Lecture 27+. The Bootstrap Method: Simulation Resultszuev/teaching/2013Spring... · Math 408 -...
Transcript of Lecture 27+. The Bootstrap Method: Simulation Resultszuev/teaching/2013Spring... · Math 408 -...
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
Konstantin Zuev (USC) Math 408, Lecture 27+ April 8, 2013 3 / 7
Confidence Intervals for µ, n = 100
Konstantin Zuev (USC) Math 408, Lecture 27+ April 8, 2013 4 / 7
Confidence Intervals for σ, n = 100
Konstantin Zuev (USC) Math 408, Lecture 27+ April 8, 2013 5 / 7
Confidence Intervals for µ, n = 1000
Konstantin Zuev (USC) Math 408, Lecture 27+ April 8, 2013 6 / 7
Confidence Intervals for σ, n = 1000
Konstantin Zuev (USC) Math 408, Lecture 27+ April 8, 2013 7 / 7