Questions tagged [nonparametric-density]

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2
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2answers
39 views

what are the Kernels with zero variance (in KDE)?

I am studying about Kernels in Kernel Density Estimation and I came to understand that the bigger the $n$ that satisfies $\int_{-\infty}^{\infty}K(u)\cdot u^{j}du=0$ for all $1\leq j \leq n$ the more ...
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1answer
42 views

Density plot with epanechnikov with exceedance data

I'm trying to replicate empirical density plot from the paper "Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution". The data is ...
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0answers
15 views

Kernel Density Bandwith Estimation - Summary

I just read the fantastic answer posted by Glen_b back in 2016 on the topic of Kernel Density Bandwidth Estimation (KDBE). Due to taking classes during the COVID-19 pandemic, my knowledge of density ...
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0answers
21 views

Goodness of fit methods for density estimation

If we want to estimate the probability distribution function (pdf) of finite-sampled real continuous data using one of the following approaches: Parametric density estimation: fit a well-known ...
0
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0answers
40 views

Computation of the density of the ratio of two random variables

Background: For two continuous random variables, $X$ and $Y$, the density of $Z := \frac{X}{Y}$ is given by \begin{equation} p_Z(z) = \int_{-\infty}^\infty \lvert y\rvert\, p_{XY}(zy, y) \, \text{...
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1answer
335 views

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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0answers
47 views

What is Gaussian kernel function in kernel density estimation of scipy.stats.gaussian_kde based on Scott rule?

I wanna know what is the Gauss kernel function in scipy.stats.gaussian_kde. According to source, we know scotts_factor=n**(-1./(d+4)), so what is the Gaussian kernel function for kernel density ...
2
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0answers
58 views

Predictive density via LOOCV

I am looking for a way to generate a density prediction (in contrast to a point prediction or a prediction interval) in a multiple regression setting without relying on stringent parametric ...
3
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1answer
28 views

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?...
4
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1answer
146 views

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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0answers
70 views

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 ...
6
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1answer
84 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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0answers
49 views

Does the limit of c exist or not

Let say m is dimension $\exists$ $f(x)$ $f$ is density function and \begin{equation*} f(x) = \frac{c(m,a,b)}{\|x\|^a\left(\log\frac{e}{\|x\|}\right)^{b}}\mathbf{1}_{\|x\|\leq 1} \geq 0 \end{...
4
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2answers
351 views

how to know this integral finite or infinite

In here, i want to show this entropy exist or not exist, namely i should calculate the integral of $\int_0^c\frac{1}{x\log^2\frac{e}{x}}\frac{1}{2} \log\frac{e}{x}\,dx$. If the result is $ <\...
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1answer
2k views

Bandwidth parameters in multivariate KDE using scipy.stats.gaussian_kde

I am working on a project which involves implementing in Python two different density estimation functions over multivariate data; one using N-d histograms and the other using kernel density ...
0
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0answers
26 views

Best way to conduct and present simulation results of nonparametric density estimation

I am conducting a procedure where I first estimate some auxiliary functions (nonparametrically using kernels) and then, knowing their relations to the densities of interest, I use these auxiliary ...
3
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0answers
251 views

Kernel density estimation with FFT for a univariate non-parametric regression

The non-parametric regression model to be estimated looks like the following x_t = b(x_t-1) + epsilon_t Forfinding the optimal bandwith h in the kernel ...
4
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0answers
67 views

Distribution (CDF) estimation for strictly increasing, continuous distribution with compact support

For all $t\in 1,\dots,T$, suppose $x_t\in [0,1]$ is a draw from a distribution with unknown CDF $F:[0,1]\rightarrow [0,1]$. For future use, define $\tilde{x}\in [0,1]^T$ to be a vector containing $x_1,...
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0answers
13 views

Intensity deconvolution

We have a set of intensities (measured) $I_{j} = \cos(\theta_{j}) + N_j$ where $\theta_{j}$ is distributed according to some distribution between 0 and 180 degrees (well, in reality between 0 and ...
4
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2answers
3k views

Leave one out cross validation in kernel density estimation

I am taking a look at : http://pages.cs.wisc.edu/~jerryzhu/cs731/kde.pdf Where they define the following loss function for kernel density estimates $$J(h) = \int \hat{f_n}^2(x)dx -2\int\hat{f_n}(x)...
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0answers
146 views

Generalized linear mixed model with time lags

I'm attempting to understand how random variables and one fixed variable are influencing an animal population over time. The trouble I am having is that my population density estimates were only ...
1
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0answers
47 views

Which distance and generative model?

I am wondering what is a suitable measure to separate the blue, green and red points? I tried 'cosine' but some of the red gets confused with green. My goal is to make two generative models; one ...
6
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2answers
3k views

Density estimation for large dataset

I have a unidimensional data set with more than 1000000 observations. Assuming that those observations are independent realizations of the same random variable I need to estimate the underling ...
1
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1answer
735 views

Is there a difference between 1D Mean Shift and KDE for clustering 1 d data?

I need to cluster (or group) large one dimensional data sets into a set of fixed bins. I started out using K-means, but I want to look into other approaches. Two that I have found are Mean Shift and ...
4
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0answers
82 views

Nonparametric estimation of the logarithm of a density

I was wondering whether there is an equivalent to Kernel Density Estimation to estimate nonparametrically the logarithm of a density. Or if there is any nonparametric method for that. (Taking the ...
4
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2answers
168 views

Nonparametric Identification from Order Statistics

Suppose a vector of random variables $(X_1,...,X_n,Y_1,...,Y_m)$ is such that $X\sim F(\cdot)$ and $Y\sim G(\cdot)$. So $X$ are distributed independently and identically as $F(\cdot)$ and $Y$ as $G(\...
2
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1answer
905 views

What statistic does R's sm use to test equality of densities?

I'd like to ask what kind of test statistic is used in the R package 'sm' to test for equality of two density distributions. This is the package: https://cran.r-project.org/web/packages/sm/index.html ...
2
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1answer
643 views

Understanding “the kernel has zero mean”

I am trying to understand kernel density estimation and found the graphic below illustrating different kernel functions on Wikipedia. I have no trouble reconciling it with the two statements "the ...
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1answer
96 views

Density Function Estimation

Given a sample of $n$ observations, which are assumed to be $i.i.d.$ and generated from a continuous probability law. Consider the question of estimating the density function $f(x)$. There are two ...
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1answer
170 views

question about a Rosenthal inequality

What is the usefulness of Rosenthal inequalities in (kernel) density estimation where $\xi _i .... \xi _n$ are independent random variables, $\mathbb{E}\xi_{i} =0$ and $c(p)=15p/lnp$ for $p>2$ ...
6
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2answers
6k views

How to get percentiles from empirical density in R?

The density() function in R allows me to enter observations and get an empirical density that I can plot x and y values. I like ...
3
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1answer
3k views

R scatterplot matrix with nonparametric density

I normally use MATLAB, or JMP but right now am working with R. I have ~150 dimensional data with a few hundred thousand rows. Some of the columns are non-informative, they only have one value. This ...