# Questions tagged [estimators]

A rule for calculating an estimate of a given quantity based on observed data [Wikipedia].

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### What is the difference between a consistent estimator and an unbiased estimator?

I'm really surprised that nobody appears to have asked this already... When discussing estimators, two terms frequently used are "consistent" and "unbiased". My question is simple: what's the ...
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### What is the relation between estimator and estimate?

What is the relation between estimator and estimate?
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### When is a biased estimator preferable to unbiased one?

It's obvious many times why one prefers an unbiased estimator. But, are there any circumstances under which we might actually prefer a biased estimator over an unbiased one?
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### Correlation between OLS estimators for intercept and slope

In a simple regression model, $$y = \beta_0 + \beta_1 x + \varepsilon,$$ the OLS estimators $\hat{\beta}_0^{OLS}$ and $\hat{\beta}_1^{OLS}$ are correlated. The formula for the correlation ...
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### How does one explain what an unbiased estimator is to a layperson?

Suppose $\hat{\theta}$ is an unbiased estimator for $\theta$. Then of course, $\mathbb{E}[\hat{\theta} \mid \theta] = \theta$. How does one explain this to a layperson? In the past, what I have said ...
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### Estimating unconditional variance in time series

Consider a time series process with a well-defined, finite unconditional variance. Given a realization of the process (a time series) and a model for it, there are at least two ways of estimating the ...
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### Paired comparison of instruments using different measurement samples

I have instruments A, B, C and D - I'm in search of the best one. The problem: For illustrative purposes, let's use an example of evaluating the best among the instruments measuring difference in ...
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### parameter estimator

I have a probability density function $$\frac{4x\arctan(\frac{x}{a})}{a^2(\pi-2)}$$ $0≤x≤a\,,\quad$ where $a>0$. I need to find an estimator using some order statistic. Does maximum ...
### constant $\times$ distribution
I know that if $U\sim\chi^2(k)$ then $aU\sim \Gamma(k/2,2a)$ for $a>0$. But i read about the estimator and its distribution \hat{\sigma}_k^2=\frac{1}{2k}\sum_{i=1}^k (X_{2i}-X_{2i-1})^2=\frac{2\...