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Thread: Joint distribution, score function, likelihood

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    Post Joint distribution, score function, likelihood

    Can anyone help me with this problem?


    Consider the following statistical model

    Yi=μ+(1+α xi)*εi, εi ~ iid N(0,1) i= 1,....,n
    Where μ ∊ R and α ]-1,1[ are unkown parameters, while xi ∊ ]-1,1[ are known numbers.

    1. Determine the joint distribution of Y1,....,Yn and find the distribution of the mean of the Ys. Explain that the mean of the Ys is a consistent estimator of μ.

    2. Find the score function and the expected information. Give the approximate distribution of the maximum likelihood estimator of (α, δ) in large samples.

    3. Set up the score statistic for the hypothesis H0: α = 0 and specify its approximate distribution under the hypothesis.
    Attached Thumbnails Attached Thumbnails Joint distribution, score function, likelihood-16586659_10154952699419417_832136412_o.png  
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