Complete Statistics, Ancillary Statistics, and Basu's Theorem

Learn about ancillarity, complete statistics, and Basu’s Theorem!
Sufficient Statistics: • Sufficient Statistics ...
Minimal Sufficient Statistics: • Minimal Sufficient Sta...
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[@廖景鑫]

Great video!! But in 11:51, when stating "if the parameter space contains an open set", you should explictly state that inside which metric space or topological space(I assume it's R^k in this theorem) is it considered open, to avoid confusion. This is important because it could happen that M⊆B⊆A, and M is not open in A but M is open in B, due to definition of openess in metric space.
For example in 16:51, a set containing only an integer is not open in R(set of all real number), but open in Z(set of all integers), when consider both R and Z as metric space with Euclidean distance as metric.

[@statswithbrian]

Yes, R^k.

[@jakeaustria5445]

Thank You

[@st8k490]

great content, keep it up

[@emiliovillagran8187]

I’ve exam tomorrow and noticed you uploaded the video 20 minutes ago 😂 That’s a signal

[@statswithbrian]

😂

[@MarcoBova]

really neat video, could you do one on estimators and LME?

[@statswithbrian]

If by LME you mean linear mixed-effects models, probably not any time soon, but that's a good idea. I have lots of videos on estimators and their properties though (MLE, MoM, Consistency, Unbiasedness, CRLB etc)

[@nickmillican22]

I don't understand the first "not-complete" example. E[X_1 - X_2] = E[X_1] - E[X_2] = mu - mu = 0, no?

[@statswithbrian]

Correct - it’s 0. The definition of completeness tells us that if that expected value is zero, then the function must also be 0 everywhere. But X1-X2 is basically never 0.