{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Section11Notes

# Section11Notes - Section Notes for Week 11 In this section...

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: Section Notes for Week 11 In this section, we are going to discuss ”Pivot Method” for confidence intervals, which is one of the most important methods to find confidence intervals, and is convenient to implement. Definition : If X 1 , ··· ,X n ∼ f ( x,θ ), and θ is unknown. A pivot is a function of the data X = ( X 1 , ··· ,X n ) and of θ whose distribution does not depend on θ . Note: A pivot is not a statistics, but a statistics is a pivot. Exp1: If X 1 , ··· ,X n ∼ N ( θ, 1) and are i.i.d, and θ is unknown: ¯ X ∼ N ( θ, 1 /n ), and ¯ X- θ ∼ N (0 , 1 /n ). Thus, ¯ X- θ is a pivot. There are two important types of pivots: t-pivot and F-pivot: Definition :A t-pivot has the following form: T ( x )- q ( θ ) S ( x ) , where S ( x ) > Recall how we introduced t distribution to get some idea of why this is called ”t-type”. Definition :A F-pivot has the following form: T ( x ) q ( θ ) , where T ( x ) > ,q ( θ ) > ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Section11Notes - Section Notes for Week 11 In this section...

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

View Full Document
Ask a homework question - tutors are online