Un théorème d'itération stochastique multidimensionnelle
Uniform asymptotic normality for the Bernoulli scheme
It is easy to notice that no sequence of estimators of the probability of success θ in a Bernoulli scheme can converge (when standardized) to N(0,1) uniformly in θ ∈ ]0,1[. We show that the uniform asymptotic normality can be achieved if we allow the sample size, that is, the number of Bernoulli trials, to be chosen sequentially.
Using an Approximate Kiefer-Weiss Solution for Testing Insect Population Densities.