Informatica

The paper presents analytic and stochastic methods of structure parameters estimation for a model selection problem. Structure parameters are covariance matrices of parameters of linear and non-linear regression models. To optimize model parameters and structure parameters we maximize a model evidence, a convolution of a data likelihood with a prior distribution of model parameters. The analytic methods are based on the derivatives computation of the approximated model evidence. The stochastic methods are based on the model parameters sampling and data cross-validation. The proposed methods are tested and compared on the synthetic and real data.

This article gives ideas for developing statistics software which can work without user intervention. Some popular methods of bandwidth selection for kernel density estimation (the nearest neighbour, least squares cross-validation, “plug-in” technique) are discussed. Modifications of the cross-validation criterion are proposed. Two-stage estimators combining these methods with multiplicative bias correction are investigated by simulation means.