Questions tagged [kernel-smoothing]
Kernel smoothing techniques, such as kernel density estimation (KDE) and Nadaraya-Watson kernel regression, estimate functions by local interpolation from data points. Not to be confused with [kernel-trick], for the kernels used e.g. in SVMs.
667 questions
0 votes
0 answers
31 views
Role of Z-Tests in Kernel Density Estimation for Cluster Classification
In a recent bioinformatics paper, the authors describe a statistical/machine learning approach to classify clusters of cells using kernel density estimation (KDE) and Z-scores. While the details of ...
1 vote
0 answers
73 views
Pointwise bandwidth selection for kernel density estimation
Consider an estimation for $f(x)$ for a function $f$ at a fixed point $x$. We may use kernel density estimator $\hat{f}_n$ to estimate the $f$, then calculate $\hat{f}(x)$. If I understand correctly, ...
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6 votes
2 answers
123 views
Asymptotic distribution of kernel density estimator as a process over $\mathbb{R}$
Consider the task of estimating a density function $f : \mathbb{R} \to \mathbb{R}$ from independent samples $X_1, \ldots, X_n \sim f$. Let $f_n$ be the kernel density estimator of $f$, that is, $$ f_n ...
- 161
4 votes
1 answer
98 views
Question about proving consistency for $L^2$ norm estimator
I'm reading a paper by Gine where a estimator $T_n$ for $\int f(x)^2dx$ was introduced, where $f$ is the true density function. $T_n$ is defined as $$T_n(h)=\frac{2}{n(n-1)h}\sum_{1\leq i<j\leq n}K\...
- 113
0 votes
0 answers
51 views
Can I use different kernel functions for different independent variables (features)? And should I?
I'm using kernel regression to model a non-linear relationship between several independent variables and a dependent variable. I understand kernel functions and bandwidth selection, but I’m wondering ...
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0 votes
0 answers
139 views
Linear PDF Approximation
I am trying to estimate the shape parameter alpha of the PDF of a Pareto distribution, given that I have incomplete data. Specifically, the true dataset spans values between $10$ and $50,$ but my ...
- 117
5 votes
3 answers
271 views
Cross-validated bandwidth for the derivative of the function with local quadratic estimation
I am trying to estimate non parametrically the first order derivative of a function g(x). I am estimating $g(x)$ using a local polynomial (quadratic) procedure. I know how to compute the leave-one-out ...
- 239
0 votes
0 answers
82 views
How to do kernel-smoothed estimation of the probability $\Pr((U,V)\in A)$ and show its consistency?
Suppose I'm interested in estimating the probability $p=\Pr((U,V)\in A)$ with a random sample $\{(U_i,V_i)\}_{i=1}^N$. The easiest way of doing it is to use the sample mean: $\widehat{p}=1/N\times \...
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