On an accuracy of change points. (English) Zbl 1014.62022

Formulas are derived for estimators of change points, and for characterization of the accuracy in their determination. The problem is solved by linearized simplification of the model of measurements with constraints of type II. The linearization region of the model is also derived. A numerical example illustrates the paper.


62F10 Point estimation
62J05 Linear regression; mixed models
65C60 Computational problems in statistics (MSC2010)
Full Text: EuDML


[1] ANTOCH J.-HUŠKOVÁ M.-JARUŠKOVÁ D.: Change point problem after ten years. ROBUST’98, JČMF, 1998, pp. 1-42.
[2] BATES D. M.-WATTS D. G.: Relative curvatures measures of nonlinearity. J. Roy. Statist. Soc. Ser. B 42 (1980), 1-25. · Zbl 0455.62028
[3] GEN L.-DEVYATOVA T.-IVANOV V.: Some analytical aspects of the use of the isobestic point. J. Anal. Chem. (USSR) 38 (1983), 147-157.
[4] KUBÁČEK L.-KUBÁČKOVÁ L.: Statistics and Metrology. Univerzita Palackého, Olomouc, 2000.
[5] PATNAIK P. B.: The noncentral \(\chi^2\) and \(F\)-distributions and their applications. Biometrika 36 (1949), 202-232. · Zbl 0033.29204
[6] RAO, C R.: Linear Statistical Inference and Its Applications. John Wiley &: Sons, New York - London - Sydney, 1965. · Zbl 0137.36203
[7] SCHEFFÉ H.: The Analysis of Variance. J. Wiley, New York, 1959. · Zbl 0086.34603
[8] WELCH B. L.: The generalization of Students problem when several different population variances are involved. Biometrika 34 (1947), 28-35. · Zbl 0029.40802
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.