All Questions
4
questions
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Maximum bias for NW estimator when $r(x)$ is Lipschitz (question 17, chapter 5 All of Non-Parametric Statistics)
The general condition is that $Y_i = r(X_i) + \epsilon_i$, and we want to estimate $r$ using Nadaraya–Watson kernel regression.
We additionally assume $r\colon [0,1] \to \mathbb{R}$ is lipschitz, so $|...
- 636
3
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Pros and cons of Nadaraya–Watson estimator vs. RKHS method?
Recently I've been reading some materials about nonparametric methods. Two methods related to the word "kernel" rasied my interest-- Nadaraya–Watson estimator and RKHS method.
What's the ...
- 31
3
votes
1
answer
85
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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
3
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upper bound for expected maximum of difference of two kernel-Estimations
I'm searching for an upper bound for a function like
$$
E\left[
\max_{x \in R} \left(
\frac{ \sum_{i=1}^n K(\frac{x-X_i}{f(x,X_1, \dots X_n)}) \cdot Y_i }
{ \sum_{i=1}^n K(\frac{x-X_i}{f(x,...
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