18.5 Exercises

EXERCISE 18.1   Calculate the Simplicial Depth for the Swiss bank notes data set and compare the results to the univariate medians. Calculate the Simplicial Depth again for the genuine and counterfeit bank notes separately.

EXERCISE 18.2   Construct a configuration of points in $\mathbb{R}^2$ such that $x_{med,j}$ from (18.2) is not in the ``center'' of the scatterplot.

EXERCISE 18.3   Apply the SIR technique to the U.S. companies data with $Y = \,market \,value$ and $X = \,all \,other\, variables$. Which directions do you find?

EXERCISE 18.4   Simulate a data set with $X \sim N_4(0,I_4), Y=(X_1+3 X_2)^2 + (X_3-X_4)^4 + \varepsilon$ and $\varepsilon \sim N(0, (0.1)^2)$. Use SIR and SIR II to find the EDR directions.

EXERCISE 18.5   Apply the Projection Pursuit technique on the Swiss bank notes data set and compare the results to the PC analysis and the Fisher discriminant rule.

EXERCISE 18.6   Apply the SIR and SIR II technique on the car data set in Table B.3 with $Y = price$.