01.01.05 (Probability theory and mathematical statistics)
Birth date:
04.10.1963
Keywords:
probability theory; mathematical statistics; discrete mathematics; Markov chain; random allocations; statistical tests.
Subject:
Limit distributions for number of s-dimensional chains, which are absent in a sequence of independent trials, were obtained. A number of papers (with V. P. Chistyakov) were devoted to analysis of pseudo- random sequences.
Biography
Graduated from Faculty of Applied Mathematics of Moscow Institute of Electronical Mechanical Engineering (department of probability theory and mathematical statistics) in 1986. Ph.D. thesis was defended in 1998. A list of my works contains more than 10 titles.
Main publications:
Tikhomirova M. I. Ob asimptoticheskoi normalnosti chisla nepoyavivshikhsya s-tsepochek // Diskret. matem., 1992, t. 4, v. 2, 122–129.
Tikhomirova M. I., Chistyakov V. P. Ob odnoi skheme markovskikh razmeschenii po gruppam yacheek // Diskret. matem., 1995, t. 7, v. 2, 131–139.
Tikhomirova M. I., Chistyakov V. P. Skolzyaschii khi-kvadrat // Diskret. matem., 2000, t. 12, v. 4, 46–52.
M. I. Tikhomirova, V. P. Chistyakov, “On the asymptotic normality of some sums of dependent random variables”, Diskr. Mat., 27:4 (2015), 141–149; Discrete Math. Appl., 27:2 (2017), 123–129
M. I. Tikhomirova, V. P. Chistyakov, “Asymptotic normality of numbers of non-occurring values of $m$-dependent random variables”, Diskr. Mat., 26:2 (2014), 143–158; Discrete Math. Appl., 24:5 (2014), 305–317
M. I. Tihomirova, V. P. Chistyakov, “Asymptotic normality of the number of non-appeared values in random $m$-dependent sequences”, Mat. Vopr. Kriptogr., 2:1 (2011), 119–129
M. I. Tikhomirova, V. P. Chistyakov, “On properties of the likelihood function in the problem of estimation of the instants of changes of the success probability in nonhomogeneous Bernoulli trials”, Diskr. Mat., 22:2 (2010), 60–65; Discrete Math. Appl., 20:2 (2010), 213–220
M. I. Tikhomirova, V. P. Chistyakov, “On the estimation of the periods of noisy binary periodic sequences”, Diskr. Mat., 21:3 (2009), 24–32; Discrete Math. Appl., 19:4 (2009), 361–370
7.
M. I. Tikhomirova, “Asymptotic normality of the number of absent noncontinuous chains of outcomes of independent trials”, Diskr. Mat., 21:2 (2009), 112–125; Discrete Math. Appl., 19:3 (2009), 293–308
M. I. Tikhomirova, “Limit distributions of the number of absent chains of identical outcomes”, Diskr. Mat., 20:3 (2008), 40–46; Discrete Math. Appl., 18:3 (2008), 293–300
M. I. Tikhomirova, “Some characteristics of dependencies in discrete random sequences”, Diskr. Mat., 20:1 (2008), 151–158; Discrete Math. Appl., 18:2 (2008), 173–180
10.
M. I. Tikhomirova, V. P. Chistyakov, “Some statistics of $\chi^2$ type dependent on the frequencies of long tuples of outcomes in independent trials”, Tr. Diskr. Mat., 11:1 (2008), 144–150
11.
M. I. Tikhomirova, “Joint limit distributions of the numbers of missing tuples of identical outcomes”, Tr. Diskr. Mat., 11:1 (2008), 138–143
2007
12.
M. I. Tikhomirova, V. P. Chistyakov, “On the homogeneity of samples testing based on the frequencies of tuples of outcomes in a sequence of trials with unknown probabilities of outcomes”, Tr. Diskr. Mat., 10 (2007), 319–325
13.
M. I. Tikhomirova, “Sequential $\chi^2$-test based on statistics which are functionally dependent on the estimates of unknown parameters”, Tr. Diskr. Mat., 10 (2007), 314–318
2006
14.
M. I. Tikhomirova, V. P. Chistyakov, “Statistical tests for the identification of some types of dependencies between random sequences”, Tr. Diskr. Mat., 9 (2006), 357–376
M. I. Tikhomirova, V. P. Chistyakov, “On some $\chi^2$-type statistics that depend functionally on estimators of unknown parameters”, Diskr. Mat., 17:1 (2005), 22–34; Discrete Math. Appl., 15:1 (2005), 33–46
M. I. Tikhomirova, V. P. Chistyakov, “Multidimensional $\chi^2$-statistics in disorder problems”, Tr. Diskr. Mat., 8 (2004), 281–298
2003
17.
M. I. Tikhomirova, V. P. Chistyakov, “On two chi-square-type statistics constructed from the frequencies of tuples of states of a multiple Markov chain”, Diskr. Mat., 15:2 (2003), 149–159; Discrete Math. Appl., 13:3 (2003), 319–329
M. I. Tikhomirova, “A limit distribution of a $\chi$-square statistics of frequences of equal outcomes runs in a polynomial scheme”, Tr. Diskr. Mat., 7 (2003), 191–200
M. I. Tikhomirova, V. P. Chistyakov, “Approximate computation of limit distributions of some statistics functionals”, Tr. Diskr. Mat., 6 (2002), 213–225
21.
M. I. Tikhomirova, V. P. Chistyakov, “On some characteristic of two-stage procedure for multiple hypotheses selection”, Tr. Diskr. Mat., 5 (2002), 241–246
2001
22.
M. I. Tikhomirova, V. P. Chistyakov, “Normal approximation of multidimensional $\chi^2$ distribution”, Tr. Diskr. Mat., 4 (2001), 259–272
2000
23.
M. I. Tikhomirova, V. P. Chistyakov, “Moving chi-square”, Diskr. Mat., 12:4 (2000), 46–52; Discrete Math. Appl., 10:5 (2000), 469–475
V. P. Chistyakov, M. I. Tikhomirova, “Statistical tests based on $s$-tuples from some set”, Tr. Diskr. Mat., 3 (2000), 295–302
1999
25.
M. I. Tikhomirova, V. P. Chistyakov, “Some characteristics of two-stage designs of experiments”, Diskr. Mat., 11:3 (1999), 83–90; Discrete Math. Appl., 9:4 (1999), 365–373
1998
26.
M. I. Tikhomirova, V. P. Chistyakov, “On $\chi^2$-type statistics constructed from the output of a finite automaton”, Tr. Diskr. Mat., 2 (1998), 305–314
M. I. Tikhomirova, V. P. Chistyakov, “On the asymptotics of moments of the number of nonappearing $s$-chains”, Diskr. Mat., 9:1 (1997), 12–29; Discrete Math. Appl., 7:1 (1997), 13–32
M. I. Tikhomirova, V. P. Chistyakov, “On a scheme for Markov allocations by groups of cells”, Diskr. Mat., 7:2 (1995), 131–139; Discrete Math. Appl., 5:3 (1995), 269–275
1992
30.
M. I. Tikhomirova, “Asymptotic normality of the number of nonappearing $s$-chains”, Diskr. Mat., 4:2 (1992), 122–129; Discrete Math. Appl., 3:1 (1993), 89–96
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