A two-sample test for the error distribution in nonparametric regression based on the characteristic function
A test for the equality of error distributions in two nonparametric regression models is proposed. The test statistic is based on comparing the empirical characteristic functions of the residuals calculated from independent samples of the models. The asymptotic null distribution of the test statistic cannot be used to estimate its null distribution because it is unknown, since it depends on the unknown common error distribution. To approximate the null distribution, a weighted bootstrap estimator is studied, providing a consistent estimator. The finite sample performance of this approximation as well as the power of the resulting test are evaluated by means of a simulation study. The procedure can be extended to testing for the equality of \(d>2\) error distributions.
Abstract A procedure is given for calculating the NMR lineshape of a cluster of spins imbedded in a molecule which is rotating with free or restricted motion. It is shown that for the isotropic diffusion model (assuming a correlation time τ c such that 1/ τ c ⪢ H DD / lstrok ; h where H DD is the dipole interaction) the line shape is Lorentzian as expected and has a width equal to that obtained from a standard T 2 calculation using the appropriate autocorrelation function. For τ c which do not satisfy this condition the lineshape is no longer Lorentzian, and an example for this condition is shown. The usefulness of the procedure lies in obtaining lineshapes for systems whose motion is too complex for an autocorrelation function to be obtained unambiguously.