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.

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22 views

How obtain , using R code , the p-order quantile by inverting CDF estimated non-parametrically by kernel method [closed]

I try to estimate nonparametrically the p-order quantile by generalized inversion of the conditional distribution function from a program R. But I can't really find the solution. Could you help me to ...
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Kernel density estimation and boundary bias

What sort of kernel density estimator does one use to avoid boundary bias? Consider the task of estimating the density $f_0(x)$ with bounded support and where the probability mass is not decreasing ...
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Hat Matrix of Semiparametric Regression Model

In semiparametric regression, I have found very limited work which deals with Hat matrix. All available work is related to splines for nonparametric portion. Now I am trying to perform this with ...
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Nonparametric regression - bias and variance [migrated]

TL;DR - will be glad if someone will help me write a code (preferably in MATLAB) that recovers the figure below using Gaussian kernel. I am particulary interested in understanding how to recover the ...
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Sampling from dataset according to distribution obtained from another dataset

Suppose we have dataset $A$ with several categorical and numerical features: $A_{cat_1}$, $A_{cat_2}$, $\ldots;$ $A_{num_1}$, $A_{num_2}$, $\ldots;$ Also we have another dataset $B$ with the same ...
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Find the CI for a given interval of HDI?

I'm working with big data that doesn't fit well to a distribution but often exhibits a peak (maybe two). I'm looking for a method to calculate the confidence for a given range around the mode. For ...
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55 views

Smoothing histograms with kernel methods

I have a problem where I can receive as output, multidimensional counts in "histogram" form. I can also adjust the size of the bins I receive (i.e., many or few bins). I want to smooth the data and ...
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Looking for a sample that proves that KDE behaves worse than the Dirichlet Process

I am trying to find an example that clearly shows that the kernel density estimator does worse than the Dirichlet process in terms of estimating the distribution of a sample. But eventually, I always ...
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Recent advances in the use of the spectra of kernel integrals following Yoshua Bengio's 2004 paper that links kernel PCA and spectral clustering?

In Yoshua Belgio's 2003 technical report http://www.iro.umontreal.ca/~lisa/pointeurs/TR1232.pdf, and subsequent 2004 paper http://www.iro.umontreal.ca/~lisa/pointeurs/bengio_eigenfunctions_nc_2004.pdf,...
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Gaussian kernel normalization/weights question (python), boundary correction?

I'm trying to decipher some code ... ...
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Inferential properties of Two-Dimensional Kernel Density Estimation

In r, I create a 70% density contour from a two-dimensional kernel density estimation using ...
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72 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}...
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Kernel Matching

I wish to estimate a treatment effect using Kernel Matching, but I'm confused about the process. From a high level, Is A or B correct? Or are both considered Kernel matching? A (1) Estimate ...
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Mean of PDF in Kernel Density Estimation using Python sklearn

I am using Kernel Density estimation to find the PDF of demand for a product using historical data. I am using the numpy library. Here is the code below ...
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25 views

Kernel Estimation to Estimate Treatment Effect

I am trying to determine whether an estimator I came up with is just a non-parametric kernel estimator. I am performing a simulation study to estimate a treatment effect that I impose on my data. My ...
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how to understand this math formula for bandwidth calculation?

I am reading a paper that uses the following equation to calculate the optimal bandwidth, however, I am confused about the position of "4" and "3" in the equation. is this a typo? or what does it mean?...
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Leave-one-out cross validation for histogram smoothing

I am studying about nonparametric kernel density estimation from the below source: [https://web.as.uky.edu/statistics/users/pbreheny/621/F12/notes/10-16.pdf][1] At page 23, there is an explanation ...
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Reducing the dataset size for KDE

I have GPS data, so 2 coordinates, and I want to estimate the busiest places (i.e. the places with more data points). However, I have a lot of points: currently ~4 million for 12 days, and I will be ...
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Expected value and variance of KDE

I need to find the expected value and variance of KDE given that $$(i) E[u] = 0 \to \int u\phi(u)du=0\\ (ii)V[u] = \sigma^2 \to \int u^2\phi(u)du=\sigma^2$$ where $\phi$ is the kernel function. I've ...
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Computing a KDE and its point-wise error from data with measurement errors

I have a set of measurements and their associated errors. I would like to compute a kernel density estimate (KDE) and the error of the KDE at each point. The KDE and the KDE error should take into ...
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What is cross validation doing in my spatial ecology model, and how necessary is it to run?

I'm currently using the R latticeDensity package to estimate home ranges of animals. Within the documentation, The minimum uvc (Unbiased CrossValidation ...
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Kernel density estimate vs Dirichlet process mixture

Nowadays the Dirichlet process mixture (DPM) seems to be the default Bayesian approach for density estimation. My question is why not simply use the kernel density estimate (KDE) to model the density? ...
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Estimate size of each group with uncertainties from a KDE plot

I want to know the percentage of individuals in the "low-squeak" and "high-squeak" groups with uncertainties. How do I calculate it given the following bimodal distribution? For example, I need to ...
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How can probability be equal to pdf times volume of area?

I'm studying pattern recognition and I'm at the part about Kernel density estimators. During the introduction of the subject, the book I'm studying (Pattern Recognition & Machine Learning by ...
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What does it mean to “renormalize” the density of a kernel distribution?

I'm a marine spatial ecologist looking to remove land from some kernel density estimations of tagged sharks. I've seen numerous methods for this approach, with one such method described succinctly in ...
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Naive Bayes + KDE = Lazy?

If I in Naive Bayes use Kernel Density Estimation to estimate logarithms of the conditional probabilities of the attributes in each class $\ln p(x_j|C_k)$ can we consider this classifier to be an ...
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t test and kde plot does not match

I cannot understand the results of scipy independent two samples tests on my my dataset. the results of the test as I understand it suggest there is a significant difference between the means of the ...
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Interpolating Regression Models Across Geographical Space

I have 50 timeseries datasets from 50 cities across the United States (1 for each city). The timeseries are of different lengths (they are daily timeseries anywhere from 3-30 years long), but they are ...
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Behavior of kernel density estimation

Consider the random variable $X=YZ$, where $Y\sim\text{Normal}(0,1)$ and $Z\sim\text{log-Normal}(0,1)$ are independent. I wanted to assess the accuracy of kernel density estimates for the density ...
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60 views

Density estimation as an optimization problem

Density estimation is the estimation of a probability density function from observed data. Can some of the common approaches to density estimation, such as kernel density estimation, be formulated as ...
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Sampling from transformed KDE representation

Let's say that I have a random variable $X$ distributed according to some prior distribution $p(x)$, for simplicity assume that it's a Log Normal distribution. I then sample $N$ elements from this ...
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“Simple” boundary correction method in kernel density estimation

I'm new to kernel density estimation and have a rough idea on boundary bias. When correcting for boundaries, I tried to use boundary correction method as "simple" which is available in R. Once I ...
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How does one choose the bandwidth for the confidence intervals of a kernel density estimate?

My lecturer estimated a kernel density, then wanted to give confidence intervals for it. So, he used a bandwidth $$h_c = h_g \times \frac 1{n^{0.05}}$$ where $h_g$ was the bandwidth of the original ...
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Demmler-Reinsch basis for smoothing splines

I have seen some papers about using the so-called Demmler-Reinsch basis for smoothing spline because it is a basis for natural spline space and also Sobolev space. For example, these papers: A ...
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How to generate random samples from a 2D dataset?

Suppose I'm given a data set consisting of many pairs of $(x,y)$ values which are correlated in some arbitrary complex way. How would I go about 'generating' more pairs of $(x,y)$ coordinates which ...
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Fitting KDE with scikitlearn and pandas to plot. However, distributions lie outside the range of data

I am fitting a distribution of scores ranging from 1-13 for a set of data using scikitlearns KDE functions and Pandas plot.kde. I have set the bandwidth with a gridsearchCV method. However, when the ...
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Gaussian Kernel and Feature Space [duplicate]

I have been reading this paper for a few days. There is one section (Section 3.3) that confuses me. We start by gathering local features from training images of a particular class into a single ...
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MSE for the kernel-based HAC long-run covariance matrix itself (in the Frobenius norm sense)

Consider the stationary multivariate time series $X_1, \ldots, X_T$ and the HAC-consistent long-run covariance matrix estimator $$\hat{\Gamma} = \hat{\Gamma}_0 + \sum_{l=1}^{T-1} K\left(\frac{l}{h_T}\...
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How does this algorithm converge?

From https://en.wikipedia.org/wiki/Kernel_density_estimation, we have this formula for the optimal bandwidth for a kernel density estimator. Note that we need $R(f'')$ which is unknown. An ...
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A comparison of the global optimal binwidth and local optimal binwidth of the histogram estimator

Suppose we have $X_1, \dots, X_n$ to be an i.i.d sample with unknown pdf $f(x)$ and cdf $F(x)$, and define $\hat{f} (x)$ to be the histogram estimator. We also define its Mean Integrated Square Error ...
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139 views

Gaussian Kernel density estimation by hand

I'm trying to understand the logic behind kernel density estimation. I found the explanation in wikipedia very useful, but I'm not capable yet, of having a full understanding of this method so I want ...
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Minimizing MISE to find consistent estimator

Consider kernel regression estimation of the mean function $m$ of the process $$y_t = m(x_t) + \epsilon_t,$$ where $\epsilon_t$' s are correlated with covariance function $R(s,t) = \exp \{-\lambda|s-...
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Does local linear regression include a weighting Kernel?

I am applying a Regression Discontinuity Design (RDD) to estimate the effect of a policy change. In RDD I can apply the parametric approach (polynomial regression) and the non-parametric approach (...
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state of the art in density estimation

I have seen density estimation methods which are pretty old. Specifically, I am referring to Parzen Window method. When I read the original Parzen's paper, I was amazed by it's beauty and I know that ...
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25 views

Kernel density, why does my subset appear to have a larger spread than the original series?

I have a series that is 1500 observations long called alt_intercept. From it, I created a subset that contains values only if another series (called pvalue) is less ...
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52 views

why does y axis sometimes change from normal histogram to kernel density?

Consider the distributions I have plotted below. They are of the same variables, one in normal histogram form and another in kernel density (Epachanov). As far as I know, the auc of the kernel ...
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86 views

Kernel Density Estimation - Physical Interpretation?

I just read this article about the motivation for KDE. From what I understand, you are using Gaussian probability density distributions for each datapoint and then, depending on the selected kernel ...
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How can I estimate bivariate probability density for support restricted data?

I have a bivariate sample with the following kernel density estimation The issue is that there is actually a cutoff for log(Age) at about 2.5, so value greater than 2.5 has probability 0. The fitted ...
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Transformation of a random variable and KDEs — when is reweighting needed?

Suppose I have been given some data $X$ that I wish to resample according to their empirical distribution. For whatever reason, I decided to transform these variables to some other space $Y = f(X)$ ...
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How to choose sample size from probability density for computing mutual information based on continuous variables

I need to compute mutual information gain based two continuous variables $X$ and $Y$ $I(X|Y) = \int_X\int_Y p_{x.y}(x,y) \log(\frac{p_{x.y}(x,y)}{p_{x}(x)p_{y}(y)})$. I have used Kernel Density ...

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