Estimators

What?

Statistical functions used to estimate a population parameter based on sample data.

Keep in Mind:

• Bias: An estimator is unbiased if the expected value of the estimation is equal to the true value of the population parameter.
  • $\text{bias}=E[\hat{\theta }-\theta ]=E[\hat{\theta }]-\theta$
• Consistency: A consistent estimator gives you increasingly accurate estimates of the population parameter as the sample size grows

What about the variance (Mean Squared Error) of it?

Typical variance definition. Ideally, your estimator varies vary little.

• $\text{MSE}=E[(\hat{\theta }-\theta {)}^2]$

Variance & Bias