Questions tagged [nonparametric-density]

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density function estimation in r

I firstly generate data from a bivariate normal distribution. Here comes the code. ...
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Dealing with bimodal residuals

I want to run linear models to understand the effect of single predictors on an outcome. This is quite straightforward, but I am facing a situation where my residuals appear to be bimodal. I can't ...
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Nonparametric Methods for Two Sample Quantile Test

Background I want to compare two populations' quantile, e.g. 99.99% quantile, 95% quantile. So I am searching for methods for two sample quantile testing. Unfortunately, the population does not obey ...
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Optimal rate of convergence of nonparametric density estimators

Suppose that $X_1, X_2, \dots, X_n$ forms an independent and identically distributed sample from some $d$-dimensional probability distribution with unknown probability density function $f$. Let $x$ be ...
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2 answers
165 views

How to write a joint kernel density of two random variables with known individual densities?

Consider two random variables $X$ and $Y$ with densities $${f}_1(x) = \frac{1}{n_1h_1} \sum\limits_{i=1}^{n_1}K\left(\frac{x-u_i}{h_1}\right) ~~~~\text{and} ~~~~ {f}_2(y) = \frac{1}{n_2h_2} \sum\...
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Driver based forecasting using past distributions

I have reduced my original forecasting problem (Short context : I need to forecast hotel bookings and checkins for the next 3 months. I already have a reasonable forecast for bookings and need to ...
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2 votes
2 answers
64 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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1 answer
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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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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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843 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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70 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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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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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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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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6 votes
1 answer
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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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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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2 answers
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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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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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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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278 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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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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4 votes
2 answers
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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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1 vote
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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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2 votes
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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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8 votes
2 answers
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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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1 vote
1 answer
854 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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4 votes
0 answers
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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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5 votes
2 answers
205 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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3 votes
1 answer
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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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2 votes
1 answer
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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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1 vote
1 answer
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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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-1 votes
1 answer
186 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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6 votes
2 answers
7k 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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3 votes
1 answer
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 ...
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