# Questions tagged [unbiased-estimator]

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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### Model for population density estimation

A database of (population, area, shape) can be used to map population density by assigning a constant value of population/area to each shape (which is a polygon such as a Census block, tract, county, ...
Suppose $X \sim \mathcal{N}(\mu_x, \sigma^2_x)$ and $Y \sim \mathcal{N}(\mu_y, \sigma^2_y)$ I am interested in $z = \min(\mu_x, \mu_y)$. Is there an unbiased estimator for $z$? The simple estimator ...
### Unbiased estimator with minimum variance for $1/\theta$
Let$X_1, ...,X_n$ be a random sample feom a distribution $Geometric(\theta)$ for $0<\theta<1$. I.e, $$p_{\theta}(x)=\theta(1-\theta)^{x-1} I_{\{1,2,...\}}(x)$$ Find the unbiased estimator ...