Let fn denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let (t) be a positive continuous function such that ‖ f β‖∞ < ∞ for some 0 < β < 1/2. Under natural smoothness conditions, necessary and sufficient conditions for the sequence √ nhn 2| loghn | ‖ (t)(fn(t)−Efn(t))‖∞ to be stochastically bounded and to converge a.s. to a constant are obtained...

We describe an interesting application of the principle of local learning to density estimation. Locally weighted fitting of a Gaussian with a regularized full covariance matrix yields a density estimator which displays improved behavior in the case where much of the probability mass is concentrated along a low dimensional manifold. While the proposed estimator is not guaranteed to integrate to...

PURPOSE To describe subcortical low intensity on T2- and proton density-weighted MR images in early cortical ischemia and to discuss a cause of these findings. METHODS Nine patients with early cortical ischemia were studied with proton density- and T2-weighted images, and T1-weighted images at 1.5 T. Gadolinium enhancement was added in six cases. RESULTS In all cases there was high to inter...