Assume you have $10$ covariates, $\mathbf{X}_1$ to $\mathbf{X}_{10}$, each of them uniformly distributed in the interval $[0,1]$. To predict a new test observation $(\mathbf{X}_1^{(0)},...,\mathbf{X}_{10}^{(0)})$. In a K-nearest neighbour (KNN) approach, we use all observations within $20\%$ of the range closest to each of the covariates (that is, in each dimension). Which proportion of available (training) observations can you expect to use for prediction?
If $20\%$ of the closest observations are used for each dimension, then I believe that would would mean $0.2$ of the available observations are used for the prediction? Unless Im overlooking something.