# 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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### 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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### 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 ...
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 ...
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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### 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 ...
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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### 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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### 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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### 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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### 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 ...
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 ...
142 views