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Inference for the Mean

February 7, 2019 @ 4:30 pm - 5:30 pm

2/7/2019 Colloquium

Speaker: Ulrich Mueller (Princeton)

Title: Inference for the Mean

Abstract: Consider inference about the mean of a population with finite variance, based on an i.i.d. sample. The usual t-statistic yields correct inference in large samples, but heavy tails induce poor small sample behavior. This paper combines extreme value theory for the smallest and largest observations with a normal approximation for the t-statistic of a truncated sample to obtain more accurate inference. This alternative approximation is shown to provide a refinement over the standard normal approximation to the full sample t-statistic under more than two but less than three moments, while the bootstrap does not. Small sample simulations suggest substantial size improvements over the bootstrap.


February 7, 2019
4:30 pm - 5:30 pm
Event Category:


20 Garden Street
Cambridge, MA 02138 United States
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