Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [nonparametric-density]

34 questions
8
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2 answers

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 density function. This estimated density function will…
Mur1lo
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1 answer

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 infinite-dimensional optimization problems? That…
user76284
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6
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2 answers

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 it because it allows me to weight observations according to how important they are, and it allows me to specify the…
user52291
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5
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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}…
Shanks
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5
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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 $G(\cdot)$. We only observe $n+m$ ordered variables…
419
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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? One can surely use a Bayesian sampler (e.g.…
Frank
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2 answers

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 $ <\infty$, we can say the entropy exists, otherwise it…
mhmt
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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 $x_1,\dots,x_T$ sorted into increasing order. Suppose…
cfp
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4
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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 $$J(h) = \int \hat{f_n}^2(x)dx -2\int\hat{f_n}(x)f(x)dx$$ which comes from expanding the…
user2879934
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4
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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 logarithm of the kernel density estimate seems…
epsilone
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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? the optimal value of h can be calculate (sic)…
flashing sweep
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3
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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 regression a cross-validation method (leave a point out and estimate it with the rest of the…
InDubio
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1 answer

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 There is a function called sm.density.compare,…
anymous.asker
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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 makes some of the descendants of "pairs" to fail.…
EngrStudent
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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 the bound on the bias is smaller in the MSE. I…
Lazag
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