Variance, Clustering, and Density Estimation Revisited

In some cases, it could be just 0 or 1, with 1 meaning that there is a training set data point close to the location in question in the grid, 0 meaning that you are far enough away from any neighbor. To compute density estimates on each cell of the grid, draw a 3x3 window around each yellow cell, and add 1 to all locations (cells) in that 3x3 window. In our example, the number of groups (g 3: low risk, medium risk, high risk of default) will be multiplied by 2 (M / F) x 3 (young / medium / old), resulting in 18 groups, for instance "young females with medium risk of default" being one of these 18 groups. Of course, accessing a cell in the grid (represented by a 2-dim array), while extremely fast and not depending on the number of observations, still requires a tiny bit of time, but it is entirely dependent only on the size of the array, and its dimension.