Thread: Exercise 3.4 View Single Post
#9
10-13-2017, 09:50 AM
 johnwang Junior Member Join Date: Oct 2017 Posts: 2
Re: Exercise 3.4

I still don't understand why "eq1" leads to zero. I know that e_i and e_j are zero mean independent variables. However, H_ij is dependent on both e_i and e_j,, so I don't know how to prove that the sum of H_ij*e_i*e_j has an expected value of zero.

Quote:
 Originally Posted by tomaci_necmi In my textbook, there is a statement mentioned on the topic of linear regression/machine learning, and a question, which is simply quoted as, Consider a noisy target, , for generating the data, where is a noise term with zero mean and variance, independently generated for every example . The expected error of the best possible linear fit to this target is thus . For the data , denote the noise in as , and let ; assume that is invertible. By following the steps below, ***show that the expected in-sample error of linear regression with respect to is given by***, Below is my methodology, Book says that, In-sample error vector, , can be expressed as , which is simply, hat matrix, , times, error vector, . So, I calculated in-sample error, , as, Since it is given by the book that, , and also is symetric, I got the following simplified expression, Here, I see that, And, also, the sum formed by , gives the following sum, I undestand that, However, I don't understand why, should be equal to zero in order to satisfy the equation, ***Can any one mind to explain me why leads to a zero result ?***