Loading in 5 sec....

All of Statistics: Chapter 7PowerPoint Presentation

All of Statistics: Chapter 7

- 66 Views
- Uploaded on

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

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:

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

- L(x)=max{ ,0}
- U(x)=min{ ,1}
- Where
- For an F

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

- The plug-in estimator for linear functional
- Assume we can find se, then for many cases:
- Normal-based interval for 95% CL

Examples:

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

Examples Continued

- The Skewness:
- Correlation:

Download Presentation

Connecting to Server..