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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Expected Value of Continuous Data in R
I am currently working with data involving three continuous variables in R, and I want to calculate the expected value of the joint probability distribution.
I attempted to use the ...
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Convergence rate of Nadaraya–Watson estimator in Holder Space
I'm currently learning non-parametric regression using some online public materials.
Specifically, consider the model
$$
y_{i} = f_{0}(x_{i}) + \epsilon_{i}
$$
where $x_{i}\in \mathcal{X} \subset \...
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Convert any arbitrary window into a tskernel in R [closed]
Although,this question looks like a programming query,
it needs a good understanding of the underlying statistics.
For instance, although in my comment I have posted that I no longer see the error, I ...
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Local linear kernel regression
It is know that the prediction for a given point $x$ is given by:
$$\hat{f}_h(x) = \hat{\beta}_0(x)$$
where
$$\hat{\beta}(x) = \arg\min_{\beta_0, \beta_1}\sum_{i=1}^nK\left(\frac{x - x_i}{h}\right)(...
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L1 error of kernel density estimator is also total variation distance empirical measure and true measure
In the following lecture notes called 'A Gentle Introduction to Empirical Process theory', they make the following statement in Example 3.25.
$\textbf{Example 3.25}$ (Kernel density estimation).Let $...
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How to accurately estimate the probability of a rare event in a large dataset?
I have a dataset of 30,155 names and out of curiosity I verified that the longest name has 68 characters, which is quite big considering the mean and SD were 24.78 and 5.64, respectively. Based on ...
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Estimating Probability Density for Sample
I have a dataset of over 20,000+ samples. The objective here is to define a distribution for the sample so that I can plot all possible outcomes. However, I am unable to find an appropriate ...
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Intensity outliers/anomalies in 2D plot
I wonder what kind of method better to use to see outliers on z value of 2D plot. For example, I have measurements of x and y values both in range of 1 to 16 with step of 1. Next I calculate how many ...
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How to show $\sup_{x\in [a,b]}|f_n(x)-f(x)|=O_p(\sqrt{\frac{\log n}{nh}}+h^2)$ when the kernel $K(\cdot) $ is of bounded variation?
Consider the kernel estimate $f_n$ of a real univariate density defined by $$f_n(x)=\sum_{i=1}^{n}(nh)^{-1}K\left\{h^{-1}(x-X_i)\right\}$$
where $X_1,...,X_n$ are independent and identically ...
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Scaling of different kernels when estimating densities in R
The implementation of the density function in R says that the kernels are scaled so that the bandwidth becomes the standard deviation of the smoothing kernel.
For the Gaussian kernel, it is ...
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Help in simulation for bivariate residual entropy
I am reading a research paper research paper. Let $X=(X_1,X_2)$ be a bivariate random vector with survival function $\bar{F}(x_1,x_2)$.
The the condition residual entropy for the condition ...
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Linear regression with smoothed time-series as independent and dependent variables
I'm pretty sure I'm misunderstanding something quite obvious here but I'm rather confused.
I have multiple time-series that have been smoothed with a gaussian kernel. My goal is to regress the time-...
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Why does re-scaling my density plot using counts change the y-axis so much?
When I make a histogram I get the actual distribution of my samples, with the appropriate counts, but when I try making a density plot the scales go up to 800, and when I try using ...
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Is there a way to accommodate multiple nominal datasets in one-class classification with KDE?
I have 50 sets of time series data, which are collected from 50 'good' runs of the fabrication process, and I would like to utilize all of these nominal datasets to train my model.
From what I`ve ...
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Implementing Convolution Function for Gaussian Kernel in Python for PDF Estimation
I am currently working on estimating a probability density function (PDF) nonparametrically using a Gaussian kernel. My goal is to determine the optimal bandwidth $h$ that minimizes the cross-...
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