{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# lec11 - .1 Sufficient statistic(Textbook Section 6.7 We...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture 11 11.1 Sufficient statistic. (Textbook, Section 6.7) We consider an i.i.d. sample X 1 , . . . , X n with distribution θ from the family { θ : θ ∈ Θ } . Imagine that there are two people A and B, and that 1. A observes the entire sample X 1 , . . . , X n , 2. B observes only one number T = T ( X 1 , . . . , X n ) which is a function of the sample. Clearly, A has more information about the distribution of the data and, in par- ticular, about the unknown parameter θ. However, in some cases, for some choices of function T (when T is so called sufficient statistics) B will have as much information about θ as A has. Definition. T = T ( X 1 , ··· , X n ) is called sufficient statistics if θ ( X 1 , . . . , X n | T ) = ( X 1 , . . . , X n | T ) , (11.1) i.e. the conditional distribution of the vector ( X 1 , . . . , X n ) given T does not depend on the parameter θ and is equal to . If this happens then we can say that T contains all information about the param- eter θ of the disribution of the sample, since given T the distribution of the sample is always the same no matter what θ is. Another way to think about this is: why the second observer B has as much information about θ as observer A? Simply, given T , the second observer B can generate another sample X 1 , . . . , X, ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

lec11 - .1 Sufficient statistic(Textbook Section 6.7 We...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online