# 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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### Asymptotic normality of MLE in exponential with higher-power x

Given the distribution: $f(x;\theta) = \frac{3}{\theta}x^2e^{-x^3/\theta}$ if $x>0$ the MLE for $\theta$ is $\frac{1}{n}\sum_{i=1}^n x_i^3$. It's an unbiased estimator with variance $\theta^2/n$. ...
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### Is sample kurtosis hopelessly biased?

I am looking at the sample kurtosis of a fairly skewed random variable, and the results seem inconsistent. To simply illustrate the problem, I looked at the sample kurtosis of a log-normal RV. In R (...
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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, ...
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### Microsoft Excel formula for variance

According to Microsoft Excel Help: VAR uses the following formula: where x is the sample mean AVERAGE(number1,number2,…) and n is the sample size. Shouldn't it be n, rather than n - 1, in the ...
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### OLS is BLUE. But what if I don't care about unbiasedness and linearity?

The Gauss-Markov theorem tells us that the OLS estimator is the best linear unbiased estimator for the linear regression model. But suppose I don't care about linearity and unbiasedness. Then is ...
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### Unbiased estimation of covariance matrix for multiply censored data

Chemical analyses of environmental samples are often censored below at reporting limits or various detection/quantitation limits. The latter can vary, usually in proportion to the values of other ...
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