STAT 541: JMP and L and M estimators

Statistics 541: JMP and L and M estimators

Admistrivia

JMP

Look at repairs.jmp.

Mathematics of robustness

Goal is to provide framework to discuss properties of estimators.

L estimators

M estimators

Invariance

Shift invariance: T(y + c) = T(y) + c

scale invariance: T(ay) = aT(y)

Obvious for L esitimators. Not always true for M estimators.

Clasic m-estimator

The clasic m-estimator is the biweight;

phi(u) = u(1 - u2)2 (for |u| < 1)

Sensitivity and influence

sensitivity is the effect of adding one observation to a small dataset.

Influence curve is n times the effect of adding one observation to a large number of observations.

Claim: The influence curve is proportional to the phi-function

Properties of estimators