1 answer

2. Let X1, X2, ...,Xbe i.i.d. Poisson with parameter .. (a) Find the maximum likelihood estimator...

Question:

2. Let X1, X2, ...,Xbe i.i.d. Poisson with parameter .. (a) Find the maximum likelihood estimator of . Is the estimator minim

2. Let X1, X2, ...,Xbe i.i.d. Poisson with parameter .. (a) Find the maximum likelihood estimator of . Is the estimator minimum variance unbi- ased? (b) Derive the asymptotic (large-sample) distribution of the maximum likelihood estimator. (c) Suppose we are interested in the probability of a zero: Q = P(Xi = 0) = exp(-). Find the maximum likelihood estimator of O and its asymptotic distribution.

Answers

a) The pmf of X is f(x) ,x = 0,1,2,. Let X, X, X be a random sample of sizen is taken from above poisson distributi on 2 The

b) The likelihood function is L T,A) i-1 =f (x, A)(A)(%.A) ,-а джа e eMA +In AIn (( 1)) x; In A-In (T(x) = -nA ln e i-1 =-nA

.

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