# 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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I wrote this code to compute the bhattacharyya coefficient between two probabilities distributions. The idea behind was to compute a kernel transformation on the original data, compute 3 estimators (...
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### integrate multi-variate KDE over intervals to approximate probabilities in scipy

Background is I would like to work out the probabilities of certain events occurring to do this, Say I have three intervals: First (-inf, -1) Second ...
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### Is it necessary to normalize the dataset before kernel density estimation?

Is it necessary to normalize (Z-score) the dataset (high dimension) when the dimensionality of features varies greatly? If I normalize the dataset, then the probability density (f1) obtained by KDE ...
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### Create KDE based on Histogram using the weighted KDE approach

In Kernel density estimation with binned data a binned kernel estimator is defined as : $g_n(x) = \frac{1}{nh} \sum_{j=-\infty}^{\infty} n_j K(\frac{x-t_j}{h})$ where $t_j$ denotes the centre of the ...
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### k-nearest neighbor kernel density estimation for a an unknown stochastic process?

Suppose we have a sequence of random variables $\{X_t:t=1,\cdots,T\}$ following an unknown stochastic process (possibly stationary or non-stationary). Now I have two questions: 1- Would it be ...
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### Prediction error of interpolation using Gaussian kernel smoothed intensity

I'll like to know how to calculate the prediction error (or interpolation error) between Gaussian kernel smoothed intensity images created if I comparing all data set (census) with a sample of the ...
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### Examples for integration estimator

suppose I'm interested in estimating $C=\int_{a}^{b}g(x)dx$, where $a$ and $b$ are known, and $g(x)=E(Y|X=x)$ is an unknown function of $x$. The data I have is $\{Y_{i},X_{i}\}_{i=1}^{n}$, then a ...
Suppose I have local linear estimator at $x$ defined as $(\widehat{a}_{x},\widehat{b}_{x})=\underset{a_{x},b_{x}}{argmin}\sum_{i=1}^{n}(Y_{i}-a_{x}-b_{x}(X_{i}-x))^2k(\frac{X_{i}-x}{h})$, where $x$ ...