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Let F be the family of all distributions with probability density and finite variance, and $X_1, ..., X_n$ be random samples from F.

Does UMVUE for variance exists for this situation?

kjetil b halvorsen
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  • Do you mean UMVUE of any function $g(\theta)$ where the family $F$ is parametrised by $\theta$ or the UMVUE of $\text{Var}(X_i)$ in particular? – StubbornAtom Jun 13 '18 at 17:26
  • I meant the UMVUE for Var(X). For example the sample variance is umvue for variance (simga^2) when the family is normal distribution with arbitrary mean and variance, and I was trying to generalize it. – 456 123 Jun 14 '18 at 04:44

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