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Results tagged with unbiased-estimator
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user 127096
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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For OLS to be unbiased, do we need $x_i$ to be uncorrelated with $\epsilon_i$ or with $\epsi...
In some textbooks I've read, it is said that an assumption for OLS to be unbiased in the standard cross-sectional model $y_i=\alpha + \beta \cdot x_i +\epsilon_i$, we can use the assumption $E(\epsilo …
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Proving OLS unbiasedness without conditional zero error expectation?
The OLS estimate $b$ is equal to $(X^TX)^{-1}X^Ty$ for the linear regression model. If we assume that $E(\epsilon|X)=0$ then it is easy to prove simply by taking the conditional expectation, of $b$ su …
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Standard errors of OLS estimate if regressor is a stochast?
Assume the model classical linear regression model (with for simplicity only one regressor)
$$y=X\beta +u,$$
with $u$, $X$ independent, and $\operatorname{Var}(u|X)=\sigma^2I_n$. Assume for simplicity …
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Is the mean (Bayesian) posterior estimate of $\theta$ a (Frequentist) unbiased estimator of ...
I am wondering about the different ways that Bayesian and Frequentist statistic connect with each other.
I recalled that the Maximum Likelihood estimate of a parameter $\theta$ is not necessarily an u …
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