Theory of Statistics

Suppose Y1, . .., Yn are i.i.d. Poisson(A). Consider the testing problem: Ho : 1 = do VS H1 : d * do. (a) show that the log-likelihood ratio statistic is given by -2 log A(Y) = 2n (10 - A) - Alog (do/A) , where A = _; Yi. (b) Using Taylor expansion, prove the Wilk's phenomenon directly: -2log >(Y) +d Xi