Abstract Gaussian Process (GP) regression models typically assume that residuals are Gaussian and have the same variance for all observations. However, applications with input-dependent noise (heteroscedastic residuals) frequently arise in practice, as do applications in which the residuals do not have a Gaussian distribution. In this paper, we propose a GP Regression model with a latent variab...

Regression models with compositional response have been studied from the beginning of the log-ratio approach for analysing compositional data. These early approaches suggested the statistical hypothesis of logistic-normality of the compositional residuals to test the model and its coefficients. Also, the Dirichlet distribution has been proposed as an alternative model for compositional residual...

An alternative to the Engle-Granger tests is the Cointegration Regression Durbin-Watson (CRDW) test of Sargan and Bhargava (1983). The test involves a simple regression of one variable on the other, and the standard Durbin-Watson test on the residuals. Recall the null for the DW test is that the residuals form a nonstationary random walk, whereas the alternative hypothesis is that the residuals...

We present a comparison of different depth notions which are appropriate for classical and orthogonal regression with and without intercept. We consider the global depth and tangential depth introduced by Mizera (2002) and the simplicial depth studied for regression in detail at first by Müller (2005). The global depth and the tangential depth are based on quality functions. These quality funct...