- #1

- 26

- 0

*(T,K)∼BiNormal((μT,μS),(σT,σS),ρ)*

I observe the realisations of T for a sample consisting of those individuals with K<

*a,*where the selection threshold

*a*is unknown. Let

*t*denote the minimum observed realisation of T in this sample.

In terms of the distributions and parameters above, what is

*t*an estimator of?

To be more precise, I am trying to establish what information is contained in

*t*that is not already contained in the truncated sample mean and variance. My intuition is that there must be some information: if selection was taking place on T itself, then it would seem intuitive to think of

*t*as an estimator of a; but that's not the case here...