# Unbiased Estimators

In this article we will limit our-self to the class of estimators with the same bias for $\theta$.

$$C_\tau = {W: E_\theta[W]=\tau(\theta)}$$

In this article we will first define an unbiased estimator. Then, we will go through different techniques to find the best unbiased estimator if it exists.

In many critical applications it is required to find unbiased estimators. For such applications it is preferred to find the best unbiased estimator.

# 1. Best Unbiased Estimator Definition

An estimator $W^*$ is best unbiased estimator for for $\tau(\theta)$ if it satisfies $E_\theta[W^*]=\tau(\theta)$ for all $\theta$ and for any other estimator $W$ satisfying $E_\theta[W]=\tau(\theta)$ for all $\theta$.… Read more