Fourier methods for smooth distribution function estimation

In this paper we show how to use Fourier transform methods to analyze the asymptotic behavior of kernel distribution function estimators. Exact expressions for the mean integrated squared error in terms of the characteristic function of the distribution and the Fourier transform of the kernel are employed to obtain the limit value of the optimal bandwidth sequence in its greatest generality. The assumptions in our results are mild enough so that they are applicable when the kernel used in the estimator is a superkernel, or even the sinc kernel, and this allows to extract some interesting consequences, as the existence of a class of distributions for which the kernel estimator achieves a first-order improvement in efficiency over the empirical distribution function.Comment: 12 pages, 2 figure

Dark Matter Halo Structure in CDM Hydrodynamical Simulations

We have carried out a comparative analysis of the properties of dark matter halos in N-body and hydrodynamical simulations. We analyze their density profiles, shapes and kinematical properties with the aim of assessing the effects that hydrodynamical processes might produce on the evolution of the dark matter component. The simulations performed allow us to reproduce dark matter halos with high resolution, although the range of circular velocities is limited. We find that for halos with circular velocities of $[150-200] km s^{-1}$ at the virial radius, the presence of baryons affects the evolution of the dark matter component in the central region modifying the density profiles, shapes and velocity dispersions. We also analyze the rotation velocity curves of disk-like structures and compare them with observational results.Comment: 28 pages, 15 figures (figures 3ab sent by request), 2 tables. Accepted for publication MNRA

Combinando testes de Mardia e BHEP na avaliação duma hipótese multivariada de normalidade

https://thekeep.eiu.edu/den_1998_feb/1015/thumbnail.jp

Boundary kernels for distribution function estimation

Boundary effects for kernel estimators of curves with compact supports are well known in regression and density estimation frameworks. In this paper we address the use of boundary kernels for distribution function estimation. We establish the Chung-Smirnov law of iterated logarithm and an asymptotic expansion for the mean integrated squared error of the proposed estimator. These results show the superior theoretical performance of the boundary modified kernel estimator over the classical kernel estimator for distribution functions that are not smooth at the extreme points of the distribution support. The automatic selection of the bandwidth is also briefly discussed in this paper. Beta reference distribution and cross-validation bandwidth selectors are considered. Simulations suggest that the cross-validation bandwidth performs well, although the simpler reference distribution bandwidth is quite effective for the generality of test distributions