consistency issue on page 65
Example 2.8, the target function is sin(pi*x). But both target function graph labels in the second figure show sin(x) instead. Someone in the know should see that the graphed function, its label, and the target function coincide.

Re: consistency issue on page 65
On the same page, I've been able to confirm the biases stated for H0 and H1, as well as the variance for H0. But for the variance of 1.69 for H1, I am obtaining 2.44 instead.
I have this problem whether I calculate the variance directly, or I calculate the outofsample error and subtract the bias. It would be reassuring if I could show that my 2.44 figure is wrong, but as yet I have not succeeded. 
Re: consistency issue on page 65
Quote:
Is this what you have done to come up with a numerical answer equal to ? Hint: It is much easier to MonteCarlo. 
Re: consistency issue on page 65
My ETA having a closer look at this is 12 days. Schedule. I'm definitely interested in resolving this matter, and I'm happy to participate. :)
Update: wrapping up some computations; I'm testing an idea as to what might have happened. But the test is not quick. 
Re: consistency issue on page 65
Alas, I got bit by that old dog, numerical instability. When I run 1,000 hypotheses, I get the much higher figure I reported. 10,000 brought me a lot closer, and 100,000 has me at 1.70 variance (and presumably moving in the direction of 1.69).
These tests take a lot longer than they might, because I solve the line equation with waay too many CPU cycles. The upside is that the same code works with several other hypothesis sets to meet a shortterm need. I feel in general like I've faced a couple of numerical stability challenges in very recent time, and it's beneficial when students have to deal with it. I imagine there might be more ahead. 
Re: consistency issue on page 65
It is somewhat late but I'd like to give analytic solution for , bias and var and the verification of values here. Firstly,
and are parameters we get after minimising squared error function on some : and we can get them by solving the following system of equations (condition for extreme value of function): The solution is: Now, So, Now we can calculate all the terms: So, we see that the following holds: 
Re: consistency issue on page 65
Thanks for the detailed analysis :)

All times are GMT 7. The time now is 12:50 AM. 
Powered by vBulletin® Version 3.8.3
Copyright ©2000  2020, Jelsoft Enterprises Ltd.
The contents of this forum are to be used ONLY by readers of the Learning From Data book by Yaser S. AbuMostafa, Malik MagdonIsmail, and HsuanTien Lin, and participants in the Learning From Data MOOC by Yaser S. AbuMostafa. No part of these contents is to be communicated or made accessible to ANY other person or entity.