Questions tagged [density-estimation]
Estimation of probability density functions, whether by kernel density estimation, log-spline estimation or other methods.
335
questions
3
votes
0
answers
29
views
How to identify hot spots in one-dimension
I am looking to identify stretches of a road along which a notably high number of accidents occur. My data can be represented as a two column table in which each row represents one accident, and the ...
- 395
4
votes
1
answer
49
views
How to accurately estimate the probability of a rare event in a large dataset?
I have a dataset of 30,155 names and out of curiosity I verified that the longest name has 68 characters, which is quite big considering the mean and SD were 24.78 and 5.64, respectively. Based on ...
- 141
0
votes
0
answers
22
views
estimation of multivariate probability
Let $(X_{1}, \dots, X_{n})$ be a multivariate distribution and I can generate the sample from it. Next, assume that I have to compute
$$
P(X_{1}\in A_{1}, \dots, X_{n}\in A_{n}),
$$
where $A_{1}, \...
- 676
0
votes
0
answers
32
views
MLE of marginal distribution for continuous random variable
Let $\mathcal{F}$ be a family of multivariate probability densities such that for a sufficiently large data sample, there always exists a unique MLE. Assume also that all marginal and conditional ...
- 213
1
vote
0
answers
40
views
How to show $\sup_{x\in [a,b]}|f_n(x)-f(x)|=O_p(\sqrt{\frac{\log n}{nh}}+h^2)$ when the kernel $K(\cdot) $ is of bounded variation?
Consider the kernel estimate $f_n$ of a real univariate density defined by $$f_n(x)=\sum_{i=1}^{n}(nh)^{-1}K\left\{h^{-1}(x-X_i)\right\}$$
where $X_1,...,X_n$ are independent and identically ...
- 31
0
votes
0
answers
21
views
Scaling of different kernels when estimating densities in R
The implementation of the density function in R says that the kernels are scaled so that the bandwidth becomes the standard deviation of the smoothing kernel.
For the Gaussian kernel, it is ...
- 681
1
vote
0
answers
31
views
Density estimation vs estimation
Given a statistical model $(\mathcal{X},\Sigma,\mathcal{P})$, where $\mathcal{P}$ is a collection of probability measures on $\mathcal{X}$, and given a random sample with values in $\mathcal{X}$, we ...
- 125
3
votes
1
answer
67
views
Is this a known or valid divergence between two densities?
I am testing various metrics for learning a density estimate. Specifically, I have a sample of data from a distribution $p$, and am learning a function $f$ to estimate $p$ by minimizing a distance or ...
- 181
0
votes
0
answers
24
views
Reference datasets for conditional density estimation
[In case you feel inclined to close this question because I'm asking for a dataset - I'm looking for solutions in the spirit of point 2 (on-topic) in the accepted answer to this question about asking ...
- 2,439
1
vote
0
answers
21
views
Developing a Confidence Interval of Density Functions for Uniform Periods in Seasonal Time Series Data
Suppose I have a set of observational data as a time series where the observations are collected at uniform interval over the course of several years. The data exhibits seasonality over the course of ...
- 11
0
votes
0
answers
66
views
Measuring the Distance Between KDE Distributions with Different Bin Counts
I have two KDE distributions, each with a different number of bins. I'd like to compare them effectively, and I'm wondering if there's a recommended technique for this. Should I unify the number of ...
- 135
0
votes
0
answers
20
views
Is there a method to estimate the distribution of error term in linear model?
Consider the linear model where $A$ is not known
$$
y = Ax + \epsilon
$$
where we want to estimate the distribution $\epsilon$ from a set of samples. To prevent over-fitting, we want to impose some ...
- 163
1
vote
0
answers
23
views
At what circumstances will the difficulty for the tasks of density evaluation and sampling be different?
In this tutorial video of normalizing flow, the presenter mentioned that for the original autoregressive flow, the density evaluation is fast and the sampling is slow. In contrast, for the inverse ...
- 141
1
vote
0
answers
21
views
Kernel density estimation for noisy samples with known non-iid noise
I'm interested in the following variant of the usual one-dimensional density-estimation problem:
I wish to estimate some unknown density $\rho$. There are iid samples $Y_{1},\ldots,Y_{n} \sim \rho$, ...
- 11
1
vote
0
answers
82
views
Kernel Density Estimation on a Log-Scale: Log Transformation vs. Geometric Space
I’m working on a project where I need to plot a Kernel Density Estimation (KDE) on a log-scale x-axis. I’ve come across two different methods and I’m unsure which one would be more appropriate for my ...
- 11