Exercise 2

Mutlivariate KDE

Consider bivariate kernel density estimation. Simulate data from the bivariate normal distribution \(\mathcal{N}((0,0), (1, 0.3; 0.3, 1))\).

1. Try different bandwidths and different kernels (use the bivariate normal kernel as well as the product kernel with the univariate Epanechnikov kernel)

2. Find ways to visually compare your estimates with the real density (3d plots of the density or density contour plots)

3. R functions such as kde2d of package MASS, contour and persp might be helpful