Domains of attraction of the real random vector (x,x²) and applications

Abstract:

Many statistics are based on functions of sample moments. Important examples are the sample variance S2(n), the sample coefficient of variation S2(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 (∑ni=1Xi∑ni=1X2i plays an important role. In the paper we obtain conditions under which the vector (X,X2) belongs to a bivariate domain of attraction of a stable law. Applying simple transformations then leads to a full discussion of the asymptotic behaviour of SV(n) and t(n).

Año de publicación:

2009

Keywords:

Fuente:

scopus