All Questions
Tagged with nonparametric density-estimation
39
questions
0
votes
0
answers
337
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Is a non-parametric density estimation required for a bimodal distribution?
How to approach the following two cases is clear, I am mentioning them to set up my question.
(Case 1): For data that appears to be a Gaussian distribution, we can assume the distribution is Gaussian ...
- 893
1
vote
1
answer
353
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How Parzen window density estimate $f_n$ converges to f
I am trying to understand how Parzen window density estimate converges to actual density function f(x).[Actually i am trying to learn machine learning on my own using available free resources. Please ...
3
votes
1
answer
100
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Usefulness of MISE
I'm currently in a class on nonparametric smoothing, and, while talking about density estimation in general, the professor introduced the notion of MISE (mean integrated square error):
$\text{MISE}\...
- 229
4
votes
1
answer
2k
views
Is it appropriate to examine the density plot for time series data?
Usually we use time plot to examine the behaviour of time series data cause it reveals the chronological characteristic. Does it make sense that one looks at the data distribution using some non-...
- 120
2
votes
1
answer
839
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Convergence of kernel density estimate as the sample size grows
Let $X\sim\text{Normal}(0,1)$ and let $f_X$ be its probability density function. I conducted some numerical experiments in the software Mathematica to estimate $f_X$ via a kernel method. Let $\hat{f}...
- 285
1
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0
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131
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What is the resulting distribution of a data set that was originally normally distributed but has been quantized and had all negative values removed?
I am trying to benchmark a seasonal forecasting model and calculate not just the point forecasts but the forecast densities from the model.
To do this, I generated a simulated data set in the ...
- 1,381
5
votes
1
answer
698
views
Expected value and variance of KDE
I need to find the expected value and variance of KDE given that $$(i) E[u] = 0 \to \int u\phi(u)du=0\\
(ii)V[u] = \sigma^2 \to \int u^2\phi(u)du=\sigma^2$$ where $\phi$ is the kernel function.
I've ...
- 361
1
vote
0
answers
42
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Difficulties with orthogonal density estimation
I am working on an implementation of an orthogonal density estimator, using the basis
$$ \psi_0(t) = 1, \quad \psi_{2j}(t) = \sqrt{2}\text{cos}(2\pi j t), \quad \psi_{2j+1}(t) = \sqrt{2}\text{sin}(2\...
- 21
4
votes
1
answer
1k
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Properties of Kernel Density Estimators
Given
Let $X \in \mathbb{R}$ be a real-valued random variable with theoretical probability density function (pdf) $f(x)$ and corresponding cumulative distribution function (cdf) $F(x)$. Let $X_1, X_2,...
- 335
1
vote
1
answer
160
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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) ...
- 421
2
votes
2
answers
159
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Dvoretzky-Kiefer-Wolfowitz Vs. KDE fractional convergence
The DKW bound says, roughly and under very general assumptions, that the empirical CDF of $n$ iid samples of a random variable $X$ converges to the exact CDF of $X$ exponentially with the number of ...
- 223
1
vote
2
answers
173
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Closeness of 2-parametric discrete distributions when first 2 moments are matching
Let $\mathcal{D}$ be a particular 2-parameter uni-variate discrete distribution family, and let $D(\theta_1, \theta_2) \in \mathcal{D}$ be one particular distribution from this family, where $\theta_i ...
2
votes
1
answer
183
views
What are some of the common techniques for density estimation?
I'm trying to estimate the probability density function of a real random variable given its iid realizations. What are some of the standard techniques to do this?
One method I have heard of is the ...
4
votes
2
answers
4k
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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)...
- 543
9
votes
2
answers
3k
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Estimating the gradient of log density given samples
I am interested in estimating the gradient of the log probability distribution $\nabla\log p(x)$ when $p(x)$ is not analytically available but is only accessed via samples $x_i \sim p(x)$.
There ...
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