Question

In: Statistics and Probability

Problem 4 (unbiased, efficient, and consistent estimators). Suppose we have n i.i.d. samples distributed according to...

Problem 4 (unbiased, efficient, and consistent estimators). Suppose we have n i.i.d. samples distributed according to N (µ, σ2 ). Consider two estimators for µ: X¯ = 1 n Pn i=1 Xi and Xˆ = 1 2 (X1 + Xn).

A) Calculate the mean of X¯ and Xˆ. Are they unbiased?

B) Calculate the variance of X¯ and Xˆ. Which one is more efficient?

C) If n → ∞, X¯ and Xˆ will converge to what? which one is the consistent estimator?

Solutions

Expert Solution

Above are mean and variance of normal for reference


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