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2. (10 points) Let XP, and let ^ denote the MLE of . Suppose that h i.pdf

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2. (10 points) Let XP, and let ^ denote the MLE of . Suppose that h is a one-to-one function from onto h(). Define =h() and let f(x,) denote the density or frequency function of X in terms of (i.e., reparametrize the model using ). Show that the MLE of is h(^) (i.e., MLEs are unaffected by reparametrization, they are equivariant under one-to-one transformations)..

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2. (10 points) Let XP, and let ^ denote the MLE of . Suppose that h is a one-to-one function from onto h(). Define =h() and let f(x,) denote the density or frequency function of X in terms of (i.e., reparametrize the model using ). Show that the MLE of is h(^) (i.e., MLEs are unaffected by reparametrization, they are equivariant under one-to-one transformations).

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  • 1. 2. (10 points) Let XP, and let ^ denote the MLE of . Suppose that h is a one-to-one function from onto h(). Define =h() and let f(x,) denote the density or frequency function of X in terms of (i.e., reparametrize the model using ). Show that the MLE of is h(^) (i.e., MLEs are unaffected by reparametrization, they are equivariant under one-to-one transformations).