note6c - STAT5044: Regression and Anova Inyoung Kim Outline...

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STAT5044: Regression and Anova Inyoung Kim
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Outline 1 How to make an inference without normality assumption
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Inference without normality in one population Example1 : you want estimate the median of a population but don’t know the functional form of the density Step1. Take a random sample y 1 , y 2 , ..., y n from the population Step2. Calculate the sample median, let’s call it ˆ M this is a point estimate but we have no idea of its dist. and so can’t build C.I. Step3. Repeat step 1 and 2, many times say B Now you have B independent ˆ M 1 , . . . , ˆ M B Your estimate for the pop. median is their average ˆ M = B b = 1 ˆ M b B Problem: You only take 1 random sample in real life, not some large number NB of seperate random samples Bootstrap solution: Take NB random samples with replacement of size n from the original data y 1 , y 2 , ..., y n
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Inference without normality in one population Example1: you want test whether your the median of a population is zero or not Your CI with 95% confidence is 2.5 percentile and 97.5 percentile of your ˆ M 0 s If your CI includes zero, there is statistical evidence that median is zero.
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note6c - STAT5044: Regression and Anova Inyoung Kim Outline...

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