In science, the most widespread statistical quantities are perhaps $p$-values. A typical advice is to reject the null hypothesis $H_0$ if the corresponding p-value is sufficiently small (usually smaller than 0.05). Many criticisms regarding p-values
have arisen in the scientific literature. The main issue is that in general optimal p-values (based on likelihood ratio statistics) are not measures of evidence over the parameter space $Theta$. Here, we propose an emph{objective} measure of evidence for very general null hypotheses that satisfies logical requirements (i.e., operations on the subsets of $Theta$) that are not met by p-values (e.g., it is a possibility measure). We study the proposed measure in the light of the abstract belief calculus formalism and we conclude that it can be used to establish objective states of belief on the subsets of $Theta$. Based on its properties, we strongly recommend this measure as an additional summary of significance tests. At the end of the paper we give a short listing of possible open problems.
This paper develops a method for estimating parameters of a vector autoregression (VAR) observed in white noise. The estimation method assumes the noise variance matrix is known and does not require any iterative process. This study provides consiste
nt estimators and shows the asymptotic distribution of the parameters required for conducting tests of Granger causality. Methods in the existing statistical literature cannot be used for testing Granger causality, since under the null hypothesis the model becomes unidentifiable. Measurement error effects on parameter estimates were evaluated by using computational simulations. The results show that the proposed approach produces empirical false positive rates close to the adopted nominal level (even for small samples) and has a good performance around the null hypothesis. The applicability and usefulness of the proposed approach are illustrated using a functional magnetic resonance imaging dataset.
This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the $Delta$ matrices (required for the assessment of local influence) for a quite general model which includes the one pr
oposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage. The matrix formulation has a considerable advantage, since although the complexity of the postulated model, all general formulas are compact, clear and have nice forms.
