Consider n independentobservationsfroma N(, 2) distribution. (a) Focusingon , findthelikelihoodfunction.Showthatthelog-likelihoodfunctionisa concave,parabolicfunctionof . FindtheMLestimator . (b) Considering 2
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Consider n independentobservationsfroma N(μ, σ2) distribution.
(a) Focusingon μ, findthelikelihoodfunction.Showthatthelog-likelihoodfunctionisa concave,parabolicfunctionof μ. FindtheMLestimator ˆμ.
(b) Considering σ2 to beknown,findtheinformationusing(i)equation(4.3),(ii)equation
(4.4). Usethemtoshowthatthelarge-samplevarianceof ˆμ is σ2~n. Explainwhy ˆμ is the minimumvarianceunbiasedestimator.
(c) ShowthattheMLestimator ˆσ of σ is
¼
[Σi(Yi − Y )2]~n. Showthatthe large-sample varianceof ˆσ is σ2~2n.
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Foundations Of Statistics For Data Scientists With R And Python
ISBN: 9780367748456
1st Edition
Authors: Alan Agresti
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