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# All of Statistics: Chapter 7 - PowerPoint PPT Presentation

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: .

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### All of Statistics:Chapter 7

Toby Xu

07/02/07

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

• Where

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:

• L(x)=max{ ,0}

• U(x)=min{ ,1}

• Where

• For an F

• 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

• The plug-in estimator for linear functional

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

• Normal-based interval for 95% CL

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

• The Variance:

• The Skewness:

• Correlation: