Suppose that a given population is endowed with a pair of characteristics T and K. Let's think of these characteristics as random variables(adsbygoogle = window.adsbygoogle || []).push({});

(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 thresholdais unknown. Lettdenote the minimum observed realisation of T in this sample.

In terms of the distributions and parameters above, what istan estimator of?

To be more precise, I am trying to establish what information is contained intthat 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 oftas an estimator of a; but that's not the case here...

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# A Information contained in minimum value of truncated distribution

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