Improvement of the Predicted Least-Squares-Estimates in Multiple Linear Regression by Means of an Examination of Residuals.
Inference in linear models with inequality constrained parameters
In many econometric applications there is prior information available for some or all parameters of the underlying model which can be formulated in form of inequality constraints. Procedures which incorporate this prior information promise to lead to improved inference. However careful application seems to be necessary. In this paper we will review some methods proposed in the literature. Among these there are inequality constrained least squares (ICLS), constrained maximum likelihood (CML) and...
Insensitivity region for variance components in general linear model
In linear regression models the estimator of variance components needs a suitable choice of a starting point for an iterative procedure for a determination of the estimate. The aim of this paper is to find a criterion for a decision whether a linear regression model enables to determine the estimate reasonably and whether it is possible to do so when using the given data.
Interval linear regression analysis based on Minkowski difference – a bridge between traditional and interval linear regression models
In this paper, we extend the traditional linear regression methods to the (numerical input)-(interval output) data case assuming both the observation/measurement error and the indeterminacy of the input-output relationship. We propose three different models based on three different assumptions of interval output data. In each model, the errors are defined as intervals by solving the interval equation representing the relationship among the interval output, the interval function and the interval...
Intrinsic priors for hypothesis testing in normal regression models.
Testing that some regression coefficients are equal to zero is an important problem in many applications. Homoscedasticity is not necessarily a realistic condition in this setting and, as a consequence, no frequentist test there exist. Approximate tests have been proposed. In this paper a Bayesian analysis of this problem is carried out, from a default Bayesian model choice perspective. Explicit expressions for intrinsic priors are provided, and it is shown that the corresponding Bayes factor is...
Inversion of partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters
The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas in estimation...