Nonparametric change-point estimation for data from an ergodic sequence
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 910-917
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In the framework of the series scheme we assume that an observations sequence $\{X_i^n,1\le i\le n\} $ is such that $X_i^n=U_i I(1\le i\le[\theta n])+V_i I([\theta n]+1\le i\le n)$, where $(U_i,V_i)$ is a stationary ergodic sequence the marginal distributions of which are different, and $\theta $ is a change-point in the probabilistic characteristics such that $\theta\in(0;1)$. The main result of this paper is the proof of the fact that the sequence $(\theta n)_{n\ge1} $ of nonparametric estimations constructed here is consistent $(\theta n\to\theta)$.
Keywords:
nonparametric estimation of a change-point in the probabilistic characteristics, consistency of estimations.
@article{TVP_1993_38_4_a15,
author = {E. Carlstein and S. Lele},
title = {Nonparametric change-point estimation for data from an ergodic sequence},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {910--917},
publisher = {mathdoc},
volume = {38},
number = {4},
year = {1993},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a15/}
}
TY - JOUR AU - E. Carlstein AU - S. Lele TI - Nonparametric change-point estimation for data from an ergodic sequence JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1993 SP - 910 EP - 917 VL - 38 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a15/ LA - en ID - TVP_1993_38_4_a15 ER -
E. Carlstein; S. Lele. Nonparametric change-point estimation for data from an ergodic sequence. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 910-917. http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a15/