All Questions
11
questions
1
vote
0
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32
views
Strong consistency of kernel density estimator
I am studying the book Nonparametric and Semiparametric Models written by Wolfgang Hardle and have difficulty with the following exercise:
$\textbf{Exercise 3.13}$ Show that $\hat{f_h}^{(n)}(x) \...
- 111
4
votes
1
answer
188
views
Proving that the bias of the derivative of Parzen-Rosenblatt (kernel density) estimator is of order $O(h^2) $ and $O(h)$ when $h$ approaches $0$
I came across this property that I don't get and I couldn't find the proof anywhere:
Suppose we have a density $K$ of the standard normal distribution and $K'$ its derivative. Suppose that the density ...
- 241
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
5
votes
1
answer
362
views
Nonparametric estimation of regression function: kernel estimation vs series estimation
I am working on a small research project trying to estimate regression function nonparametrically when I have only one regressor. Basically, I am trying to estimate the regression function
$$r(x)=E[Y∣...
- 578
12
votes
1
answer
257
views
What is the name of the density estimation method where all possible pairs are used to create a Normal mixture distribution?
I just thought of a neat (not necessarily good) way of creating one dimensional density estimates and my question is:
Does this density estimation method have a name? If not, is it a special case of ...
- 6,840
4
votes
2
answers
316
views
Compute moment and quantiles of a stream of data
I'd like to compute the moments and quantiles of a random variable which is the output of a sensor.
I don't intend to store all the values this sensor outputs (let's say it outputs one value each 15 ...
3
votes
3
answers
223
views
Literature on nonparametric density estimation
I am about to write my bachelor thesis about non-parametric density estimation, especially kernel density estimators and their application in classification. As I am quite new to looking for academic ...
- 33
8
votes
1
answer
2k
views
What practical application is there for the Asymptotic Mean Integrated Squared Error in kernel density estimation?
Introduction
For some time now I have been struggling to understand how theoretical results can be applied in practice. Fortunately in most cases the link between theory and practice is not hard to ...
10
votes
2
answers
9k
views
Advantage of kernel density estimation over parametric estimation
Is there any particular reason you will choose the kernel density estimation over the parametric estimation? I was learning to fit distribution to my data. This question came to me.
My data size is ...
- 101
4
votes
1
answer
126
views
Compare two nonparametric curve estimation approaches: kernel and orthogonal basis
I know there're at least two approaches for nonparametric curve estimation: kernel and orthogonal basis.
What are their advantages and disadvantages over each other?
And what are the typical ...
- 171
6
votes
4
answers
2k
views
Nonparameteric multivariate density approximation -- where do I start?
I am currently working on a research project that requires a reliable method for non-parametric kernel density estimation. Some specifics about my problem:
I have $N$ sample points $X_1,X_2...X_N$, ...
- 5,075