Tradeoff Between Bias and Efficiency in Variance Estimation
Consider a scenario in which an estimator \(\hat{\theta}\) of a parameter \(\theta\) is unbiased, meaning \(E[\hat{\theta}] = \theta\), and has variance \(Var(\hat{\theta})\). Another estimator \(\tilde{\theta}\) is slightly biased, but with a lower mean squared error (MSE). (a) Explain, with proof, how a linear transformation of an unbiased estimator affects its unbiasedness. Under what specific condition […]