# HUeff

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

## Syntax

• ceff=HUeff(eff,v)example
• ceff=HUeff(eff,v,shapeeff)example

## 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

expand all

### 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

## References

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