Suppose X is uniformly distributed on {-1,1} and Z has probability
density function -1
fz(z)=σ exp(-z/σ)I(z>=0),where σ>0 and
I(z>=0) equals 1 if z>=0 and 0otherwise.
For an odd n, let Y1,...Yn be a random sample on Y=XZ+μ,
where -∞<μ<∞.
(a) Find the MME of μ
(b) Find the MLE of μ and σ
(c) Derive the asymptotic distribution of the estimators of μ in(a)
and (b) and compare them
(d) Derive an approximately levelα test for H0:μ<=0 versus H1:μ>0
這類有指標函數混雜的題型 我不知到該從何處下手
請高手指導解惑 感謝!
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