Fisher information, sufficiency, and ancillarity: some clarifications

摘要

Misconceptions are many when it comes to Fisher information, sufficiency, and ancillarity, especially among beginners. Many believe that I_(T_1)(θ) + I_(T_2)(θ) should equal I_(T_1)+I_(T_2)(θ) for all θ. We exhibit precise scenarios where I_(T_1)+I_(T_2)(θ) is ＜, =, or ＞I_(T_1)(θ) + I_(T_2)(θ) for all θ. Then, we clarify the process of verifying ancillarity of a statistic with concrete examples.