Statistical estimation of parameters for binary Markov chain models with embeddings

Abstract

Markov chains with embeddings as steganography models are considered. Statistical estimators of the model parameters based on frequencies and correlation statistics are constructed and analysed. A polynomial algorithm for likelihood function computing is developed. The maximum likelihood estimators based on this algorithm are constructed. The results of computer experiments are presented.

Statistical analysis of multivariate discrete-valued time series

“…The FBE approach is successively developed for some other types of discrete-valued time series (19): semibinomial [80], binary [78,84], Poisson, geometric, negative binomial [75], regression time series [81], and also for Binomial conditionally nonlinear model for spatio-temporal data [85]; it is used for statistical forecasting of COVID-19, see [83], for more references.…”

Statistical Analysis of Discrete-valued Time Series by Parsimonious High-order Markov Chains

“…Finally, we plan to develop the results of this paper in three main directions: 1) robust statistical analysis of discrete-valued time series based on asymptotical risk expansion methods published in (Kharin 1997(Kharin , 2011Kharin and Zhuk 1998); 2) robust sequential testing of hypotheses for discrete-valued time series using approaches from (Kharin 2017;Kharin and Kishylau 2015;Kharin and Tu 2017); 3) applications in steganography (Kharin and Vecherko 2013) and in marketing (Pashkevich and Kharin 2004).…”

Robustness Analysis in Sequential Statistical Decisions

“…The assumed hypothetical probability models used in the sequential approach are quite often distorted in practice (Huber and Ronchetti 2009), (Maevskii and Kharin 2002), (Kharin 2011), (Kharin 2005). Therefore, the problem of robustness analysis (Kharin and Zhuk 1998), (Kharin 1997), (Kharin and Vecherko 2013), (Galinskij and Kharin 1999) for sequential statistical decision making under distortions is an important one.…”