23:1987;183-208.
8. Brodsky B.E., Darkhovsky B.S. Nonparametric Methods in Change Point Problems. 1993;Kluwer, Dordrecht.
9. Dueker M.J. The response of market interest rates to discount rate changes. Federal Reserve Bank of St. Louis Review. 74(4):1992;78-91.
10. Dümbgen L. The asymptotic behavior of some nonparametric change point estimators. Ann. Statist. 19:1991;1471-1495.
11. Gombay E., Horváth L. Limit theorems for change in linear regression. J. Multivariate Anal. 48:1994;43-69.
12. Guthery S.B. Partition regression. J. Ameri. Stat. Assoc. 69:1974;945-947.
13. Horváth L. Detecting changes in linear regressions. Statistics. 26:1995;189-208.
14. Horváth L., Hušková M., Serbinowska M. Estimators for the time of change in linear models. Statistics. 29:1997;109-130.
15. Huang W.-T., Chang Y.-P. Nonparametric estimation in change-point models. J. Statist. Plann. Inference. 35:1993;335-347.
16. Hušková, M., 1996a. Tests and estimators for change point based on M-statistics. Statist. Decisions 14, 115-136.
17. Hušková, M., 1996b. Estimation of a change in linear models. Statist. Probab. Lett. 26, 13-24.
18. Kim H.J., Siegmund D. The likelihood ratio test for a change point in simple linear regression. Biometrika. 76:1989;409-423.
19. Krishnaiah P.R., Miao, B.Q., 1988. Review about estimation of change points. In: Krishnaiah, P.R., Rao, C.R. (Eds.), Handbook of Statistics, vol. 7. Elsevier, New York, pp. 375-402.
20. Picard D. Testing and estimating change-points in time series. Adv. Appl. Probab. 17:1985;841-867.
21. Pollard, D., 1990. Empirical Processes: Theory and Applications. CBMS Conference Series in Probability and Statistics, vol. 2. Institute of Mathematical Statistics.
22. Pollard D. Asymptotics for least absolute deviation regression estimators. Econometric Theory. 7:1991;186-199.
23. Quandt R.E. The estimation of parameters of a linear regression system obeying two separate regimes. J. Amer. Statist. Assoc. 53:1958;873-880.
24. Roley, V., Wheatley, S.M., 1990. Temporal variation in the interest rate response to money announcements. NBER No. 3471.
25. Shaban S.A. Change point problem and two-phase regression. an annotated bibliography Internat. Statist. Rev. 48:1980;83-93.
26. Yao Y.-C. Estimating the number of change-points via Schwarz' criterion. Statist. Prob. Lett. 6:1988;181-189.
27. Yao, Y.-C., Au, S.T., 1989. Least squares estimation of a step function. Sankhy ā 51 Ser. A 370-381.
28. Yin Y.Q. Detection of the number, locations, and magnitudes of jumps. Comm. Stat. Stoch. Models. 4:1988;445-455.
29. Zacks, S., 1983. Survey of classical and Bayesian approaches to the change-point problem, fixed sample and sequential procedures of testing and estimation. In: Rivzi, M.H., Rustagi, J.S., Siegmund, D. (Eds.), Recent Advances in Statistics. Academic Press, New York, pp. 245-269.