Questions tagged [nonparametric-density]

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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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16 views

Rescaling a Kernel Density Estimator

I want to estimate an unknown density using the Kernel Density estimator $$\hat f_h(x) = \frac{1}{nh}\sum_{i=1}^nK\left(\frac{x - X_i}{h}\right).$$ I want to apply the estimator to data with different ...
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48 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 ...
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1answer
21 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?...
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1answer
73 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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61 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 ...
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1answer
67 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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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{...
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344 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
1k 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 ...
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22 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 ...
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227 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 ...
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58 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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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 ...
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2answers
2k 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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137 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 ...
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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 ...
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2k 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 ...
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1answer
644 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 ...
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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 ...
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2answers
142 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(\...
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827 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 ...
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1answer
516 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
94 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
152 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 $p>2$ ...
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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 ...
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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 ...