My questions:
Is an estimator both a function and a random variable?
Example:
when we say an estimator $$ T(X)$$ we mean :1. the rule,which is a function $T(X)$ 2.and the result $T=T(X)$,which is a random variable.
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1$\begingroup$ Yes, both. As an estimator, $T$ is a function of the possible observations, and if you apply it to a particular observation $x$ then it gives an estimate $T(x)$. Since (before actually observing) the observation $X$ is a random variable, a function of it $T(X)$ is another random variable $\endgroup$– HenryCommented May 11, 2019 at 10:46
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$\begingroup$ An estimator is a statistic, which by definition is a function of sample observations (random variables) independent of the parameter of interest. $\endgroup$– StubbornAtomCommented May 11, 2019 at 11:10
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$\begingroup$ @Henry hi,henry.So, T is a function that can apply to a random variable X (before the observing) ,which will result in another random variable ,and also can apply to a observation x(after the observing),which will result in an estimate.Am i right? $\endgroup$– dawenCommented May 11, 2019 at 16:39
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$\begingroup$ That is how I understand it. That is why people talk about things like the "variance of the maximum likelihood estimator/estimate" $\endgroup$– HenryCommented May 11, 2019 at 18:04
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