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Refers to an estimator of a population parameter that "hits the true value" on average. That is, a function of the observed data $\hat{\theta}$ is an unbiased estimator of a parameter $\theta$ if $E(\hat{\theta}) = \theta$. The simplest example of an unbiased estimator is the sample mean as an estimator of the population mean.
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Is there an unbiased estimator of the Hellinger distance between two distributions?
In a setting where one observes $X_1,\ldots,X_n$ distributed from a distribution with density $f$, I wonder if there is an unbiased estimator (based on the $X_i$'s) of the Hellinger distance to anothe …
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expectation of log of expectation by Monte Carlo
When considering the approximation by Monte Carlo of an expectation of the form$$\mathfrak{I}=\mathbb{E}^X[\log\{\mathbb{E}^{Y|X}[h(X,Y)|X]\}]$$using a resolution of the form$$\hat{\mathfrak{I}}=\frac …