Hello! I have a question about the following problem, not sure how to approach it... This...

Hello! I have a question about the following problem, not sure how to approach it...

This is from Mathematical Statistics and Data Analysis, Chapter 11, Problem 11.41

The Hodges-Lehmann shift estimate is defined to be d =median(Xi −Yj), where X₁ , X₂ , . . . , X_n are independent observations from a distribution F and Y₁,Y₂,...,Y_m are independent observations from a distribution G and are independent of the X_i.

Show that if F and G are normal distributions, then E(d) = μ_x − μ_y.
Why is d robust to outliers?
Use the bootstrap to approximate the sampling distribution and the standard error of d.
From the bootstrap approximation to the sampling distribution, form an approximate 90% confidence interval for d

Thank you

Expert Solution

orchestra answered 2 years ago

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