Slides19-2010 - Mean Squared Error and Maximum Likelihood:...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

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

Unformatted text preview: Mean Squared Error and Maximum Likelihood: Lecture XVIII Charles B. Moss October 18, 2010 Charles B. Moss () Mean Squared Error October 18, 2010 1 / 10 1 Data Reduction 2 Sufficiency Principle Charles B. Moss () Mean Squared Error October 18, 2010 2 / 10 Data Reduction The typical mode of operation in statistics is to use information from a sample X 1 , · · · X 2 to make inferences about an unknown parameter θ . I Put slightly differently, the researcher summarizes the information in the sample (or the sample values) with a statistic. I Thus, any statistic T ( X ) summarizes the data, or reduces the information in the sample to a single number. We use only the information in the statistic instead of the entire sample. Charles B. Moss () Mean Squared Error October 18, 2010 3 / 10 Continued I Put in a slightly more mathematical formulation, the statistic partitions the sample space into two sets F Defining the sample space for the statistic T = { t : t = T ( x ) , x ∈ X } (1) F Thus, a given value of a sample statistic T ( x ) implies that the sample comes from a space of sets A t such that t ∈ T , A t = { x : T ( x ) = t } ....
View Full Document

This note was uploaded on 07/15/2011 for the course AEB 6180 taught by Professor Staff during the Spring '10 term at University of Florida.

Page1 / 10

Slides19-2010 - Mean Squared Error and Maximum Likelihood:...

This preview shows document pages 1 - 5. Sign up to view the full document.

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