gradual changes in location model; estimators; confidence regions
A number of papers has been published on the estimation problem in location models with abrupt changes (e.g., Cs" org\H o and Horváth (1996)). In the present paper we focus on estimators in location models with gradual changes. Estimators of the parameters are proposed and studied. It appears that the limit behavior (both the rate of consistency and limit distribution) of the estimators of the change point in location models with abrupt changes and gradual changes differ substantially.
Antoch J., Hušková M., Veraverbeke N.: Change-point estimators and bootstrap
. J. Nonparam. Statist. 5 (1995), 123-144. MR 1346891
Chow Y.S., Teicher H.: Probability Theory. Springer Verlag New York (1987).
Csörgö M., Horváth L.: Limit theorems in change point analysis
. Wiley New York (1997). MR 2743035
Feder P.I.: On asymptotic distribution theory in segmented regression problems
. Ann. Statist. 3 (1975), 49-83. MR 0378267
| Zbl 0324.62014
Hinkley D.: Inference in two-phase regression
. J. Amer. Statist. Assoc. 66 (1971), 736-743. Zbl 0226.62068
Jarušková D.: Testing appearance of linear trend. submitted, 1996.
Ratkowski D.A.: Nonlinear Regression Models. Marcel Dekker New York (1983).
Seber G.A.F. and Wild C.J.: Nonlinear Regression
. Wiley New York (1988). MR 0986070
Siegmund D., Zhang H.: Confidence region in broken line regression
. Change-point problems IMS Lecture Notes - Monograph Series 23 (1994), 292-316. MR 1477932