- (i) Using the Gaussian product kernel, the joint density is estimated as \(\hat{f}(x,y) = \frac{1}{N}\sum_{i=1}^N \phi_{\lambda}(x-x_i)\phi_{\lambda}(y-y_i)\) where \(\phi_{\lambda}(t)\) is the Gaussian density function with mean 0 and standard deviation \(\lambda\).
- (ii) Compute conditional mean \(E(Y\mid X)\) w.r.t. the above function.
- (ii) Note that \(\int_{-\infty}^{\infty} y \phi_{\lambda} (y-y_i)dy = y_i\). Why?
Hints for problem 6.8
Published Sep. 17, 2025
- Last modified Sep. 18, 2025