A new method for testing linear restrictions in linear regression models is suggested. It allows to validate the linear restriction, up to a specified approximation error and with a specified error probability. The test relies on asymptotic normality of the test statistic, and therefore normality of the errors in the regression model is not required. In a simulation study the performance of the...

        This paper proposes a new forecasting model for investigating relationship between the price of crude oil, as an important energy source and GDP of the US, as the largest oil consumer, and the UK, as the oil producer. GMDH neural network and MLFF neural network approaches, which are both non-linear models, are employed to forecast GDP responses to the oil price changes. The resul...

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...

BACKGROUND Our aim was to investigate the existence of a reciprocal relationship between patients' assessment of quality of life and their appraisal of health. If present, this relationship will interfere with the interpretation of heart surgery's effect on overall quality of life. METHODS Path analysis was used to investigate reciprocal causal relationships between general health perceptions...

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...

Probablistic Model: We start with the assumption that prior to starting a sequence of experiments we have a family of random variables with means that vary linearly with respect to some deterministic independent variable. That is, there exist an intercept β0 and a slope β1 such that for each value of the independent variable x, we have a random variable Y with mean β0 + β1x. We are then given p...

We consider a set of linear regression models that differ in their choice of regressors, and derive a method for inference that controls for the set of models under investigation. The method is based around an estimate of the distribution for a class of statistics, which can depend on two or more models. An example is the largest R2 over a set of regression models. The distribution will typical...

This paper proposes a solution method to solve linear di¤erence models with lagged expectations in the form of

fuzzy linear regression models are used to obtain an appropriate linear relation between a dependent variable and several independent variables in a fuzzy environment. several methods for evaluating fuzzy coefficients in linear regression models have been proposed. the first attempts at estimating the parameters of a fuzzy regression model used mathematical programming methods. in this the...