STAT 541: Centers and transformations
Statistics 541: Centers and transformations
What is a center?
Measures of center?
- distribution of Y = f(y;theta,lambda) = f(Y-theta;0,lamdba)
- center is "obvious" center of density
Example (see page 10.)
- best for normal
- also for many other exponential families (does this make it robust?)
- Not resistant
- trimmed mean (used in Olympic diving)
- 25% trimmed mean is midmean (50% data tossed!)
- trimean = 25% + 50% + 75%
data: 1,2,3,4,5,6,7,8,9, oops, 20
Efficiency (see page 11)
Scale is measure of spread
- standard deviation is most common (extreamly sensitive to outliers)
- MSE = s2
- E|X - EX| = (uncommon)
- E|X - median| = nicer theory
- MAD = median of distance to median (similar to IQR)
Centers only make sense if symetric. If not symetric, maybe a small
change in the data will make it symetric.
- ayalpha + b (alpha not equal to zero)
- c log(y) + d (taking limit as alpha goes to zero)
- see page 15 for graphs
- Goal: after transformation data is symetric
- Goal: keep it natural! Logs, 1/Y, Y^2 are about all I use.
Last modified: Thu Jan 18 08:43:09 2001