notes-10-04

notes-10-04 - M4056 Lecture Notes. Monday, October 4, 2010...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
M4056 Lecture Notes. Monday, October 4, 2010 We now look at methods for evaluating the quality of estimators. Ultimately, we will show that MLEs have many desirable properties (even though they may be biased). The following refers to 7.3.1, page 330–331. To be able to compare MLEs with other estimators, we need some general measures of quality that we may apply to many estimators. Here is possibly the most useful one: Defnition 7.3.1. Suppose we have a sample X 1 , . . ., X n from a f X ( x | θ ) (where we imagine θ to be unknown). Let W = W ( X 1 , . . ., X n ) be a statistic (which we want to use as an estimator for θ ). Then, the mean squared error (MSE) of W is E θ ( W - θ ) 2 . The subscript on the E reminds us that the expectation is dependent on the value of the parameter. The MSE can be viewed as a (number-valued) function of the parameter. (When calculating the MSE, always use the same value of θ in both places.) Note that E θ ( W - θ ) 2 = Var θ W + (E θ W - θ ) 2 . ( * ) The quantity E
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

notes-10-04 - M4056 Lecture Notes. Monday, October 4, 2010...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online