We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) nonadaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L2([0, 1]d)-norm and also p...

We consider the problem of testing for additivity in the standard multiple nonparametric regression model. We derive optimal (in the minimax sense) nonadaptive and adaptive hypothesis testing procedures for additivity against the composite nonparametric alternative that the response function involves interactions of second or higher orders separated away from zero in L2([0, 1]d)-norm and also p...

In the common nonparametric regression model with high dimensional predictor several tests for the hypothesis of an additive regression are investigated The corresponding test statistics are either based on the di erences between a t under the assumption of additivity and a t in the general model or based on residuals under the assumption of additivity For all tests asymptotic normality is esta...

Assessing for interactions among chemicals in a mixture involves the comparison of actual mixture responses to those predicted under the assumption of zero interaction (additivity), based on individual chemical dose-response data. However, current statistical methods do not adequately account for differences in the shapes of the dose-response curves of the individual mixture components, as occu...

It is widely believed that semantic activation from print is not capacity limited (i.e., that it does not need attentional resources). Prior research has tested this assumption by examining the Stroop effect in the context of the psychological refractory period (PRP) paradigm. These studies yielded additivity of the Stroop effect and SOA on RT, consistent with the hypothesis that semantic activ...

The additivity principle allows to compute the current distribution in many one-dimensional (1D) nonequilibrium systems. Using simulations, we confirm this conjecture in the 1D Kipnis-Marchioro-Presutti model of heat conduction for a wide current interval. The current distribution shows both Gaussian and non-Gaussian regimes, and obeys the Gallavotti-Cohen fluctuation theorem. We verify the exi...

A large literature has used choice experiments involving time-dated monetary rewards, to test whether time discounting is exponential or hyperbolic, with mixed results. One explanation, proposed by the psychologist Daniel Read (2001), is that the observed choice patterns reflect a type of framing effect, known as sub-additivity, rather than hyperbolic or exponential discounting. An alternative ...

We describe two tests of the hypothesis that human judgments of the proximity of colors are consistent with a Euclidean geometry on color matching space. The first test uses proximity judgments to measure the angle between any two intersecting lines in color space. Pairwise estimates of the angles between three lines in a plane were made in order to test the additivity of angles. Three differen...