TBc

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

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.

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]