LFD Book Forum - View Single Post

yaser · #4 04-28-2012, 11:36 PM

Quote:

Originally Posted by dudefromdayton

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 out-of-sample 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.

This is curious. To calculate $E_{\rm out}$ , you generate the two points

and

uniformly and independently, then connect them with a line. Since $y_1=\sin(\pi x_1)$ and $y_2=\sin(\pi x_2)$ , you get the equation for the line (tangent to the sine if the two points coincide). You then integrate the difference squared between the line and the sine with respect to

(times the probability density which is ${1\over 2}$ ) to get $E_{\rm out}$ for this data set, and double-integrate that with respect to

and

(times the probability density which is ${1\over 2}$ for each variable) to get the expected $E_{\rm out}$ .

Is this what you have done to come up with a numerical answer equal to $E_{\rm out}=2.44+0.21$ ?

Hint: It is much easier to Monte-Carlo.