All Questions
13 questions
0
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0
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49
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Implementing Convolution Function for Gaussian Kernel in Python for PDF Estimation
I am currently working on estimating a probability density function (PDF) nonparametrically using a Gaussian kernel. My goal is to determine the optimal bandwidth $h$ that minimizes the cross-...
- 273
0
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0
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65
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How to prove symmetry of a Uniform kernel?
I am trying to prove this kernel is valid,
$$
K(x) = \frac{1}{2}I(-1 < x < 1)
$$
So far I can integrate to 1, but how do I prove $$k(x) = k(-x)$$
Also, how do we satisfy that k(x) is $\ge$ 0 for ...
1
vote
0
answers
291
views
histogram vs. kernel in density estimation
Assume we have a problem of estimation of a density $f(x)$ over an interval $[0, 1]$. Can a regular histogram (i.e. with equal-sized bins) be viewed as some kind of a kernel?
- 668
2
votes
1
answer
123
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Density plot with epanechnikov with exceedance data
I'm trying to replicate empirical density plot from the paper "Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution".
The data is ...
- 8,655
0
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0
answers
29
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Group comparison for bivariate distributions
For two groups A and B that consist of n and m individual samples. Each individual sample has a unique 2-dimensional joint probability density functions (PDFs)of two variables. These PDFs are ...
- 1
1
vote
0
answers
71
views
Term for assessing unknown distribution
I come from the field of Numerical Analysis, and I look for the term which describes the problem of fitting a probability distribution to statistical numerical continuous data, without a-priori ...
- 223
12
votes
1
answer
260
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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 ...
- 6,880
16
votes
3
answers
5k
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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
3
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0
answers
2k
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How to calculate confidence intervals using subsampling after a nonparametric estimator about the empirical distribution function?
I have a problem where I think subsampling is more appropriate than the bootstrap. (Reason in another post.)
However, I found no quick reference on subsampling CIs, and my naive inversion of the ...
- 987
3
votes
0
answers
281
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Is excess mass estimation smooth enough to bootstrap? At what rate might a bunching estimator converge?
The recent public finance literature often estimates relative excess mass around specific points of the earnings distribution ("kink points" or "notches" of tax schedules, say), and then bootstraps to ...
- 987
4
votes
3
answers
255
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Fast multivariate unimodal density estimator
I have a sample $\boldsymbol{x}_i$ for $i$ in $1,\dots, n$, from a $d$ dimensional density $f(\boldsymbol{x})$ and I would like to estimate this unknown density. In addition I know that $f(\boldsymbol{...
- 3,284
6
votes
3
answers
2k
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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 $\hat{\sigma}^2$...
- 3,284
16
votes
1
answer
13k
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Is there an optimal bandwidth for a kernel density estimator of derivatives?
I need to estimate the density function based on a set of observations using the kernel density estimator. Based on the same set of observations, I also need to estimate the first and second ...
- 1,183