From Algorithms to Z-Scores - matloff - University of California, Davis

Chapter 12
General Statistical Estimation and
Inference
Earlier, we often referred to certain estimators as being “natural.” For example, if we are estimating
a population mean, an obvious choice of estimator would be the sample mean. But in many
applications, it is less clear what a “natural” estimate for a parameter of interest would be. 1 We
will present general methods for estimation in this section.
We will also discuss advanced methods of inference.
12.1 General Methods of Parametric Estimation
Let’s begin with a simple motivating example.
12.1.1 Example: Guessing the Number of Raffle Tickets Sold
You’ve just bought a raffle ticket, and find that you have ticket number 68. You check with a
couple of friends, and find that their numbers are 46 and 79. Let c be the total number of tickets.
How should we estimate c, using our data 68, 46 and 79?
It is reasonable to assume that each of the three of you is equally likely to get assigned any of the
numbers 1,2,...,c. In other words, the numbers we get, Xi, i = 1,2,3 are uniformly distributed on
the set {1,2,...,c}. We can also assume that they are independent; that’s not exactly true, since
1 Recall that we are using the term parameter to mean any population quantity, rather an an index into a parametric
family of distributions.
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