Supervisors info:
Νικόλαος Παπαδάτος Αναπλ. Καθηγ. (Επιβλέπων), Ευτυχία Βαγγελάτου Επίκ. Καθηγ., Δημήτριος Χελιώτης Επίκ. Καθηγ.
Summary:
The purpose of this dissertation is to give some more light on the
limiting behavior of the vector of sample central moments as In particular,
we shall investigate in some detail the singular cases, i.e., the cases where
Also we shall show that, among the distributions having finite moments of any
order, the asymptotic independence of sample mean and the sequence
characterizes the normal distribution. This fact provides, in a sense, a
limiting counterpart of the wellknown result that independence of and (for some fixed ), where is the sample variance, characterizes normality. Here the assumption
of independence is weakened to asymptotic independence (as ) but, of course,
the requirement of the existence of all moments and the fact that has to be
asymptotically independent of all (and not only ), seems to be quite restricted. However, we shall prove that for any fixed
there exist (infinitely many) nonnormal distributions for which and are
asymptotically independent.
Keywords:
Asymptotic Behavior, Sample Central Moments, Singular Distributions, Method Delta, Theorems Taylor