# 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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### How does Rao-Blackwellization of the Metropolis-Hastings algorithm work?

I've read the paper A vanilla Rao-Blackwellization of Metropolis-Hastings algorithms, but I don't get what their actually suggested estimator is. To give some detail, we are considering the following ...
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### Understanding the Rao-Blackwell Theorem

I've been reading up a lot on the practical applications of the Rao-Blackwell theorem. I do understand how the Bias and Variance and MSE aspects of the theorem fall in place (i.e. the mathematical ...
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### Finding UMVUE of function of poisson parameter

I am to estimate $\exp(-\lambda)\lambda^2/2$ from the distribution $Exp(\lambda) \sim \frac{e^{-\lambda}\lambda^x}{x!}$ I used the indicator function $W=\mathbb I_{2}(X_1)$ as an initial unbiased ...
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### Using all Metropolis-Hastings proposals to estimate an integral

Suppose we run the Metropolis-Hastings with target distribution $\mu$ to compute the integral $\int f\:{\rm d}\mu$. Usually, we use the estimator $$A_n:=\frac1n\sum_{i=0}^{n-1}f(X_i).$$ However, ...
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### Minimum-variance unbiased estimator to estimate quantiles when the errors are normal distributed

What is the minimum-variance unbiased estimator to estimate quantiles when the errors are normal distributed? median When we wish to estimate the median, $\mu$, of a normal distributed variable then ...
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### Rao-Blackwellization in variational inference

The Black box VI paper introduces Rao-Blackwellization as a method to reduce the variance of the gradient estimator using score function, in section 3.1. However I don't quite get the basic idea ...
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The Rao-Blackwell Theorem states Let $\hat{\theta}$ be an estimator of $\theta$ with $\Bbb E (\hat{\theta}^2) < \infty$ for all $\theta$. Suppose that $T$ is sufficient for $\theta$, and let $\... 2 votes 0 answers 82 views ### The normal and bernoulli distributions I'm working on this problem and am a little stumped. I was wondering if someone could give me a hint?$x_1,...,x_n$are iid$N(\mu,\sigma^2)$where$\mu$is unknown and$\sigma$is known.$n>3$... 2 votes 1 answer 247 views ### How does one can guarantee that any unbiased estimator is MVUE due to it containing a minimal sufficient statistic? Sufficiency is okay. But I don't really get it why the fact guarantees it has minimal variance? Can anyone explain to me somewhat intuitively? 10 votes 2 answers 1k views ### Find the joint distribution of$X_1$and$\sum_{i=1}^n X_i$This question is from Robert Hogg's Introduction to Mathematical Statistics 6th version question 7.6.7. The problem is : Let a random sample of size$n$be taken from a distribution with the pdf$...
According to the Rao-Blackwell theorem, if statistic $T$ is a sufficient and complete for $\theta$, and $E(T)=\theta$, then $T$ is a uniformly minimum-variance unbiased estimator (UMVUE). I am ...