Assume that X, X,... is a sequential sample from a N(0, o2) density (o known), and that it is desired to estimate under squared-error decision

Assume that X₁, X₂,... is a sequential sample from a N(0, o2) density (o known), 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 clog(m+1). If the parameter has a N(μ, 2) prior density, find the optimal sampling procedure.