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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: tpivot and Fpivot: Definition :A tpivot 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 ”ttype”. Definition :A Fpivot has the following form: T ( x ) q ( θ ) , where T ( x ) > ,q ( θ ) > ....
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This note was uploaded on 09/22/2009 for the course ORIE 3500 taught by Professor Weber during the Summer '08 term at Cornell.
 Summer '08
 WEBER

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