For my simulations, I have to simulate paths of
Normal(mu*, sigma*).random variables. It so happens, that each path
has few  observations, AND sigma is large [compared to mu]. Thus
the realized values of mu are often very different from mu*. I
discovered that in my particular application, it makes sense to take
1) estimate mu and sigma
2) if mu is not equal to m*, then "massage the data" - for each path,
convert the data into N(0,1) [by subtracting the estimated mu [for
this path] from each observation, etc], and then convert the data into
N(M*, Sigma*)I [by adding m* to each value, etc].
I was wondering whether there is a formal Statistics term describing
this "massaging the data" procedure. I really need to know this, to
be able to put my research into context of existing work.
Thank you very much for your kind help