Let Y₁, Y2, Y3,..., Yn ind 1. Find the asymptotic distribution of Z := the asymptotic distribution of μ? N(μ, o²), where ² μμ √o²/n = 25 is known. where is the MLE. Hint: what is 2. Suppose now we do not know o2 and instead plug in the MLE estimator 2 1/1(Y₂-μ)² to obtain Z := μμ Is the asymptotic distribution still N(0, 1)? If yes, why? (hint: what do we know about consistency of MLEs? Slutsky's theorem?). √ô²/n 3. Suppose we collect data of size n = 16 and the MLE turns out to be û = 2 and ² = 25. Using the result from the previous part, conduct an a = .05 level test of Hoμ = 0 in favor of Haµ ‡0. Find the critical value, rejection region, and p-value. Interpret the p-value. Do you reject or fail to reject the null?
Let Y₁, Y2, Y3,..., Yn ind 1. Find the asymptotic distribution of Z := the asymptotic distribution of μ? N(μ, o²), where ² μμ √o²/n = 25 is known. where is the MLE. Hint: what is 2. Suppose now we do not know o2 and instead plug in the MLE estimator 2 1/1(Y₂-μ)² to obtain Z := μμ Is the asymptotic distribution still N(0, 1)? If yes, why? (hint: what do we know about consistency of MLEs? Slutsky's theorem?). √ô²/n 3. Suppose we collect data of size n = 16 and the MLE turns out to be û = 2 and ² = 25. Using the result from the previous part, conduct an a = .05 level test of Hoμ = 0 in favor of Haµ ‡0. Find the critical value, rejection region, and p-value. Interpret the p-value. Do you reject or fail to reject the null?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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
Transcribed Image Text:Let Y₁, Y2, Y3,..., Ynd N(μ, o²), where o²
1. Find the asymptotic distribution of Z =
the asymptotic distribution of μ?
n
= 25 is known.
=
2. Suppose now we do not know o² and instead plug in the MLE estimator ²
Ĥ-μ
-, where is the MLE. Hint: what is
√o²/n'
Σ1(Yi - μ)² to obtain Z := Is the asymptotic distribution still N(0, 1)? If
yes, why? (hint: what do we know about consistency of MLEs? Slutsky's theorem?).
.
=
3. Suppose we collect data of size n = 16 and the MLE turns out to be û = 2 and ô² = 25.
Using the result from the previous part, conduct an a = .05 level test of Hou 0
in favor of H₁ : µ ‡0. Find the critical value, rejection region, and p-value. Interpret
the p-value. Do you reject or fail to reject the null?
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