• New methods of statistical inference for linear and nonlinear models

New methods of statistical inference for linear and nonlinear models

Projects: VEGA 1/0264/03 and VEGA 2/4026/04

Investigators: V. Witkovský, A. Savin, B. Arendacká, M. Grendár, K. Hornišová

New results have been derived for estimation of parameters and statistical inference in linear and nonlinear models. The invariant quadratic estimators of variances in the orthogonal linear regression time series model with finite discrete spectrum have been derived and the problems of unbiasedness and consistency of these estimators have been investigated. The statistical properties of the estimators have been compared (with respect to their mean square error) under the assumption that the fixed effects model was the true model as well as under the assumption that the random effects was the true model. The estimators were compared also with the estimators based on the maximum likelihood method (ML and REML). Further, we have suggested a new method for a linearization of the nonlinear regression and the confidence region of the parameters, new estimators in the Errors-In-Variables model, new methods for construction of the confidence intervals in models with variance components. We have also suggested new algorithms for finding the mode of multinomial distribution as well as for computing the distribution of a linear combination of independent t random variables. New results have been derived for the Maximum Entropy method (MaxEnt), which belongs into the toolkit for solving ill-posed inverse problems. A probabilistic justification of the method was extended to the case of non-convex feasible set of probability mass functions. A concept of μ-projection, closely related to the Method of Maximum Probability was introduced and its relationship to I-projection was studied. A method for determination of μ- projections was suggested.

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