Effective WLLN, SLLN and CLT in statistical models

Ryszard Zieliński. "Effective WLLN, SLLN and CLT in statistical models." Applicationes Mathematicae 31.1 (2004): 117-125. <http://eudml.org/doc/279365>.

@article{RyszardZieliński2004,
abstract = {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.},
author = {Ryszard Zieliński},
journal = {Applicationes Mathematicae},
keywords = {weak laws of large numbers; strong laws of large numbers; central limit theorems; statistical models; effective limit laws; uniform limit laws; Bernoulli scheme; exponential distribution; quantiles},
language = {eng},
number = {1},
pages = {117-125},
title = {Effective WLLN, SLLN and CLT in statistical models},
url = {http://eudml.org/doc/279365},
volume = {31},
year = {2004},
}

TY - JOUR
AU - Ryszard Zieliński
TI - Effective WLLN, SLLN and CLT in statistical models
JO - Applicationes Mathematicae
PY - 2004
VL - 31
IS - 1
SP - 117
EP - 125
AB - 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.
LA - eng
KW - weak laws of large numbers; strong laws of large numbers; central limit theorems; statistical models; effective limit laws; uniform limit laws; Bernoulli scheme; exponential distribution; quantiles
UR - http://eudml.org/doc/279365
ER -