arXiv subjects

Alexey Shashkin

Publications and source records attributed to Alexey Shashkin.

4 recordsLinked to original sources

arXiv2020

Strong Gaussian approximation for cumulative processes with heavy tails

This paper is a continuation of work arXiv:2006.09583 devoted to establishment of the convergence rate in the strong invariance principle for cumulative processes. We establish optimal rate of convergence for the case when regeneration periods and increments over them have only power moments of order greater than 2. Under this power-type conditions two types of approximation by Wiener process are proved: the rate of convergence in the Strassen's invariance principle and inequalities for the probability that random process deviates from the approximating one.

math.PR↗

arXiv2020

Strong Gaussian approximation for cumulative processes

We establish optimal logarithmic rates of convergence in the strong invariance principle for multivariate cumulative processes in the Smith's sense. Exponential probabilistic inequalities of Komlós-Major-Tusnády type are obtained. Provided examples include applications to stopped sums and birth and death processes.

math.PR↗

arXiv2011

Statistical methods of SNP data analysis with applications

Various statistical methods important for genetic analysis are considered and developed. Namely, we concentrate on the multifactor dimensionality reduction, logic regression, random forests and stochastic gradient boosting. These methods and their new modifications, e.g., the MDR method with "independent rule", are used to study the risk of complex diseases such as cardiovascular ones. The roles of certain combinations of single nucleotide polymorphisms and external risk factors are examined. To perform the data analysis concerning the ischemic heart disease and myocardial infarction the supercomputer SKIF "Chebyshev" of the Lomonosov Moscow State University was employed.

math.PR↗

arXiv2006

Strong invariance principle for dependent random fields

A strong invariance principle is established for random fields which satisfy dependence conditions more general than positive or negative association. We use the approach of Csörgő and Révész applied recently by Balan to associated random fields. The key step in our proof combines new moment and maximal inequalities, established by the authors for partial sums of multiindexed random variables, with the estimate of the convergence rate in the CLT for random fields under consideration.

math.PR↗