Effective WLLN, SLLN and CLT in statistical models

• Autorzy: Ryszard Zieliński
• Języki publikacji: EN

Abstrakty

EN

Weak laws of large numbers (WLLN), strong laws of large numbers (SLLN), and central limit theorems (CLT) in statistical models differ from those in probability theory in that they should hold uniformly in the family of distributions specified by the model. If a limit law states that for every ε > 0 there exists N such that for all n > N the inequalities |ξₙ| < ε are satisfied and N = N(ε) is explicitly given then we call the law effective. It is trivial to obtain an effective statistical version of WLLN in the Bernoulli scheme, to get SLLN takes a little while, but CLT does not hold uniformly. Other statistical schemes are also considered.

Kategorie tematyczne

• 60F15: Strong theorems
• 60F05: Central limit and other weak theorems
• 62E20: Asymptotic distribution theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2004
• Tom: 31
• Numer: 1
• Strony: 117-125

Daty

wydano

2004

Twórcy

autor

Ryszard Zieliński

• Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21, 00-956 Warszawa 10, Poland

Identyfikatory

DOI

10.4064/am31-1-10