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Uniform asymptotic normality for the Bernoulli scheme

Wojciech Niemiro, Ryszard Zieliński (2007)

Applicationes Mathematicae

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.

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