The asymptotic distribution of weighted empirical distribution functions

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Asymptotic Distribution of Divergence Measure with Applications

Asymptotic Distribution of Normalized Arithmetical Functions

Let f(n) be an arbitrary arithmetical function and let A N and B N be sequences of real numbers with 0< B N . + oe with N. We give a sufficient condition for (f(n)-AN)/BN to have a limiting distribution. The case when f(n) is defined by f(n ) = Zg(d), where the summation is over all divisors d of n and g(d) is any given arithmetical function, is discussed in more detail . A concrete example is ...

Oscillations of empirical distribution functions under dependence

Abstract: We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as the one obtained under independence. The dependence conditions are expressed in terms of physical dependence measures which are directly related to ...

Comparing Distribution Functions via Empirical Likelihood

This paper develops empirical likelihood based simultaneous confidence bands for differences and ratios of two distribution functions from independent samples of right-censored survival data. The proposed confidence bands provide a flexible way of comparing treatments in biomedical settings, and bring empirical likelihood methods to bear on important target functions for which only Wald-type co...