I'm trying to calculate the bias of the estimator $p(h)=n^{-1}\displaystyle\sum_{i=1}^{n}(Y_{j}-\hat{m}_{h}(X_{j})^{2}w(X_{j})$ of the averaged squared error. The result I find in the literature is this:

enter image description here

but I am not able to calculate the expectation of the term $C_{1n}(h)$. Any idea of how to proceed or where to find it?

  • $\begingroup$ You may want to try substituting $Y_i = m(X_i) + \epsilon_i$ into (5.1.1). $\endgroup$ – Michael Oct 8 '20 at 18:22
  • $\begingroup$ it worked, thanks! $\endgroup$ – heyou Oct 9 '20 at 16:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.