Geodesic
A Markov chain of order~$s$ with~$r$ partial connections and statistical inference on its parameters
Diskretnaya Matematika, Tome 19 (2007) no. 2, pp. 109-130.

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

We consider a homogeneous Markov chain of order $s$ with $r$ partial connections for which the transition probabilities from any state to the next depend not on all $s$ preceding states but on $r$ selected states only. We construct statistical estimators of parameters and statistical tests for values of these parameters of the model and investigate their asymptotic properties. Algorithms to calculate these estimators are suggested. The results of computer simulations are also given. 
@article{DM_2007_19_2_a12,
     author = {Yu. S. Kharin and A. I. Petlitskii},
     title = {A {Markov} chain of order~$s$ with~$r$ partial connections and statistical inference on its parameters},
     journal = {Diskretnaya Matematika},
     pages = {109--130},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2007_19_2_a12/}
}
TY  - JOUR
AU  - Yu. S. Kharin
AU  - A. I. Petlitskii
TI  - A Markov chain of order~$s$ with~$r$ partial connections and statistical inference on its parameters
JO  - Diskretnaya Matematika
PY  - 2007
SP  - 109
EP  - 130
VL  - 19
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2007_19_2_a12/
LA  - ru
ID  - DM_2007_19_2_a12
ER  - 
%0 Journal Article
%A Yu. S. Kharin
%A A. I. Petlitskii
%T A Markov chain of order~$s$ with~$r$ partial connections and statistical inference on its parameters
%J Diskretnaya Matematika
%D 2007
%P 109-130
%V 19
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2007_19_2_a12/
%G ru
%F DM_2007_19_2_a12
Yu. S. Kharin; A. I. Petlitskii. A Markov chain of order~$s$ with~$r$ partial connections and statistical inference on its parameters. Diskretnaya Matematika, Tome 19 (2007) no. 2, pp. 109-130. http://geodesic.mathdoc.fr/item/DM_2007_19_2_a12/

[1] Fan J., Yao Q., Nonlinear time series, Springer, Berlin, 2003 | MR

[2] Collett D., Modelling binary data, Chapman Hall, Boca Raton, 2003 | MR | Zbl

[3] Yaffee R. A., McGee M., Time series analysis and forecasting, Academic Press, San Diego, 2000

[4] Waterman M. S, Mathematical methods for DNA sequences, CRC Press, Boca Raton, 1989 | MR | Zbl

[5] Kharin Yu. S., Bernik V. I., Matveev G. V., Agievich S. V., Matematicheskie i kompyuternye osnovy kriptologii, Novoe znanie, Minsk, 2003

[6] Zubkov A. M., “Datchiki psevdosluchainykh chisel i ikh primeneniya”, Trudy II Mezhdunarodnoi nauchnoi konferentsii “Matematika bezopasnosti informatsionnykh tekhnologii”, MGU, Moskva, 2003, 200–206 | MR

[7] Dub D., Veroyatnostnye protsessy, IL, Moskva, 1965

[8] Raftery A. E., “A model for high-order Markov chains”, J. Royal Statist. Soc., 47:3 (1985), 528–539 | MR | Zbl

[9] Kharin Yu. S., “Tsepi Markova s $r$-chastichnymi svyazyami i ikh statisticheskoe otsenivanie”, Dokl. NAN Belarusi, 48:1 (2004), 40–44 | MR

[10] Tikhomirova M. I., Chistyakov V. P., “O dvukh statistikakh tipa khi-kvadrat, postroennykh po chastotam tsepochek sostoyanii slozhnoi tsepi Markova”, Diskretnaya matematika, 15:2 (2003), 149–159 | MR | Zbl

[11] Maksimov Yu. I., “O tsepyakh Markova, svyazannykh s dvoichnymi registrami sdviga so sluchainymi elementami”, Trudy po diskretnoi matematike, 1 (1997), 203–220 | MR | Zbl

[12] Lidl R., Niderraiter G., Konechnye polya, Mir, Moskva, 1988 | Zbl

[13] Korolyuk V. S., Portenko N. I., Skorokhod A. V., Turbin A. F., Spravochnik po teorii veroyatnostei i matematicheskoi statistike, Nauka, Moskva, 1985 | MR | Zbl

[14] Basawa I. V., Prakasa Rao B. L. S., Statistical inference for stochastic processes, Academic Press, London, 1980 | MR | Zbl

[15] Kemeni D., Snell D., Konechnye tsepi Markova, Fizmatlit, Moskva, 1970

[16] Serfling R. J., Approximation theorems of mathematical statistics, Wiley, New York, 1980 | MR | Zbl

[17] Borovkov A. A., Matematicheskaya statistika, Nauka, Moskva, 1984 | MR

[18] Ivchenko G. I., Medvedev Yu. I., Matematicheskaya statistika, Vysshaya shkola, Moskva, 1984 | MR | Zbl

[19] Bolshev L. N., Smirnov N. V., Tablitsy matematicheskoi statistiki, Nauka, Moskva, 1983 | MR

[20] Aivazyan S. A., Enyukov I. S., Meshalkin L. D., Prikladnaya statistika. Issledovanie zavisimostei, Finansy i statistika, Moskva, 1985 | MR