5102-Lecture-05

# 5102-Lecture-05 - Lecture 5 Stat 5102-004 28 January 2011...

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Unformatted text preview: Lecture 5 Stat 5102-004 28 January 2011 Parametric Inference 1. Inference about the family 1.1 Point Estimation I Guess a distribution by guessing a point. 1.2 Region Estimation I Guess a set of distributions by guessing a region. 1.3 Hypothesis Testing I Choose among hypotheses by choosing among predefined regions. 2. Prediction via parametric families STAT 5102 (Theory of Statistics) Lecture 5 1 / 13 Point Estimation Suppose Y 1 , . . . , Y 25 iid ∼ N( μ, σ 2 ) with μ and σ 2 both unknown. ● μ σ 2-6-4-2 2 4 6 1 2 3 4 ¯ y =- 1 . 06 s 2 = 0 . 87 STAT 5102 (Theory of Statistics) Lecture 5 2 / 13 Point Estimation A point estimator is a function mapping data to parameter values. Traditionally, point estimators wear hats. ˆ θ : Y → ϑ ˆ θ is an estimator of θ The estimator is a function, a rule, an engine for making estimates. Suppose we choose to estimate a population mean with a sample mean....
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5102-Lecture-05 - Lecture 5 Stat 5102-004 28 January 2011...

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