Assume that X1 X2, ••• is a sequential sample from a density and that it is desired to estimate under squared-error decision loss. It is possible, at any stage, to take observations in batches of...

Assume that X₁
X₂, ••• is a sequential sample from a

density


and that it is desired to estimate

under squared-error decision loss. It is possible, at any stage, to take observations in batches of any size. A batch of m observations costs c log(m + O. If the parameter

has a

prior density, find the optimal sampling procedure.