Suppose two economists estimate (the average expenditure of British families on food) with two unbiased (and statistically independent) estimates U and V. The second economist is less careful than the first: the standard deviation of V is 3 times as large as the standard deviation of U. When asked how to combine U and V to get a publishable overall estimate, three proposals are made:
W1 =1⁄2U+1⁄2V(simpleaverage) W2 =3⁄4U+1⁄4V(weightedaverage) W3 = 1 U + 0 V (drop the less accurate estimate)
(a) Which are unbiased? (b) Which is the best estimator? The worst? (c) Is it possible to find an even better estimator?
Can you please explain this?|||Stats is all about quantifying uncertainty, so if you are absolutely sure that the additional variability of V is due to avoidable data acquisition errors, then throw them out. Who needs data that are predictably erroneous when sufficient data that meet your requirements are available?
(a) All are unbiased because U and V are both unbiased.
(b) W3 is best because it excludes V. W1 is worst because it is 50% V.
(c) Yes, with a larger sample size, conducted carefully,
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