Math 408 - Mathematical Statistics

Lecture 27+. The Bootstrap Method: Simulation Results

April 8, 2013

Konstantin Zuev (USC) Math 408, Lecture 27+ April 8, 2013 1 / 7

Example: Gaussian ModelSuppose that:

X1, . . . ,Xn ∼ N (µ, σ2), true values: µ = 1 and σ = 2

Exact Confidence Intervals:

µ : µ̂MLE ±1√n − 1

σ̂MLEtn−1(α/2) σ2 :

(nσ̂2

MLE

χ2n−1(α

2 ),

nσ̂2MLE

χ2n−1(1− α

2 )

)

Konstantin Zuev (USC) Math 408, Lecture 27+ April 8, 2013 2 / 7

Bootstrap

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Confidence Intervals for µ, n = 100

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Confidence Intervals for σ, n = 100

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Confidence Intervals for µ, n = 1000

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Confidence Intervals for σ, n = 1000

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