Chapter 8. Estimation

The code for this chapter is in For information about downloading and working with this code, see Using the Code.

The Estimation Game

Let’s play a game. I think of a distribution, and you have to guess what it is. I’ll give you two hints: it’s a normal distribution, and here’s a random sample drawn from it:

[-0.441, 1.774, -0.101, -1.138, 2.975, -2.138]

What do you think is the mean parameter, μ, of this distribution?

One choice is to use the sample mean, , as an estimate of μ. In this example, is 0.155, so it would be reasonable to guess μ = 0.155. This process is called estimation, and the statistic we used (the sample mean) is called an estimator.

Using the sample mean to estimate μ is so obvious that it is hard to imagine a reasonable alternative. But suppose we change the game by introducing outliers.

I’m thinking of a distribution. It’s a normal distribution, and here’s a sample that was collected by an unreliable surveyor who occasionally puts the decimal point in the wrong place.

[-0.441, 1.774, -0.101, -1.138, 2.975, -213.8]

Now what’s your estimate of μ? If you use the sample mean, your guess is -35.12. Is that the best choice? What are the alternatives?

One option is to identify and discard outliers, and then compute the sample mean of the rest. ...

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