All Questions
Tagged with density-function nonparametric
35 questions
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49
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Implementing Convolution Function for Gaussian Kernel in Python for PDF Estimation
I am currently working on estimating a probability density function (PDF) nonparametrically using a Gaussian kernel. My goal is to determine the optimal bandwidth $h$ that minimizes the cross-...
- 273
1
vote
0
answers
26
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estimating derivative of a random function at a point
I have a random function $f_n(x):R\to R$. At each point $x\in R$, $f_n(x)\to f(x)$ at $1/\sqrt{n}$ rate. While $f(x)$ is smooth, the functions $f_n(x)$ for fixed $n$ are more like step functions, ...
- 21
4
votes
3
answers
548
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Perfect Prediction: Why Would We Ever Use a Statistical Model?
Dear statistics experts
I need your help with something that has bothered me for a while now. My problem revolves around perfect prediction and essentially boils down to:
Why would we ever set up and ...
- 69
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65
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How to prove symmetry of a Uniform kernel?
I am trying to prove this kernel is valid,
$$
K(x) = \frac{1}{2}I(-1 < x < 1)
$$
So far I can integrate to 1, but how do I prove $$k(x) = k(-x)$$
Also, how do we satisfy that k(x) is $\ge$ 0 for ...
0
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0
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47
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Similarity measures for Probability Mass Functions
I am trying to predict whether two sets of papers are written by the same author by looking at the distribution of papers over the years (number of papers published in a given year). Suppose we have ...
3
votes
1
answer
2k
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Can non-parametric data have mean value and standard deviation?
I understand that for non-parametric data, the probability density function (pdf) cannot be obtained using parameters like (mean value) and (standard deviation), and I understand that we use Kernel ...
- 143
1
vote
0
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291
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histogram vs. kernel in density estimation
Assume we have a problem of estimation of a density $f(x)$ over an interval $[0, 1]$. Can a regular histogram (i.e. with equal-sized bins) be viewed as some kind of a kernel?
- 668
2
votes
1
answer
123
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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 ...
- 8,655
2
votes
2
answers
174
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Mean and variance of a non-standard pdf
I have tried to compute the variance and the mean for $\mu=0.5$ of the following PDF using Wolfram cloud but I failed
$$ F(z,\mu,\sigma)=\frac{2 (z-\sigma )^2 \exp \left(-\frac{(z-\sigma )^2
\...
- 181
0
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0
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29
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Group comparison for bivariate distributions
For two groups A and B that consist of n and m individual samples. Each individual sample has a unique 2-dimensional joint probability density functions (PDFs)of two variables. These PDFs are ...
- 1
1
vote
1
answer
162
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Credibility evaluation - how to model conditional continuous density from multiple variables of various types?
I recently got dataset for 37000 households with declared income and a few dozens of other variables of various types: continuous, discrete, binary.
The task is to automatically (unsupervised) ...
- 431
1
vote
1
answer
147
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What is the asymptotic distribution of the integrated MSE of the histogram for a discrete random variable?
Let $\{X_i\}_{i=1}^n$ be i.i.d. discrete random variables. Let $f_n(x) = \frac{1}{n}\sum_{i=1}^n \mathbb{1}(X_i=x)$. I am interested in the asymptotic distribution of
$$\sum_x (f_n(x)-f(x))^2$$
I've ...
- 203
1
vote
0
answers
71
views
Term for assessing unknown distribution
I come from the field of Numerical Analysis, and I look for the term which describes the problem of fitting a probability distribution to statistical numerical continuous data, without a-priori ...
- 223
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35
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Density estimation for points regularly spaced on a grid? Infer spacing between pdf peaks?
Due to a fundamental characteristic of the data, points are clustered together on a 1-D grid-like structure with equal spacing.
Plotting these points in a histogram shows a pdf with several ...
- 703
1
vote
0
answers
50
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Maximizing a non-parametric Probability Density
Assume we have a set of samples and estimate the underlying distribution with a non-parametric density estimator like the Kernel Density Estimator. Lets assume with a gaussian kernel.
In my case it ...
- 525
4
votes
1
answer
2k
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How can I approximate a pdf knowing the estimated CDF in R?
I have an estimate of a CDF in R (nonparametric) and I need to compare this distribution to another one by Kullback-Leibler. In order to do so, I need to find the pdf of this random variable. What is ...
- 213
3
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1
answer
4k
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How do I estimate a smooth cdf from a set of observations?
I have a set of observation, let's call it $X$ and would like to fit a cdf to it. $X$ has a distribution which is roughly approximable with the normal distribution. This CDF should correspond to a ...
- 949
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0
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145
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What are these "hyper-distributions" called?
This may be an elementary question. Say we have a univariate continuous random variable $X$ with unknown pdf $p(x)$, $ \forall x \in X$.
Presumably we can assign a second probability measure $Q(p)$ ...
- 61
1
vote
1
answer
485
views
Parameter estimation problem: maximum likelihood [duplicate]
Suppose I have some observations $x_{1}, x_{2}, \dots, x_{n}$. I also have a probability density function with one unknown parameter $\theta$. I would like to find such $\theta$, which would give the ...
- 21
12
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1
answer
260
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What is the name of the density estimation method where all possible pairs are used to create a Normal mixture distribution?
I just thought of a neat (not necessarily good) way of creating one dimensional density estimates and my question is:
Does this density estimation method have a name? If not, is it a special case of ...
- 6,880
4
votes
0
answers
2k
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Where is the maximum bias and variance in a histogram as non-parametric density estimator?
I am a little bit confused about bias and variance of non-parametric density estimators and hope you can help me.
Assuming a constant bandwidth and sample size, I am wondering at which points of the ...
- 755
1
vote
1
answer
108
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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 ...
- 1,304
1
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0
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62
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Risk in density estimation: grasping the definition
When generalizing estimators to an entire function what is the space in which we perform the integral to obtain the expected value (with respect to this function)?
For example, when estimating ...
- 287
8
votes
1
answer
681
views
Computing inverse probability weights -- conditional (multivariate) density estimation?
The general version:
I need to estimate $f(A | X)$ where $A$ and $X$ are continuous and multivariate. I'd rather do it nonparametrically because I don't have a good functional form in mind and $\hat{...
- 12.8k
2
votes
1
answer
56
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Modeling empirical probability densities
Say we have a classic regression problem in which we have a numeric outcome along with some predictors, both numeric and categorical. In a typical prediction problem we use to estimate some parameter ...
- 716
3
votes
1
answer
189
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Excepted conditional density and conditional expectation
Apparently one can obtain a regression analysis as
$$g(x)=\frac{\int yf(y,x)dy}{f(x)}$$
where
$$f(x)=\int f(y,x)dy$$
is the marginal density of $X_i$. In effect, I believe, the above expression ...
- 2,244
16
votes
3
answers
5k
views
Where is density estimation useful?
After going through some slightly terse mathematics, I think I have a slight intuition of kernel density estimation. But I am also aware that estimating multivariate density for more than three ...
- 469
2
votes
0
answers
154
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bootstrapping the density: bias from parametric bootstrap of polynomial fit of binned frequencies
Bootstrap examples for density estimation usually start with resampling from the empirical distribution of the "micro data", e.g. here on Normal Deviate talking about confidence intervals for ...
- 987
3
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0
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2k
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How to calculate confidence intervals using subsampling after a nonparametric estimator about the empirical distribution function?
I have a problem where I think subsampling is more appropriate than the bootstrap. (Reason in another post.)
However, I found no quick reference on subsampling CIs, and my naive inversion of the ...
- 987
3
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0
answers
281
views
Is excess mass estimation smooth enough to bootstrap? At what rate might a bunching estimator converge?
The recent public finance literature often estimates relative excess mass around specific points of the earnings distribution ("kink points" or "notches" of tax schedules, say), and then bootstraps to ...
- 987
5
votes
0
answers
685
views
Confusion related to Parzen window
I was going through this tutorial related to Parzen window at http://www.cs.utah.edu/~suyash/Dissertation_html/node11.html. However, I have some confusion related to Parzen window with gaussian kernel
...
- 6,847
4
votes
3
answers
255
views
Fast multivariate unimodal density estimator
I have a sample $\boldsymbol{x}_i$ for $i$ in $1,\dots, n$, from a $d$ dimensional density $f(\boldsymbol{x})$ and I would like to estimate this unknown density. In addition I know that $f(\boldsymbol{...
- 3,284
6
votes
3
answers
2k
views
Kernel density estimator that doesn't collapse in the tails
I have iid data-points $x_1, \dots, x_n$, generated by an unknown density $f(x)$.
So far I have approximated $f(x)$ with a normal $N(\hat{\mu}, \hat{\sigma}^2 )$, where $\hat{\mu}$ and $\hat{\sigma}^2$...
- 3,284
3
votes
2
answers
117
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Estimation of the density/distribution
Let $(x_i,y_i,z_i)_{i=1,\dots,n}$ be an i.i.d. sample of $(X,Y,Z)$. How one can estimate the following object
$$\int_{-\infty}^xf(\bar x,y|z)\mathrm{d}\bar x$$
where $f(x,y|z)$ is a density of $X,Y$ ...
- 131
16
votes
1
answer
13k
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Is there an optimal bandwidth for a kernel density estimator of derivatives?
I need to estimate the density function based on a set of observations using the kernel density estimator. Based on the same set of observations, I also need to estimate the first and second ...
- 1,183