A Method for Measuring Distance From a Training Data Set

A new method is proposed for measuring the distance between a training data set and a single, new observation. The novel distance measure reflects the expected squared prediction error when a quantitative response variable is predicted on the basis of the training data set using the distance weighted k-nearest-neighbor method. The simulation presented here shows that the distance measure correlates well with the true expected squared prediction error in practice. The distance measure can be applied, for example, in assessing the uncertainty of prediction.     

How to compare interpretatively different models for the conditional variance function

This study considers regression-type models with heteroscedastic Gaussian errors. The conditional variance is assumed to depend on the explanatory variables via a parametric or non-parametric variance function. The variance function has usually been selected on the basis of the log-likelihoods of fitted models. However, log-likelihood is a difficult quantity to interpret – the practical importance of differences in log-likelihoods has been difficult to assess. This study overcomes these difficulties by transforming the difference in log-likelihood to easily interpretative difference in the error of predicted deviation. In addition, methods for testing the statistical significance of the observed difference in test data log-likelihood are proposed.