I'm trying to replicate kde2d function, which performs bivariate kernel density estimation, just to understand how it really works, but I can't figure out how is bandwith implemented in code. Here is original code of function:
```function (x, y, h, n = 25, lims = c(range(x), range(y))){ nx <- length(x)if (length(y) != nx) stop("data vectors must be the same length")if (any(!is.finite(x)) || any(!is.finite(y))) stop("missing or infinite values in the data are not allowed")if (any(!is.finite(lims))) stop("only finite values are allowed in 'lims'")n <- rep(n, length.out = 2L)gx <- seq.int(lims[1L], lims[2L], length.out = n[1L])gy <- seq.int(lims[3L], lims[4L], length.out = n[2L])h <- if (missing(h)) c(bandwidth.nrd(x), bandwidth.nrd(y))else rep(h, length.out = 2L)if (any(h <= 0)) stop("bandwidths must be strictly positive")h <- h/4ax <- outer(gx, x, "-")/h[1L]ay <- outer(gy, y, "-")/h[2L]z <- tcrossprod(matrix(dnorm(ax), , nx), matrix(dnorm(ay), , nx))/(nx * h[1L] * h[2L])list(x = gx, y = gy, z = z)}```I don't understand why is in general bandwith divided by 4? Here is equations from which bivariate kernel density should be estimated:https://i.stack.imgur.com/Npyw8.png
I'd really appreciate any help to understand it.