All of statistics chapter 7
Download
1 / 8

All of Statistics: Chapter 7 - PowerPoint PPT Presentation


  • 66 Views
  • Uploaded on

All of Statistics: Chapter 7. Toby Xu UW-Madison 07/02/07. The Empirical Distribution Function . Def: The Empirical distribution function is the CDF that puts mass 1/n at each data point X i . Formally, Where. Theorems: .

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' All of Statistics: Chapter 7' - candace-boyer


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
All of statistics chapter 7

All of Statistics:Chapter 7

Toby Xu

UW-Madison

07/02/07


The empirical distribution function
The Empirical Distribution Function

  • Def: The Empirical distribution function is the CDF that puts mass 1/n at each data point Xi. Formally,

  • Where


Theorems
Theorems:

The supremum or least upper bound of a set S of real numbers is denoted by sup(S) and is defined to be the smallest real number that is greater than or equal to every number in S.

  • MSE=

  • DKW inequality:


Dkw confidence level
DKW: confidence level

  • L(x)=max{ ,0}

  • U(x)=min{ ,1}

  • Where

  • For an F


Statistical functions
Statistical Functions

  • A statistical function T(F) is any function of F.

  • Mean:

  • Variance :

  • Median : m=F-1(1/2)

  • Plug-in estimator of is defined by

  • If for some function r(x) then T is called a linear function


Statistical functionals continued
Statistical Functionals continued

  • The plug-in estimator for linear functional

  • Assume we can find se, then for many cases:

  • Normal-based interval for 95% CL


Examples
Examples:

  • The Mean: let , the plug-in estimator is .

  • The Variance:


Examples continued
Examples Continued

  • The Skewness:

  • Correlation:


ad