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Parameter estimation of sub-Gaussian stable distributions

Vadym Omelchenko (2014)

Kybernetika

In this paper, we present a parameter estimation method for sub-Gaussian stable distributions. Our algorithm has two phases: in the first phase, we calculate the average values of harmonic functions of observations and in the second phase, we conduct the main procedure of asymptotic maximum likelihood where those average values are used as inputs. This implies that the main procedure of our method does not depend on the sample size of observations. The main idea of our method lies in representing...

Performance analysis of least squares algorithm for multivariable stochastic systems

Ziming Wang, Yiming Xing, Xinghua Zhu (2023)

Kybernetika

In this paper, we consider the parameter estimation problem for the multivariable system. A recursive least squares algorithm is studied by minimizing the accumulative prediction error. By employing the stochastic Lyapunov function and the martingale estimate methods, we provide the weakest possible data conditions for convergence analysis. The upper bound of accumulative regret is also provided. Various simulation examples are given, and the results demonstrate that the convergence rate of the...

Probabilistic mixture-based image modelling

Michal Haindl, Vojtěch Havlíček, Jiří Grim (2011)

Kybernetika

During the last decade we have introduced probabilistic mixture models into image modelling area, which present highly atypical and extremely demanding applications for these models. This difficulty arises from the necessity to model tens thousands correlated data simultaneously and to reliably learn such unusually complex mixture models. Presented paper surveys these novel generative colour image models based on multivariate discrete, Gaussian or Bernoulli mixtures, respectively and demonstrates...

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