Apointestimator is locationinvariant if forallpossibledataandallconstants c, when weadd c to eachobservation,theestimatorincreasesby c. Itis scaleinvariant if whenwe

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Apointestimator ˆθ is locationinvariant if forallpossibledataandallconstants

c, when weadd c to eachobservation,theestimatorincreasesby

c. Itis scaleinvariant if whenwe multiplyeachobservationby c > 0, theestimatormultipliesby c.

(a) Showthat Y is locationinvariantand S is scaleinvariant.

(b) IstheBayesestimatorofthemeanofanormaldistributionlocationinvariant?Whyor whynot?

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