A biased estimator may be preferable to an unbiased estimator if:
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the unbiased estimator has substantially less variability than the biased one.
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the biased estimator has more variability than the unbiased one.
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the biased estimator has substantially less variability than the unbiased one.
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The only occasion where one would use a biased estimator is if an unbiased estimator did not exist.