03_Estimation_part4

03_Estimation_part4 - Ch8, p.53 Data reduction - the...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
NTHU MATH 2820, 2008, Lecture Notes Ch8, p.53 • Data reduction --- the concepts of sufficiency, minimal sufficiency, and completeness Question 6.4 (information and data reduction) raw (original) data order statistics histogram sample mean sample variance To present concrete information, the data reduction through useful transfor- mations is required. However, non-invertible transformations can cause the loss of information. ( Example? ) The lost information can be important or worthless to the objective of studying the data. How to examine whether the important information lose in transformation? Furthermore, what is impor- tant information ? 1 n n i =1 ( X i X n ) 2 X 1 ,X 2 ,...,X n X n X (1) (2) ( n ) (numerical or graphical) transformations of data appear all the time in statis- tics for o f ering a summary of information contained in data. For example, made by Shao-Wei Cheng (NTHU, Taiwan) Ch8, p.54 Summary (formulation of information and data reduction problem, TBp. 305) Let X 1 2 n be a sample with joint pdf/pmf f ( x | Θ ), wherer Θ is unknown parameter. X 1 2 n contains two types of information: information related to Θ information irrelevant to Θ For example, toss a coin n times, i.e., X 1 2 n are i.i.d. from Bernoulli B ( θ ), X n or T = n i =1 X i contains information about θ When T is known, the information that at which trials the head’s occur is irrelevant to θ n =5, consider the following possible results: B (0 ,1 ,1) , T = 4; (1, 0, 1, 1, 1), T =4 ; (1 ,0 , T = 4; (1, 1, 1, 0, 1), T ; ,0) , T B , T = 1; (0, 1, 0, 0, 0), T =1 ; , T = 1; (0, 0, 0, 1, 0), T ; , T
Background image of page 1

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

View Full DocumentRight Arrow Icon
NTHU MATH 2820, 2008, Lecture Notes Ch8, p.55 Definition 6.15 (sufficient, TBp. 305) A statistic T ( X 1 ,X 2 ,...,X n )issa idtobe su cient for θ
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/11/2011 for the course STA 506 taught by Professor Lisa during the Spring '11 term at West Chester.

Page1 / 4

03_Estimation_part4 - Ch8, p.53 Data reduction - the...

This preview shows document pages 1 - 3. Sign up to view the full document.

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