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)
Strong laws for weighted sums of NA random variables. (English) Zbl 1247.60036
Summary: Strong laws are established for linear statistics that are weighted sums of an negatively associated (NA) random sample. The results obtained not only generalize the results of S. H. Sung [Stat. Probab. Lett. 52, No. 4, 413–419 (2001; Zbl 1020.60016)] to NA random variables, but also extend and sharpen them.

60F15Strong limit theorems
[1]Bai ZD and Cheng PE (2000). Marcinkiewicz strong laws for linear statistics. Stat Probab Lett 46: 105–112 · Zbl 0960.60026 · doi:10.1016/S0167-7152(99)00093-0
[2]Choi BD and Sung SH (1987). Almost sure convergence theorems of weighted sums of random variables. Stoch Anal Appl 5: 365–377 · Zbl 0633.60049 · doi:10.1080/07362998708809124
[3]Chow YS and Teicher H (1997). Probability theory: independence, interchangeability, martingales, 3rd edn. Springer, New York
[4]Cuzick J (1995). A strong law for weighted sums of i.i.d. random variables. J Theor Probab 8: 625–641 · Zbl 0833.60031 · doi:10.1007/BF02218047
[5]Erdös P (1949). On a theorem of Hsu–Robbins. Ann Math Stat 20: 286–291 · Zbl 0033.29001 · doi:10.1214/aoms/1177730037
[6]Hsu PL and Robbins H (1947). Complete convergence and the law of larege numbers. Proc Natl Acad Sci USA 33(2): 25–31 · Zbl 0030.20101 · doi:10.1073/pnas.33.2.25
[7]Joag DK and Proschan F (1983). Negative associated of random variables with application. Ann Stat 11: 286–295 · Zbl 0508.62041 · doi:10.1214/aos/1176346079
[8]Petrov VV (1995). Limit theorems of probability theory sequences of independent random variables. Oxford Science Publications, Oxford
[9]Shao QM (2000). A comparison theorem on moment inequalities between Negatively associated and independent random variables. J Theor Probab 13: 343–356 · Zbl 0971.60015 · doi:10.1023/A:1007849609234
[10]Stout W (1974). Almost sure convergence. Academic, New York
[11]Su C, Zhao LC and Wang YB (1996). Moment inequalities and weak convergence for NA sequences. Sci China Ser A 26: 1091–1099
[12]Sung SH (2001). Strong laws for weighted sums of i.i.d. random variables. Stat Probab Lett 52: 413–419 · Zbl 1020.60016 · doi:10.1016/S0167-7152(01)00020-7
[13]Wu WB (1999). On the strong convergence of a weighted sums. Stat Probab Lett 44: 19–22 · Zbl 0951.60027 · doi:10.1016/S0167-7152(98)00287-9
[14]Yang SC (2000). Moment inequality of random variables partial sums. Sci Chin Ser A 30: 218–223