All Questions
4
questions
0
votes
0
answers
31
views
Biase of ASE estimation Kernel Regression
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 ...
- 3
3
votes
1
answer
85
views
What is the density of $X$ under fixed design?
We observe an i.i.d. sample $(X_1, Y_1), \ldots (X_n, Y_n).$ Let $m(x) = E(Y|X=x),$ $\sigma^2(x) = \operatorname{Var}(Y|X=x)$ and let $f(\cdot)$ be the density of $X.$
Under some regularity ...
- 238
6
votes
3
answers
2k
views
Kernel density estimator that doesn't collapse in the tails
I have iid data-points $x_1, \dots, x_n$, generated by an unknown density $f(x)$.
So far I have approximated $f(x)$ with a normal $N(\hat{\mu}, \hat{\sigma}^2 )$, where $\hat{\mu}$ and $\hat{\sigma}^2$...
- 3,264
19
votes
2
answers
838
views
If variable kernel widths are often good for kernel regression, why are they generally not good for kernel density estimation?
This question is prompted by discussion elsewhere.
Variable kernels are often used in local regression. For example, loess is widely used and works well as a regression smoother, and is based on a ...
- 57.5k