Questions tagged [kernel-smoothing]
Kernel smoothing techniques, such as kernel density estimation (KDE) and Nadaraya-Watson kernel regression, estimate functions by local interpolation from data points. Not to be confused with [kernel-trick], for the kernels used e.g. in SVMs.
667 questions
0
votes
0
answers
33
views
Role of Z-Tests in Kernel Density Estimation for Cluster Classification
In a recent bioinformatics paper, the authors describe a statistical/machine learning approach to classify clusters of cells using kernel density estimation (KDE) and Z-scores. While the details of ...
2
votes
2
answers
75
views
How can Kernel Density Estimation learn multiple classes?
So I've stumbled upon this example in the Sklearn website, where a KDE instance is trained with handwritten digits, and then used to synthesize samples : https://scikit-learn.org/stable/auto_examples/...
- 21
1
vote
0
answers
76
views
Pointwise bandwidth selection for kernel density estimation
Consider an estimation for $f(x)$ for a function $f$ at a fixed point $x$. We may use kernel density estimator $\hat{f}_n$ to estimate the $f$, then calculate $\hat{f}(x)$. If I understand correctly, ...
- 117
1
vote
0
answers
53
views
"Exactly Equivalent Kernels" example of density() function
The asymptotically optimal bandwidth for a kernel $K$ is given by
$$
h
=\Bigl(\frac{R(K)}{n\mu_2^2(K)R(f'')}\Bigr)^{1/5},
$$
where $R(g)=\int g^2(x)\,dx$, $\mu_2=\int x^2K(x)\,dx$, and $f$ is the ...
- 339
6
votes
2
answers
125
views
Asymptotic distribution of kernel density estimator as a process over $\mathbb{R}$
Consider the task of estimating a density function $f : \mathbb{R} \to \mathbb{R}$ from independent samples $X_1, \ldots, X_n \sim f$.
Let $f_n$ be the kernel density estimator of $f$, that is,
$$
f_n ...
- 161
0
votes
0
answers
24
views
Is it statistically valid to use windowed KDE-normalized patches for Jensen-Shannon Divergence comparison?
I'm working with a spatially distributed dataset where I first estimate the global empirical distribution using Kernel Density Estimation (KDE). I then divide the data into smaller spatial patches (...
- 135
4
votes
1
answer
100
views
Question about proving consistency for $L^2$ norm estimator
I'm reading a paper by Gine where a estimator $T_n$ for $\int f(x)^2dx$ was introduced, where $f$ is the true density function. $T_n$ is defined as
$$T_n(h)=\frac{2}{n(n-1)h}\sum_{1\leq i<j\leq n}K\...
- 117
0
votes
0
answers
64
views
Is there an issue with estimating a CI for a quantile by passing the CI of a posterior beta through the original distribution's inverse CDF?
say we've fit a distribution to data, we've either used minimum chi squared method of distribution fitting and if that failed we used an improved sheather jones KDE as the fall back to make the fit (...
- 1
0
votes
0
answers
51
views
Can I use different kernel functions for different independent variables (features)? And should I?
I'm using kernel regression to model a non-linear relationship between several independent variables and a dependent variable. I understand kernel functions and bandwidth selection, but I’m wondering ...
- 135
6
votes
1
answer
300
views
What returns to use for KDE & Histogram?
A very simple question, yet, I have not been able to find a straightforward answer on the internet.
When trying to estimate a probability distribution of stock returns from historical data, should I ...
- 61
0
votes
0
answers
139
views
Linear PDF Approximation
I am trying to estimate the shape parameter alpha of the PDF of a Pareto distribution, given that I have incomplete data. Specifically, the true dataset spans values between $10$ and $50,$ but my ...
- 117
0
votes
0
answers
46
views
Bootstrapping the average derivative estimator
Let $f(x)=\mathbb E[Y\mathop | X=x]$ be the regression function, and $\hat {f}(x)$ be its estimate (using kernel regression, for example). The average derivative estimator (Härdle and Stoker, 1989; ...
- 150
5
votes
3
answers
277
views
Cross-validated bandwidth for the derivative of the function with local quadratic estimation
I am trying to estimate non parametrically the first order derivative of a function g(x). I am estimating $g(x)$ using a local polynomial (quadratic) procedure. I know how to compute the leave-one-out ...
- 239
1
vote
0
answers
81
views
Extremely large bandwidth for kernel regression
I'm trying to fit my data with kernel regression using npreg() from package np. However, the bandwidth automatically selected ...
- 150
0
votes
0
answers
82
views
How to do kernel-smoothed estimation of the probability $\Pr((U,V)\in A)$ and show its consistency?
Suppose I'm interested in estimating the probability $p=\Pr((U,V)\in A)$ with a random sample $\{(U_i,V_i)\}_{i=1}^N$. The easiest way of doing it is to use the sample mean: $\widehat{p}=1/N\times \...
- 3,090