(a) Prove that a decision rule, which is admissible under squared-error loss, is also admissible under a weighted squared-error loss where the weight, w( (J), is greater than zero for all   (b) Show...

(a) Prove that a decision rule, which is admissible under squared-error loss, is also admissible under a weighted squared-error loss where the weight, w( (J), is greater than zero for all

(b) Show that the Bayes action can be different for a 'weighted squared-error loss, than for squared-error loss.

(c) Find a weighted squared-error loss for which I3c in Example 4 of Chapter 1 has a constant risk function. (The weight can depend upon c.)