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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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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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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 ...
29 views

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 ...
32 views

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 ...
10 views

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 ...
40 views

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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449 views

How to choose the bandwidth of a KDE in python

Python's Sklearn module provides methods to perform Kernel Density Estimation. One of the challenges in Kernel Density Estimation is the correct choice of the kernel-bandwidth. I have come across ...
16 views

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 ...
102 views

Estimating the population median from a kernel density estimator

I have a 1-d kernel density estimate in the form of two vectors: x_grid is a vector of x-values at which the density function was sampled ...
129 views

Can Kernel Density Estimation estimate an Exponential Distribution?

Can Kernel Density Estimation estimate an Exponential Distribution? I tried to performed to make experiments with various kernels like: "gaussian" and "exponential", but performance seems to be very ...
197 views

Isn't kernel ridge regression supposed to be the mean of gaussian processes?

I read a few times that the mean prediction of a GP should be equivalent to KRR. I tested this empirically and found (dataset is y=2x + gaussian noise): Two explanations for this come to mind: GP is ...
25 views

bandwidth setting for density comparison

I intend to compare a list of density distributions. Following one published paper (with similar type of data and same objective), I learned that I have to use Gaussian kernel density estimator, and a ...
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Derivation of AMISE and Bandwidth

Given: Let $K(\cdot)$ be a bona fide kernel. Let $f$ be a pdf and $\widehat{f}_n$ is kernel density estimator with bandwidth $h$ based on a sample $X_1,X_2,\cdots,X_n$ of size $n$ draw iid from $f$. ...
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Contribution of a predictor in Nonparametric regression

Is there an equivalent to a beta weights in a nonparametric regression? I am using the NP package in R and running a local linear regression where my bandwidth estimates are produced using least ...
63 views

Properties of Kernel Density Estimators

Given Let $X \in \mathbb{R}$ be a real-valued random variable with theoretical probability density function (pdf) $f(x)$ and corresponding cumulative distribution function (cdf) $F(x)$. Let \$X_1, X_2,...
48 views

GARCH model with t-innovations

I am modelling a time series with GARCH model with t-distributed error using RUGARCH package. My model is specified as: ...
45 views

What does bandwidth in kernel regression mean?

here https://stat.ethz.ch/R-manual/R-devel/library/stats/html/ksmooth.html is bandwidth explained as "the bandwidth. The kernels are scaled so that their quartiles (viewed as probability densities) ...