ay">\[
\textrm{err} = \hat{\theta} - \theta.
\]</span></p>
<p>If the estimate is larger than the true value, the error is positive, and if it’s smaller, then error is negative. If an estimator’s unbiased, then expected error is zero. So typically, absolute error or squared error are used, which will always have positive expectations for an imperfect estimator. <em>Absolute error</em> is defined as <span class="math display">\[
\textrm{abs-err} = \left| \hat{\theta} - \theta \right|
\]</span> and <em>squ