Which of the following parametrizations are identifiable? (Prove or disprove.) one treatment is beneficial or not often reduces to the pr9blem of deciding whether

for some parameter See Let the actions corresponding to deciding whether

be penoted by -1, 0, 1, respectively and suppose the loss function is given by (from Lehmann, 1957)

where b and c are positive. Suppose X is a sample and consider the decision rule

(a) Show that the risk function is given by

Where is the N(0, 1) distribution function.

(b) Plot the risk function when b = c = 1, n = I and

For what values of 8 does the procedure with r = -s = -1 have smaller risk than the procedure with