Qm
Statistics

Split an estimator's error into bias and variance

bias-variancemseestimators

A desk wants to estimate the true fair value θ\theta of an illiquid bond. Estimator A is unbiased (right on average) but jumps around, with variance 16. Estimator B is biased 3 units too high on average but is much steadier, with variance only 4.

The mean squared error of any estimator splits cleanly into two pieces: MSE=Variance+Bias2\text{MSE} = \text{Variance} + \text{Bias}^2.

Which estimator has the smaller MSE, and what is that value?

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Bandwidth Selection for SmoothersThe Bias-Variance DecompositionChoosing k and Distance Weighting in k-NNBias, Variance, and the Quality of EstimatorsIrreducible Error and the Bayes Rate

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