Sequential simultaneous estimation of the mean and variance: The rate of convergence (Q1084819)

Suppose \(X_ 1,X_ 2,...\), is a sequence of i.i.d. random variables each distributed \(N(\mu,\sigma^ 2)\) where both parameters \(\mu\) and \(\sigma^ 2\) are unknown. The authors consider the problem of simultaneous estimation of \(\mu\) and \(\sigma^ 2\). They define stopping rules in this estimation problem and derive the rate of convergence of the corresponding normalized quantities to normality. Other interesting topics are discussed too.