Lecture 19-2007

Lecture 19-2007 - Lecture XIX Sufficient Statistics Data...

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Unformatted text preview: Lecture XIX Sufficient Statistics Data Reduction References: Casella, G. and R.L. Berger Statistical Inference 2nd Edition, New York: Duxbury Press, Chapter 6 Principles of Data Reduction. Pp 271-309. Hogg, R.V., A. Craig, and J.W. McKean Introduction to Mathematical Statistics 6th Edition, Englewood Cliffs, New Jersey: Prentice Hall, 2004, Chapter 7 Sufficiency, pp 367-418. The typical mode of operation in statistics is to use information from a sample X 1 , X n to make inferences about an unknown parameter . Put slightly differently, the researcher summarizes the information in the sample (or the sample values) with a statistic. 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. Put in a slightly more mathematical formulation, the statistic partitions the sample space into two sets: Defining the sample space for the statistic Thus, a given value of a sample statistic T ( x ) implies that the sample comes from a space of sample sets A t such that t T , ( 29 { } : , t t T x x = = ( 29 { } : t A x T x t = =...
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This note was uploaded on 07/18/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

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Lecture 19-2007 - Lecture XIX Sufficient Statistics Data...

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