Deciphering the Definition of Complete Statistic

I have yet to find a textbook that explains this clearly, so when I found clues in some lecture notes, I pieced this together. Hopefully this video will spare you some grief!

[@vuthanhphan6565]

Thank you so much.

[@vittoriosalvatore6066]

Great explanation! ty so much!! :D

[@zhengzhang9451]

Wonderful video and it is really friendly to layman who is wanna learn more about the implications behind these theorems. I have a short question why E(h(t)) would not be necessarily zero given h(t) = u1- u2 and e(u1) = e(u2)? Looking forward to explanations! Thanks!

[@fc4511]

Assume that for a certain theta, name it theta 1, E(u1) = E(u2) = theta1, but for another theta, theta2, E(u2) != theta2 = E(u1), then E(h(t)) != 0 for all theta, thus u1(t) is not complete. If for all theta u1(t) = u2(t) it implies that u1(t) = u2(t) = u(t), thus u is unique, thus complete, does that make any sense?

[@stephennemo7676]

Exactly the same proof as for uniqueness of PDE solutions... cool...