# 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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### 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 ...
1 vote
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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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1 vote
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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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1 vote
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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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883 views

### 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 ...
4 views

### 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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1 vote
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### Image Blur - Disc Kernel [closed]

I'm trying to use the blur() function from the spatstat package in R to blur an image. One ...
62 views

### Measuring the Distance Between KDE Distributions with Different Bin Counts

I have two KDE distributions, each with a different number of bins. I'd like to compare them effectively, and I'm wondering if there's a recommended technique for this. Should I unify the number of ...
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### Exchanging integrals with inner products with kernel mean embeddings

I am doing some reading on kernel mean embeddings. In particular I am reading the survey paper by Muandet et al. On page 27 (Section 3.1) the authors begin a gentle introduction to kernel mean ...
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### The meaning of probability density functions' product followed by an integration

Scipy's KDE object allows integration of a function multiplied by another KDE object. I assume that this is meant to be used for the estimation of distance between two distributions. As far as I ...
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1 vote
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### Estimating the Distribution of the data

I wanted to know the distribution of some discrete points and they don't follow any particular distribution according to the graphical and other methods. So, I thought of applying non-parametric ...
111 views

### Textbook Recommendation other than ESL [duplicate]

My current background is as follows: (core subjects only) Math : Linear Algebra, Analysis, (half of) Measure TheoryStats : Mathematical Statistics, Regression Analysis, Multivariate Analysis "...
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### Is polynomial interpolation with RKHS in some way more advantageous than simple Lagrange interpolation?

The reproducing kernel Hilbert space associated with the polynomial kernel $K(x,z)=(1+xz)^{d-1}$ (or other similar polynomials) can be used to interpolate a continuous function $f$ at by its value at ...
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### Addition of asymmetrical uncertainties for use in KDE?

My data have asymmetrical confidence intervals (e.g. 100 with a 95% lower bound of 50 and 95% upper bound of 300). I want to perform a KDE on all my data where the bandwidth is determined by the ...
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1 vote
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### Kernel density estimation for noisy samples with known non-iid noise

I'm interested in the following variant of the usual one-dimensional density-estimation problem: I wish to estimate some unknown density $\rho$. There are iid samples $Y_{1},\ldots,Y_{n} \sim \rho$, ...
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1 vote
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### Kernel Density Estimation on a Log-Scale: Log Transformation vs. Geometric Space

I’m working on a project where I need to plot a Kernel Density Estimation (KDE) on a log-scale x-axis. I’ve come across two different methods and I’m unsure which one would be more appropriate for my ...
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634 views

### Difference between KDE, MLE and EM for density estimation

I'm reviewing kernel density estimation (KDE), maximum likelihood estimation (MLE) and expectation maximization (EM) algorithm for density estimation and struggling to differentiate what each ...
1 vote
31 views

1 vote
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### Kernel Smoothing for Time Series data [closed]

I have generated a time series data set of measurements that are a bit noisy and I want to apply kernel smoothing to the data. My time series data is not regular however, meaning that the time ...
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### Comparing models with transformation from discrete to continuous

I have two models to fit a set of categorical features. One uses an encoding followed by a Kernel Density Estimation (with cross-validated bandwidth search) to make a continuous distribution. I am ...
• 101
1k views

### How to interpret peaks in probability density function?

If a probability density function (created using kernel density estimation) exhibits peaks (not necessarily the mode), can we infer the presence of clusters or subgroups in the data?
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