4. Ancillarity

Question 1

Ancillary statistic

Answer 1

A function of the sample with distribution not depending on @ i.e. does not provide information on @

Question 2

Location family

Answer 2

X ~ F_x = f(x-@)
X=Z+@
e.g. a normal with variance 1, the mu is the location parameter

Question 3

Scale family

Answer 3

X ~ F_x=f(x/@)/@
X=@Z
e.g. in the exponential distribution @=1/lambda

Question 4

How to construct an ancillary statistic

Answer 4

Location family: differences of sample elements
Scale family: ratios of sample elements
e.g. the normal