# TBeff

Tbeff finds the constant c which is associated to the requested efficiency for Tukey's biweight

## Syntax

• ceff=TBeff(eff, v)example
• ceff=TBeff(eff, v, shapeeff)example
• ceff=TBeff(eff, v, shapeeff, approxsheff)example

## Description

 ceff =TBeff(eff, v) Find c for a given efficiency.

 ceff =TBeff(eff, v, shapeeff)

 ceff =TBeff(eff, v, shapeeff, approxsheff) Find shape efficiency.

## Examples

expand all

### Find c for a given efficiency.

The constant c associated to a nominal location efficiency of 95% in regression is c = 4.685064948559557

c=TBeff(0.95,1)

c=TBeff(0.95,1,1)

### Find shape efficiency.

Compare constant c for the range of values of p from 1 to 200 using approximate and exact formula for fixed shape efficiency Number of variables

p=200;
pp=1:1:p;
% Initialize the matrix which stores the values of c for the two
% methods
cc=[pp' zeros(p,2)];
eff=0.75;
% eff=0.99;
for i=pp
% Use exact formula for finding the value of c associated to a fixed
% level of shape efficiency
cc(i,2)=TBeff(eff,i,1);
% Use approximate formula for finding the value of c associated to a fixed
% level of shape efficiency
cc(i,3)=TBeff(eff,i,1,1);
end
figure
plot(cc(:,1),cc(:,2),'LineStyle','-','LineWidth',2)
hold('on')
plot(cc(:,1),cc(:,3),'LineStyle','-.','LineWidth',2)
legend('True value of c', 'Approximate value of c','Location','best')
xlabel('Number of variables')
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 p=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

Example: 'shapeeff',1 

Data Types: double

### approxsheff — approximate or exact calculations. Dummy scalar.

If 1, when p > 1 the approximate formula for scale efficiency is used else (default) the exact formula of the variance of the robust estimator of the scale is used

Example: 'approxsheff',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.