# Questions tagged [rao-blackwell]

The Rao-Blackwell Theorem is a result which makes possible to better an estimator by conditioning on a sufficient statistic, preserving the expectation of the estimator.

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### What is the difference between MVB UMVUE and MVUE.?

Cramer Rao inequality gives MVB and if MVB exist it is MLE. Rao Blackwell gives UMVUE, but isn’t when we have MVB estimator for unbiased it is UMVUE? Then what is MVUE? MVB minimum variance bound ...
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### Knowing both sample mean and sample range improves estimate of the the variance?

It is known that sample variance and sample mean are independent for normally distributed variables, which means knowing sample mean does not say anything about to estimate the variance of the ...
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### Conditioning a biased estimator on a sufficient statistic

I'm afraid my awareness of the Rao–Blackwell theorem has been limited to textbook accounts and exercises, and those deal only with its application to unbiased estimators. Maybe it's properly called ...
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### Rao-Blackwellization of Gibbs Sampler

I am currently estimating a stochastic volatility model with Markov Chain Monte Carlo methods. Thereby, I am implementing Gibbs and Metropolis sampling methods.Assuming I take the mean of the ...
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### The normal and bernoulli distributions

I'm working on this problem and am a little stumped. I was wondering if someone could give me a hint? $x_1,...,x_n$ are iid $N(\mu,\sigma^2)$ where $\mu$ is unknown and $\sigma$ is known. $n>3$ ...