We propose new data-driven smooth tests for a parametric regression function. The smoothing parameter is selected through a new criterion that favors a large smoothing parameter under the null hypothesis. The resulting test is adaptive rate-optimal and consistent against Pitman local alternatives approaching the parametric model at a rate arbitrarily close to 1/ √ n. Asymptotic critical values ...

Null space velocity control is essential for achieving good behaviour of a redundant manipulator. Using the dynamically consistent pseudo-inverse, the task and null space motion and forces are decoupled. The paper presents a globally stable null space velocity controller and the gradient projection technique in conjunction with the dynamically consistent pseudo-inverse. The physical meaning and...

We study a semiparametric generalized additive coefficient model, in which linear predictors in the conventional generalized linear models is generalized to unknown functions depending on certain covariates, and approximate the nonparametric functions by using polynomial spline. The asymptotic expansion with optimal rates of convergence for the estimators of the nonparametric part is establishe...

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...

We consider the non-nested testing prqblem of non-parametric regressions. We show that, when the regression functions are unknown under both the null and the alternative hypotheses, an extension of the J-test procedure of Davidson and Mackinnon (1981) will lead to a test statistic with well defined asymptotic properties. The derivation of the test statistic involves double kernel estimation. Mo...

We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the timeand space-like geodesics and invariant 1-form on the space of null geodesics. We prove a Poncelet-type theorem for null geodesics on the ellipsoid: if such a geodesic ...

Although wormholes can be treated as topological objects in spacetime and from a global point-of-view, a precise definition of what a wormhole throat is and where it is located can be developed and treated entirely in terms of local geometry. This has the advantage of being free from unnecesary technical assumptions about asymptotic flatness, and other global properties of the spacetime contain...