K-Nearest Neighbor Estimator (KNN Estimator)

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