Geodesic
The sequential chi-square test based on $s$-tuples of states of a Markov chain
Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 127-136 
B. I. Selivanov; V. P. Chistyakov. The sequential chi-square test based on $s$-tuples of states of a Markov chain. Diskretnaya Matematika, Tome 9 (1997) no. 4, pp. 127-136. http://geodesic.mathdoc.fr/item/DM_1997_9_4_a11/
@article{DM_1997_9_4_a11,
     author = {B. I. Selivanov and V. P. Chistyakov},
     title = {The sequential chi-square test based on $s$-tuples of states of a {Markov} chain},
     journal = {Diskretnaya Matematika},
     pages = {127--136},
     year = {1997},
     volume = {9},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_1997_9_4_a11/}
}
TY  - JOUR
AU  - B. I. Selivanov
AU  - V. P. Chistyakov
TI  - The sequential chi-square test based on $s$-tuples of states of a Markov chain
JO  - Diskretnaya Matematika
PY  - 1997
SP  - 127
EP  - 136
VL  - 9
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/DM_1997_9_4_a11/
LA  - ru
ID  - DM_1997_9_4_a11
ER  - 
%0 Journal Article
%A B. I. Selivanov
%A V. P. Chistyakov
%T The sequential chi-square test based on $s$-tuples of states of a Markov chain
%J Diskretnaya Matematika
%D 1997
%P 127-136
%V 9
%N 4
%U http://geodesic.mathdoc.fr/item/DM_1997_9_4_a11/
%G ru
%F DM_1997_9_4_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

A multidimensional statistic whose components are one-dimensional chi-square statistics based on frequencies of outcomes of a sequence of multinomial trials was considered previously and the density of the limit distribution of this statistic was found. We extend this result to statistics based on $s$-tuples of states of a finite homogeneous Markov chain. The research was supported by the Russian Foundation for Basic Research, grant 96-01-00531.