Order selection of linear regression models has been thoroughly researched in the statistical community for some time. Different shrinkage methods have been proposed, such as the Ridge and Lasso regression methods. Especially the Lasso regression has won fame because of its ability to set less important parameters exactly to zero. However, these methods do not take dynamical systems into accoun...

Order selection of linear regression models has been thoroughly researched in the statistical community for some time. Different shrinkage methods have been proposed, such as the Ridge and Lasso regression methods. Especially the Lasso regression has won fame because of its ability to set less important parameters exactly to zero. However, these methods do not take dynamical systems into accoun...

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-lineari...

This material is compiled for the course Empirical Modelling. Sections marked with a star (∗) are not central in the courses. The main source of inspiration when writing this text has been Chapter 4 in the book ”System Identification” by Söderström and Stoica (Prentice Hall, 1989) which also may be consulted for a more thorough treatment of the material presented here. The book is available for...

We have previously described how to model shape variability by means of point distribution models (TDMs,) in which there is a linear relationship between a set of shape parameters and the positions of points on the shape. This linear formulation can fail for shapes which articulate or bend.' we show examples of such failure for both real and synthetic classes of shape. A new, more general formu...

For a certain class of martingales, the convergence to mixture normal distribution is established under the convergence in distribution for the conditional variance. This is less restrictive in comparison with the classical martingale limit theorem where one generally requires the convergence in probability. The extension removes a main barrier in the applications of the classical martingale li...

Linear regression is probably the most popular model for predicting a RV Y ∈ R based on multiple RVs X1, . . . , Xd ∈ R. It predicts a numeric variable using a linear combination of variables ∑ θiXi where the combination coefficients θi are determined by minimizing the sum of squared prediction error on the training set. We use below the convention that the first variable is always one i.e., X1...