Question: Consider the statistical product model .Rn;Bn;Q n # W # 2 R/, where Q# is the socalled two-sided exponential distribution or Laplace distribution centred at

Consider the statistical product model .Rn;Bn;Q

˝n

W # 2 R/, where Q# is the socalled two-sided exponential distribution or Laplace distribution centred at #, namely the probability measure on .R;B/ with density

#.x/ D 1 2 e

jx#j

; x2 R:

Find a maximum likelihood estimator of # and show that it is unique for even n only. Hint:

Use Problem 4.15.

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