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I have followed the CRLB derivation, and I couldn't figure out why -

If f(x; θ) be a probability density with continuous parameter θ, and X1, . . . , Xn be independent random variables with density f(x; θ), and Θ(X1, . . . ,Xn) be an unbiased estimator of θ.

Why does the estimator, Θ, is independent of θ (the param to be estimated)?

Θ is a function of X1,...,Xn, and in the pdf of each one of them θ appears as a param. Doesn't it imply that Θ is also dependent on θ?

Jonathan
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