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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
Above are mean and variance of
normal for reference
orchestra answered 1 year agoRelated Solutions
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