\(\displaystyle{{s}_{{{p}}}^{{{2}}}}\) is an unbiased estimator for

alparcero97oy

alparcero97oy

Answered question

2022-04-01

sp2 is an unbiased estimator for σ2
We have, (n11)s12σ2X(n11)2
(n21)s22σ2x(n21)2
(n11)s12σ2+(n21)s22σ2x(n1+n22)2
Var(sp2)=2σ4n1+n22

Answer & Explanation

Carter Lin

Carter Lin

Beginner2022-04-02Added 13 answers

The variance of the Xn1+n222 distribution is 2(n1+n22).
Since your estimator is obtained by multiplying that χ{n1+n22}2 random variable by σ2n1+n22, the variance is
2(n1+n22)(σ2n1+n22)2=2σ4n1+n22.
[This is using the fact that Var(aX)=a2Var(X).

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