On Multiple Hypotheses LAO Testing With Rejection of Decision for Two Dependent Objects

Multiple statistical hypotheses testing with possibility of rejecting of decisionis considered for model consisting of two dependent objects characterized by joint discrete probability distribution. The matrix of error probabilities exponents (reliabilities) of asymptotically optimal tests is studied.

On the Effects of Signal Acuity in a Multi-Alternative Model of Decision Making

We consider the effects of signal sharpness or acuity on the performance of neural models of decision making. In these models, a vector of signals is presented, and the subject must decide which of the elements of the vector is the largest. McMillen and Holmes ( 2006 ) derived asymptotically optimal tests under the assumption that the elements of the signal vector were all equal except one. In this letter, we consider the case of signals spread around a peak. The acuity is a measure of how strongly peaked the signal is. We find that the optimal test is one in which the detectors are passed through an output layer that encodes knowledge of the possible shapes of the incoming signals. The incorporation of such an output layer can lead to significant improvements in decision-making tasks.

ROBUST OPTIMAL TESTS FOR CAUSALITY IN MULTIVARIATE TIME SERIES

Here, we derive optimal rank-based tests for noncausality in the sense of Granger between two multivariate time series. Assuming that the global process admits a joint stationary vector autoregressive (VAR) representation with an elliptically symmetric innovation density, both no feedback and one direction causality hypotheses are tested. Using the characterization of noncausality in the VAR context, the local asymptotic normality (LAN) theory described in Le Cam (1986, Asymptotic Methods in Statistical Decision Theory) allows for constructing locally and asymptotically optimal tests for the null hypothesis of noncausality in one or both directions. These tests are based on multivariate residual ranks and signs (Hallin and Paindaveine, 2004a, Annals of Statistics 32, 2642–2678) and are shown to be asymptotically distribution free under elliptically symmetric innovation densities and invariant with respect to some affine transformations. Local powers and asymptotic relative efficiencies are also derived. The level, power, and robustness (to outliers) of the resulting tests are studied by simulation and are compared to those of the Wald test. Finally, the new tests are applied to Canadian money and income data.