statistical inference - bias varaince tradeoff

Bias Variance Tradeoff

{% Mean \, Square \, Error = \mathbb{E}[(\hat{\theta} - \theta)^2] %}

{% Var[\hat{\theta}] = \mathbb{E}[(\hat{\theta} - \mathbb{E}[\hat{\theta}])^2] %}

{% Bias[\hat{\theta}] = \mathbb{E}[(\mathbb{E}[\hat{\theta}] - \theta)^2] %}

{% Mean \, Square \, Error = Var[\hat{\theta}] + Bias[\hat{\theta}] ^2 %}