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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
9 views

Bandwidth selection when comparing different local constant regression models

Let's say that I want to compare two alternative specifications of a Local Constant least squares model. If I had a single model, I would select my optimal bandwidth by cross validation. However, ...
user avatar
  • 1
1 vote
0 answers
12 views

Kernel Density: How do the terms 'global' and 'pilot' translate?

I nearly most of the articles on kernel smoothing or concepts that use kernel density estimations, authors speak of 'pilot' and 'global'. https://link.springer.com/article/10.1023/A:1008925425102 &...
user avatar
  • 131
0 votes
0 answers
11 views

Selecting the optimal bandwidth in kernel density estimation

I have a question regarding kernel density estimation. At the moment I have a set of sample date $V$, where for each $v \in V$ I have an associated standard deviation $\sigma_v$ (some measurements ...
user avatar
0 votes
0 answers
13 views

Making a distribution rougher or smoother [duplicate]

When I have a given distribution, how can I transform it to make it appear rougher or smoother? I need to give the user the option of magnifying or reducing differences in the density plot, and I don'...
user avatar
2 votes
1 answer
78 views

Is Kernel-Regression parametric or non-parametric?

As the title says, is kernel regression a parametric or non-parametric method, and how can this be motivated/explained?
user avatar
1 vote
1 answer
66 views

How to efficiently bias future samples?

My goal is to hit all of my 'targets' through a random variable $Y : [0,1] \rightarrow \mathbb{R}$. An explicit form of $Y$ is unknown but I am able to take a sample point as pass it to $Y$ and get ...
user avatar
0 votes
0 answers
15 views

How to interpret the asymptotic normality of Gaussian Kernel estimator

I am trying to estimate the return of AAPL with Gaussian kernel estimator code for reproducing: ...
user avatar
1 vote
0 answers
18 views

Intuition for bandwidth and degrees of freedom in kernel smoothers

For Kernel smoothers such as local polynomial regression smoothers (the Nadaraya-Watson smoother), we consider $y = m(x) + \epsilon$, for $m(x)$ some smooth function we are trying to estimate and $\...
user avatar
1 vote
0 answers
66 views

Kernel Density Estimation using a Two-Boundary-Kernel à la Jones

I'm trying to understand how to perform a KDE on a bounded support, i.e. with lower and upper boundary, when using a kernel that is specifically designed to ensure consistency/$h^2$-bias at the ...
user avatar
0 votes
0 answers
16 views

Is Particle Filter using Kernel Density Estimation?

I'm trying to build a Particle Filter, but all the math-stuffs are sooo difficult and I don't understand it. It's only $p(x|x)$ everywhere. Then I found some one at ...
user avatar
  • 173
0 votes
0 answers
45 views

Can "Curve Fitting" be seen as an Alternative to Numerical Differentiation?

For a long time, the following point always confused me: If the "Fundamental Theorem of Calculus" tells us that all real and continuous functions are differentiable (i.e. have derivatives) - ...
user avatar
  • 5,750
1 vote
1 answer
57 views

Bandwidth Selection for Kernel Density Estimation

Are there any heuristics for selecting the bandwidth for kernel density estimation? In other words, is a spiky curve better or a smooth one?
user avatar
2 votes
0 answers
44 views

K nearest neighbor VS Kernel density estimation (Parzen window)

I appreciate it if anyone could explain to me the advantages and disadvantages of knn and parzen relative to each other.
user avatar
0 votes
0 answers
22 views

How is Nadayara Watson KDE proof

I was looking at Wikipedia article on Nadayara-Watson Kernel regression section, in the proof part they state But I'm having trouble understand why: Turns to just yi. Sorry I'm missing something so ...
user avatar
  • 113
0 votes
0 answers
23 views

Compare multimodal distributions for different groups

I am analyzing data from 3 different gait speeds. For each group/speed, I am determining specific value called "angle". Each group has different sample size. So, I need to compare multimodal ...
user avatar
  • 1
0 votes
1 answer
83 views

Why do my GaussianProcessRegressor prediction results converge to 0?

I am using sklearn GaussianProcessRegressor to predict a time series. The kernel I use is this: ...
user avatar
0 votes
0 answers
102 views

How to calculate the probability density function for highly skewed data?

I have an experiment that shoots particles at a wall. It shoots some parts of the wall with a higher probability than others. I can record where the particles land. I need to know the underlying ...
user avatar
  • 101
1 vote
1 answer
55 views

How to get the pdf of a joint distribution from its kernel?

How could you obtain the pdf of a joint distribution from a multivariate kernel?
user avatar
0 votes
0 answers
25 views

Fit a kernel density function

I'm working on fitting a kernel density estimator and setting the correct bandwidth. The most popular technique is to minimise the following function. (see https://en.wikipedia.org/wiki/...
user avatar
2 votes
1 answer
63 views

Using kernlab::kqr(reduced = TRUE), how is the y argument missing in the call to csi()?

I'm trying to perform a kernelized quantile regression on some data using the function kqr() from the kernlab package in R. The ...
user avatar
  • 23
0 votes
0 answers
95 views

Neural network regression not learning due to non-uniform data distribution?

I am working on a non-linear multi-output regression problem. I have created a simple neural network. The net is supposed to be a point estimator of $\hat{\theta}_{MAP}$, where $\theta$ are the ...
user avatar
5 votes
2 answers
171 views

How to write a joint kernel density of two random variables with known individual densities?

Consider two random variables $X$ and $Y$ with densities $${f}_1(x) = \frac{1}{n_1h_1} \sum\limits_{i=1}^{n_1}K\left(\frac{x-u_i}{h_1}\right) ~~~~\text{and} ~~~~ {f}_2(y) = \frac{1}{n_2h_2} \sum\...
user avatar
  • 743
0 votes
0 answers
20 views

Differential entropy of a kernel density estimator

I have a set of (~500k) observations that I use to fit a parametric model (univariate three-parameter lognormal). To have an idea of the goodness of fit, I want to compute the Jensen-Shannon distance ...
user avatar
  • 183
0 votes
0 answers
22 views

Appropriate to rescale kernel densities to radians and use watson's two sample test of homogeneity?

I'm looking at activity budgets of animals derived from camera traps and gps collars. I'm pooling multiple cameras or gps collars within each group before comparing the activity of two groups against ...
user avatar
  • 103
0 votes
0 answers
20 views

Kernel regression with npreg overfitting

I am fitting a kernel regression model to 4 predictors $x_1,...,x_4$. I am not particularly familiar with the npreg and npregbw functions. From what I understand the npregbw function performs CV, then ...
user avatar
  • 308
0 votes
0 answers
29 views

Generating samples from a n-dimensional Epanechnikov kernel

I have successfully generated samples from the 1D Epanechnikov kernel, following the routine described on page 236 in "Nonparametric Density Estimation" by Devroye and Gyorfi (Also described ...
user avatar
  • 21
3 votes
1 answer
79 views

How to calculate the expectation of the KDE using little-o?

This is possibly a duplicate of this question of mine, however, here I ask for clarification regarding an estimation that is done when calculating the expectation of the kernel density estimator (KDE) ...
user avatar
  • 239
1 vote
0 answers
57 views

Expectation of kernel density estimators using sharpened data

My question regards the proof of the bias of the kernel density estimator obtained using "sharpened" data. The method comes from the paper by Choi and Hall (1999). Specifically, assume $X_1, ...
user avatar
0 votes
0 answers
81 views

Estimating conditional density, each observation being conditional on belonging to some range of values

I have iid observations $(Y_1, X_1), (Y_2, X_2), ... , (Y_n, X_n)$, where the conditional density of $Y_i|X_i$ is known to have form $$f(y|x) = \begin{cases} \frac{D(y)}{\int_{||t-x|| \leq 1} D(t)...
user avatar
  • 23
1 vote
3 answers
143 views

Practical Uses of Kernel Density Estimators

Perhaps this question is too broad, but I would like to know - how does one use a kernel density estimate in practice? I know of course that one can use it to draw pretty pictures on top of histograms,...
user avatar
2 votes
0 answers
85 views

Restricting Kernel Density Estimate to n-sided polygon

Given some arbitrarily distributed data, in this case data generated by two normal distributions, $\mathcal{N_1}(\mu_1, \Sigma_1)$ and $\mathcal{N_2}(\mu_2, \Sigma_2)$ where $\mu_1 = \begin{bmatrix}0 &...
user avatar
  • 21
2 votes
1 answer
133 views

"Efficiency" of a Kernel

My understanding is that the Epanechnikov kernel is "efficient" in a mean squared error sense. Footnote 4 of Wikipedia's page defines the "efficiency" of a kernel as $$\sqrt{\int u^...
user avatar
3 votes
2 answers
432 views

Suitable approach to cluster histogram-like dataset using HDBSCAN implementation in python

My dataset below shows product sales per price (link to download dataset csv): ...
user avatar
1 vote
0 answers
26 views

A parameter to differentiate multimodal density plots

I am trying to find a parameter that would summarize the shape of a density plot where: an insight into the symmetry is given (not a priority); and how regular/irregular the multi modals are For ...
user avatar
1 vote
1 answer
18 views

Paper on kernel smoothing directly in frequency space

I'm looking to re-read a paper I read 2-3 years back, but my search-fu is failing me now at finding it again. The paper was about a new (at the time) approach for kernel smoothing by implicitly ...
user avatar
2 votes
1 answer
90 views

Is this a kernel density plot?

I have long struggled to bring kernel density plots into the "mainstream." See Reading kernel distribution plot vs typical histogram. However, I recently came across a report that pulled off ...
user avatar
6 votes
1 answer
319 views

Basic properties of the kernel density estimator

This is a question from a mathematical statistics textbook, used at the first and most basic mathematical statistics course for undergraduate students. This exercise follows the chapter on ...
user avatar
  • 239
1 vote
1 answer
35 views

Estimate pdf on a large vector

I have a vector of 10,000 observations and I need to estimate the pdf at each point of the vector. The code I have is the following (Matlab): ...
user avatar
5 votes
1 answer
161 views

Bayesian updating of nonparametric estimate of distribution

Is there any way to perform "bayesian updating" of a nonparametric estimate of some distribution (say, a kernel density estimation) in light of a new set of observed values?
user avatar
1 vote
0 answers
26 views

Nonparametric estimation and kolmogorov sufficient statistics

Recently, I decided to revisit Cover and Thomas, and yesterday I encountered a very interesting passage in the chapter on Kolmogorov complexity: What does this "different procedure" look ...
user avatar
0 votes
0 answers
36 views

How does KernelDensity.score_samples() evaluate log density model in scikit-learn?

Prior to KernelDensity.score_samples(), we use KernelDensity.fit(). Does the fit() memorizes the datapoints $x_i$ and ...
user avatar
2 votes
0 answers
86 views

Plug-in principle with kernel density estimate

The plug-in principle says that to estimate a statistical functional of the form $$ T(\mu) = \int f(x)\ d\mu(x) $$ we can replace $\mu$ with the empirical distribution $\mu_n$ depending on data $X_1,\...
user avatar
  • 166
0 votes
1 answer
316 views

How does KernelDensity.fit() do the fitting in scikit-learn

How does sklearn.neighbors.KernelDensity.fit() fit the dataset with a probability density distribution? The bandwidth is a parameter that we are already providing; ...
user avatar
1 vote
1 answer
43 views

Simple mean or kernel estimator?

Let $X$ be a continuous random variable with support $\mathcal{X}$ and density $f(x)$. Suppose I'm interested in constructing a consistent estimator of $E(X)$ using $n$ i.i.d. observations $(X_1,..., ...
user avatar
  • 276
2 votes
2 answers
64 views

what are the Kernels with zero variance (in KDE)?

I am studying about Kernels in Kernel Density Estimation and I came to understand that the bigger the $n$ that satisfies $\int_{-\infty}^{\infty}K(u)\cdot u^{j}du=0$ for all $1\leq j \leq n$ the more ...
user avatar
  • 33
1 vote
0 answers
60 views

Time Varying Coefficient Model with Uniform Kernel and Spline Estimator

I'm working on the BMACS data set data(BMACS) from library(npmlda). I'm looking at the the time-varying coefficient model of post-CD4 versus smoking $X_1$, pre-HIV CD4 percent $X_2$ (centered) and age ...
user avatar
  • 13
1 vote
0 answers
40 views

KDE Classifier: Mean of the bandwidths of features produces better results than a bandwidth for each feature. Why?

I'm building a Univariate Bayesian Kernel Density Estimation Classifier. It works like the Naives Bayes Classifier but instead of using the normal density function, it uses the Kernel Density ...
user avatar
  • 11
0 votes
1 answer
67 views

How to clean data to produce a smooth histogram

Is there any way to 'clean' a set of data to produce a smooth histogram, ie. without overrepresentative bins? Looking for solution in python3. At the moment I have a histogram with overcounted bins: ...
user avatar
1 vote
0 answers
40 views

Probability Density Estimation vs Function Approximation [closed]

I have a function $f: \mathbb{R} \to \mathbb{R}_+$ and I would like to estimate it. The data pairs $\{(x_i, f(x_i))\}$ arrive at different times $t$. I have two questions: In this case, since the ...
user avatar
0 votes
0 answers
121 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?
user avatar
  • 406

1
2 3 4 5
12