# 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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### What are some well-known unbiased estimator of regression coefficient besides OLS estimator?

Is there any other unbiased estimator of regression coefficient than OLS? For instance, one might consider using unbiased estimator with less computational cost (since OLS involves matrix inversion)?
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### Show unbiased OLS estimator and expression for variance of OLS estimator

Consider the usual linear mixed model: $$Y=X \beta+ZB+\epsilon$$ where Y and $\epsilon$ are $n$-dimensional random variables and $B$ is a $q$-dimensional random variable independent of $\epsilon$ so ...
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### Correct bias with known DAG

I have the following causal graph: $T \to P$ $(T, P) \to S$ So $T$ causes $P$ (partially) and $T$ and $P$ both cause $S.$ If I just regress $S\,\text{~}\,T + P,$ I will get an overestimated effect for ...
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### Unbiased Estimator for Mean Response to Treatment

$\newcommand{\eps}{\varepsilon}\newcommand{\szdp}[1]{\!\left(#1\right)}$ Problem Statement: Consider the following model for the responses measured in a randomized block design containing $b$ blocks ...
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### If $T$ is a complete sufficient statistic, then $Cov(T, U)=0$ for all unbiased $U$ [duplicate]

I want to prove the following- Show that if $T$ is complete sufficient for $θ$, then $Cov_θ(T, U) = 0$ for all $θ ∈ Θ$ and for all $U$ satisfying $E_θ(U) = 0$ for all $θ ∈ Θ$. I think in essence it ...
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### Unbiased estimator of minimum order statistic

Let $X_1,X_2$ and $X_3$ be a random sample taken from a continuous population with distribution function F. Consider the function $E(X_{1:3})$ , where $X_{1:3}$ is the minimum order statistic. Can ...
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### Does the biased estimator always have less variance than unbiased one?

Suppose I am estimating one of the parameter. Now if we plot the biased estimator of that and unbiased estimator of that can we say for sure that biased one has less variance than unbiased one always. ...
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### What is an "unbiased forecast"?

Assume we estimate a model from the data $(X, Y)$, with some estimator $W(X, Y)$, which is estimating parameters $\theta$ for the model we chose. Then, we would like to perform a forecast for $Y_h$ ...
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### How to explain intuitively to a lay audience that the variance is an unbiased estimator?

I have data for the concentration of several chemicals in the milk of 10000 cows and have to explain to policymakers and the lay public (i.e. people with no or limited knowledge of statistics) that ...
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There is a theorem (here, Theorem 3.2.) which says: Let $x_i \sim p_i(\mu_i, \sigma_i^2)$ for $1 \leq i \leq n$ be a set of pairwise uncorrelated random variables. Consider the linear estimator \$y_{n,...