Sadly that word doesn't work at all as is, and the mid-word capitalizations do not work either. Good effort tho :)

The random sample (Stichprobe) has to go last, as it is the subject. Extreme is probably the "extreme case" not "extreme value" in here, so Extremfall, but we need plural to consider all extremes at the same time - which has the added "aesthetic" bonus of adding another German umlaut in Fälle. Full Confirmation is just Bestätigung I'd say. So maybe

Extremfälle-Bestätigungs-Stichprobe = Extremfällebestätigungsstichprobe

(to make it plural, just add an n)

See this is cooler because it has EXTREME at the front.