0
$\begingroup$

I am learning about non parametric estimation, and more specifically about regressogram:

Let $(X_i,Y_i)_{i = 1}^n$ be a sequence of random variables in $[0,1]$ variables and $E[Y_i|X_i] = f(X_i)$. Let $I_1,\dots,I_K$ be the regular partition of the unit interval. Suppose $x\in I_k$, then $$\hat{f}_n(x) = \frac{\sum_{i=1}^nY_i1(X_i\in I_k)}{\sum_{i=1}^n1(X_i\in I_k)}.$$

I would like to know how to control the error $|\hat{f}_n(x)-f(x)|$? Is there a reference?

Improve this question
$\endgroup$
5
  • $\begingroup$ I think you are supposed to sum on i, not k. $\endgroup$
    – JohnK
    Commented Apr 15, 2020 at 15:26
  • $\begingroup$ my mistake, edited $\endgroup$
    – ess
    Commented Apr 15, 2020 at 15:29
  • $\begingroup$ What is $r(x)$? $\endgroup$
    – JohnK
    Commented Apr 15, 2020 at 15:45
  • $\begingroup$ It's certainly better to call it $\hat{f}$, it's the regressogram estimator (sorry I mixed the notations of several refs) $\endgroup$
    – ess
    Commented Apr 15, 2020 at 16:03
  • $\begingroup$ This is quite easy to do for non-random $X_i$ but for random $X_i$ it can be quite difficult. $\endgroup$
    – JohnK
    Commented Apr 16, 2020 at 5:43

0

Reset to default