Overview
On this page, we discuss general estimators of a population parameter, and possible ways to measure their “trustworthiness”: bias, variance, and mean squared error (MSE).
Basic learning objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
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When a statistic is used to estimate the value of a parameter, we refer to it an as estimator. Be able to construct the sampling distribution of an estimator. Distinguish between an estimator, which is a random variable, and an estimate, which is a particular value of that random variable.
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Understand that the bias of an estimator measures the difference between its expected value and the value of the parameter its being used to estimate, and know the precise definition of bias.
Advanced learning objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
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Be able to compute the bias, variance, and mean squared error (MSE) of an estimator from its sampling distribution, and be able to compute any of those quantities quickly from the other two using the bias-variance decomposition of the MSE.
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Understand the intuitive meaning of low & high bias, and low & high variance in the context of estimation.
To prepare for class
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Watch the following video (by Khan Academy) which shows several examples of biased and unbiased estimators of a parameter and how to intuitively recognize them from the sampling distribution:
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Watch the following video (by Brendan Cordy) which uses the median of a sample as an estimator for the (in this case known) population median, and shows the detailed calculations of its sampling distribution, bias, variance, and mean squared error:
After class
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Watch the following video (by jbstatistics) which gives an intuitive explanation (using the so-called degrees of freedom) for the correct formula for the sample variance to make it an unbiased estimator of the unknown population variance:
