The method of support as statistical inference model for instant sample

Abstract

The aim of this study is to introduce a statistical inference model applicable to the analysis of an instant sample. In this connection instant sample means an observed probability sample or designed experiment which is not repeated or aimed to be repeated. We have demonstrated that the method of support put forward by Edwards, is an appropriate statistical inference model for such an inference situation. The central inference concept of the method of support is logarithm of the likelihood ratio named support S(Θ), Because the method of support, as such is not able to measure inference uncertainty, we have proven a new theorem in order to show how the support S(Θ) measures local uncertainty. This theorem shows that the method of support is an ordinary inference model. The proof is based on Rényi's incomplete probability distribution and Rérnyi's local uncertainty concept defined for it. In the case of instant sample we observe only one event whose probability is the joint probability PΘ(y) of the sample, which is accordingly an incomplete probability distribution. In practice, applications of the method of support to the estimation and statistical test theory lead to the least local uncertainty (LLU) estimators and tests. As an empirical application we have analyzed an instant sample from Finnish pupils in 1970 with their learning achievement (Finnish IEA data). The normal linear regression analysis is used as a statistical model. Parameter estimation and diagnostics are performed using the method of support as inference model.