Thread: Exercise 3.4 View Single Post
#2
05-30-2014, 05:22 AM
 tomaci_necmi Junior Member Join Date: May 2014 Posts: 3
Re: Exercise 3.4

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 ?***