zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The weak convergence for functions of negatively associated random variables. (English) Zbl 0989.60033

Consider a sequence of stationary, negatively associated random variables, and set S j (1)=X j+k ++X j+k , S n =X 1 ++X n , and Y k,j =f({S j (k)-kμ}/k), with μ denoting the mean of X 1 , and f a real function satisfying some conditions. The author’s main results provide an asymptotic Wiener process approximation for the partial sum process of the {Y k,j :j=1,,n}, both in the case of k being a fixed positive integer as well as for k, but k/n0 as n. A corresponding result for positively associated random variables is also presented.

As a consequence of the main results, the author is able to derive asymptotic normality of some estimators of the asymptotic variance of S n , which have earlier been discussed by M. Peligrad and Q.-M. Shao [ibid. 52, No. 1, 140-157 (1995; Zbl 0816.62027)] and M. Peligrad and R. Suresh [Stochastic Processes Appl. 56, No. 2, 307-319 (1995; Zbl 0817.62019)] in case of ρ-mixing variables, and by Zhang and Shi (1998) for negatively associated variables.

60F15Strong limit theorems
60E15Inequalities in probability theory; stochastic orderings