KOLMOGOROV DISTANCE FOR MULTIVARIATE NORMAL APPROXIMATION

Multivariate spectral approximation in the Hellinger distance

We first describe a globally convergent matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. Then, we apply this approximation procedure to the estimation of multivariate spectral densities, and test its effectiveness through simulation.

Multivariate normal approximation in geometric probability

x ξxδx where the sum is over points x of a Poisson point process of intensity λ on a bounded region in d-space, and ξx is a functional determined by the Poisson points near to x, i.e. satisfying an exponential stabilization condition, along with a moments condition (examples include statistics for proximity graphs, germ-grain models and random sequential deposition models). A known general resu...

Screening for a Multivariate Mixture Normal Distribution

Multivariate spline approximation of the signed distance function

The signed distance function can effectively support many geometry processing tasks such as decimates, smoothing and shape reconstruction since it provides efficient access to distance estimates. In this talk, we present an adaptive method to approximate the signed distance function of a smooth curve by using polynomial splines over type-2 triangulation. The trimmed offsets are also studied.

List Approximation for Increasing Kolmogorov Complexity

It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. But is it possible to construct a few strings, not longer than the input string, so that most of them have larger complexity? We show that the answer is yes. We present an algorithm that on input a string x of length n returns a list with O(n) many strings, all of length n, such that 99% of them are ...