HUeff

HUeff finds the constant c which is associated to the requested efficiency for Tukey biweight estimator

Description

ceff =HUeff(eff, v) Find c in regression for 95 per cent efficiency.

ceff =HUeff(eff, v, shapeeff) Analyze constant c as a function of eff.

Examples

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Find c in regression for 95 per cent efficiency.

The constant c associated to a nominal location efficiency of 95% in regression is c = 1.344997508513144

c=HUeff(0.95,1)

Analyze constant c as a function of eff.

Initialize the matrix which stores the values of c for the two methods

eff=[0.70:0.0001:0.9999];
cc=[eff' zeros(length(eff),1)];
for i=1:length(eff)
% Use exact formula for finding the value of c associated to a fixed
% level of shape efficiency
cc(i,2)=TBeff(eff(i),1);
end
figure
plot(cc(:,1),cc(:,2),'LineStyle','-','LineWidth',2)
xlabel('Effciency')
ylabel('Value of c')

Input Arguments

eff — required efficienty. Scalar.

Scalar which contains the required efficiency (of location or scale estimator).

Data Types: single|double Generally eff=0.85, 0.9 or 0.95

v — Number of response variables. Scalar.

e.g. in regression v=1 Now it is implemented just for v=1

Data Types: single|double|int32|int64

shapeeff — Location or shape efficiency. Scalar.

If 1, the efficiency is referred to shape else (default) is referred to location (not implemented yet)

Example: 'shapeeff',1

Data Types: double

Output Arguments

ceff —Requested tuning constant. Scalar

Tuning constatnt of Tukey Biweigh rho function associated to requested value of efficiency

Maronna, R.A., Martin D. and Yohai V.J. (2006), "Robust Statistics, Theory and Methods", Wiley, New York.