The location of the maximum and asymmetric two-sided Brownian motion with triangular drift. (English) Zbl 1059.60504
Summary: The argmax distribution in Bhattacharya and Brockwell (1976) is extended to branches with unequal scalings as well as drifts. Examples show how this distribution class in change point problems with unequal variability may provide better approximations for the MLE than the symmetrical limit in Y.-C.Yao [Ann. Stat. 15, 1321–1328 (1987; Zbl 0651.62017)].
Citations:
Zbl 0651.62017References:
| [1] | Bhattacharya, P. K.; Brockwell, P. J., The minimum of an additive process with applications to signal estimation and storage theory, Z. Wahrsch. Verw. Gebiete, 37, 51-75 (1976) · Zbl 0326.60053 |
| [2] | Rudemo, M.; Stryhn, H., Approximating the distribution of maximum likelihood contour estimators in two-region images, Scand. J. Statist., 21, 41-55 (1994) · Zbl 0804.62044 |
| [3] | Stryhn, H., Spatial change point models applied to image segmentation, (Ph.D. Thesis (1994), The Royal Veterinary and Agricultural University: The Royal Veterinary and Agricultural University Copenhagen) |
| [4] | Trifonov, A.; Galun, S.; Derevyagina, E., Detection of the instant of change in the properties of a Gaussian random signal on the basis of observations corrupted by weak noise, (Telksnys, L., Detection of Changes in Random Processes (1986), Optimization Software: Optimization Software New York), 194-206 · Zbl 0608.62103 |
| [5] | Yao, Y.-C., Approximating the distribution of the maximum likelihood estimate of the change-point in a sequence of independent random variables, Ann. Statist., 15, 1321-1328 (1987) · Zbl 0651.62017 |
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