Domains of attraction of the random vector $(X,X^2)$ and applications

Details Domains of attraction of the random vector $(X,X^2)$ and applications Domains of attraction of the random vector $(X,X^2)$ and applications

2007-12-20

arxiv.org/abs/0712.3440v1

Mathematics

Probability

To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.i

Scientific paper

Many statistics are based on functions of sample moments. Important examples are the sample variance $s_{n-1}^2$, the sample coefficient of variation SV(n), the sample dispersion SD(n) and the non-central $t$-statistic $t(n)$. The definition of these quantities makes clear that the vector defined by (\sum_{i=1}^nX_i,\sum_{i=1}^nX_i^2) plays an important role. In studying the asymptotic behaviour of this vector we start by formulating best possible conditions under which the vector $(X,X^2)$ belongs to a bivariate domain of attraction of a stable law. This approach is new, uniform and simple. Our main results include a full discussion of the asymptotic behaviour of SV(n), SD(n) and $t^2(n)$. For simplicity, in restrict ourselves to positive random variables $X$.

Affiliated with

Also associated with

No associations

Rating

Domains of attraction of the random vector $(X,X^2)$ and applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Domains of attraction of the random vector $(X,X^2)$ and applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Domains of attraction of the random vector $(X,X^2)$ and applications will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-3197