Let X1,…,Xn∼i.i.d.N(0,σ2), for some σ2>0. Let σ2ˆ=1n∑i=1nX2i,andσ2˜=1n∑i=1n(Xi−Xnbar)2. Argue that both proposed estimators σ2ˆ and σ2˜ below...

Let X1,…,Xn∼i.i.d.N(0,σ2), for some σ2>0. Let σ2ˆ=1n∑i=1nX2i,andσ2˜=1n∑i=1n(Xi−Xnbar)2. Argue that both proposed estimators σ2ˆ and σ2˜ below are consistent and asymptotically normal. Then, give their asymptotic variances V(σ2ˆ) and V(σ2˜) and decide if one of them is always bigger than the other. Hint: Use the multivariate Delta method.

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orchestra answered 1 year ago

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