# TBc

TBc computes breakdown point and efficiency associated with constant c for Tukey's biweight

## Syntax

• bdp=TBc(c,v)example
• bdp=TBc(c,v,shapeeff)example
• [bdp,eff]=TBc(___)example
• [bdp,eff,approxsheff]=TBc(___)example

## Description

 bdp =TBc(c, v) Tbc with just one output argument.

 bdp =TBc(c, v, shapeeff) Tbc with 2 output arguments.

 [bdp, eff] =TBc(___) Find also approximate value of scale efficienty (for R comparability).

 [bdp, eff, approxsheff] =TBc(___) Breakdown point and efficiency.

## Examples

expand all

### Tbc with just one output argument.

[bdp]=TBc(2,1)
disp('Break down point')
disp(bdp)

### Tbc with 2 output arguments.

[bdp,eff]=TBc(2,1)
disp('Break down point and efficienty')
disp(bdp)
disp(eff)

### Find also approximate value of scale efficienty (for R comparability).

[bdp,eff,approxeff]=TBc(2,2,1)

### Breakdown point and efficiency.

Analysis of breakdown point and asymptotic efficiency at the normal distribution as a function of c in regression.

c=1:0.01:6;
[bdp,eff]=TBc(c,1);
subplot(2,1,1)
plot(c,bdp)
xlabel('c','Interpreter','Latex','FontSize',16)
ylabel('Breakdown point','Interpreter','none')
subplot(2,1,2)
plot(c,eff)
xlabel('c','Interpreter','Latex','FontSize',16)
ylabel('Asymptotic efficiency','Interpreter','none')

## Input Arguments

### c — tuning constant c. Scalar.

Scalar greater than 0 which controls the robustness/efficiency of the estimator

Data Types: single| double

### v — number of response variables. Scalar.

Number of variables of the dataset (for regression v=1)

Data Types: single| double

### shapeeff — location or shape efficiency. Scalar.

If shapeeff=1, the efficiency is referred to the shape else (default) is referred to the location estimator

Example: 1 

Data Types: double

## Output Arguments

### bdp —bdp. Scalar

Breakdown point associated to the supplied value of c

### eff —eff. Scalar

Efficiency associated to the supplied value of c Remark: if c is a vector bdp and eff will also be vectors with the same size of c. For example bdp(3) and eff(3) are associated to c(3) ....

### approxsheff —Approximate value of efficiency. Scalar

Approximate value of efficiency in case input option shapeeff=1 and v>1.

This output is left for comparability with the value which comes out from R library robustbase.

## References

Hampel, F.R., Rousseeuw, P.J. and Ronchetti, E. (1981), The Change-of-Variance Curve and Optimal Redescending M-Estimators, "Journal of the American Statistical Association", Vol. 76, pp. 643-648. [HRR]