All Questions
Tagged with nonparametric density-estimation
5
questions
9
votes
2
answers
6k
views
Density estimation for large dataset
I have a unidimensional data set with more than 1000000 observations.
Assuming that those observations are independent realizations of the same random variable I need to estimate the underling ...
- 1,375
16
votes
3
answers
5k
views
Where is density estimation useful?
After going through some slightly terse mathematics, I think I have a slight intuition of kernel density estimation. But I am also aware that estimating multivariate density for more than three ...
- 469
5
votes
1
answer
698
views
Expected value and variance of KDE
I need to find the expected value and variance of KDE given that $$(i) E[u] = 0 \to \int u\phi(u)du=0\\
(ii)V[u] = \sigma^2 \to \int u^2\phi(u)du=\sigma^2$$ where $\phi$ is the kernel function.
I've ...
- 361
2
votes
1
answer
839
views
Convergence of kernel density estimate as the sample size grows
Let $X\sim\text{Normal}(0,1)$ and let $f_X$ be its probability density function. I conducted some numerical experiments in the software Mathematica to estimate $f_X$ via a kernel method. Let $\hat{f}...
- 285
1
vote
0
answers
251
views
Bias of kernel density estimator of pdf $f$, where $f$ has bounded first derivative $f'$
Let's say the kernel density estimator is given by
$$\hat f(x) = \frac{1}{nh_n} \sum_{i=1}^n K\left(\frac{X_i-x}{h_n}\right),$$ where $h_n \to 0$, $nh_n \to \infty$, $K$ a symmetric probability ...
- 636