5 Questions
What does the K-Nearest Neighbor Estimator fix instead of the bin width h?
The value of nearest neighbors k
In K-Nearest Neighbor Estimation, what does dk(x) represent?
The distance to the kth nearest neighbor
How does the density vary in K-Nearest Neighbor Estimation as the value of k increases?
Density decreases
What is the basis of density estimation in K-Nearest Neighbor Estimation?
Value of nearest neighbors k
How is K-Nearest Neighbor Estimation similar to Kernel estimation method?
Both use Euclidean distance from the sample
Study Notes
K-Nearest Neighbor Estimation
- Fixes the number of nearest neighbors (k) instead of the bin width (h)
- dk(x) represents the distance to the k-th nearest neighbor of x
- As the value of k increases, the density varies by smoothing out the noise in the data and producing a more general estimate
- The basis of density estimation is that the probability density at a point x is proportional to the number of neighbors within a certain distance
- Similar to Kernel estimation method in that both are non-parametric methods, but K-Nearest Neighbor Estimation is simpler and more intuitive, with k controlling the amount of smoothing
Test your knowledge of the K-Nearest Neighbor Estimator, a method for density estimation based on the value of nearest neighbors k and the distance of the kth nearest neighbor from the sample.
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