# Notation in “Fast Computation of Multivariate Kernel Estimators” by M. P. Wand

I'm new to kernel estimation methods and I've reading the paper "Fast Computation of Multivariate Kernel Estimators" by M. P. Wand.

Particulary on page 434, it says "Let $$(X_1, Y_1), ..., (X_n, Y_n)$$ be a sample of pairs, where $$X_1, ..., X_n$$ are $$\mathbb{R^d}$$-valued predictor variables having $$d$$-variate density $$f$$, and $$Y_1, ..., Y_n$$ are scalar response variables. The kernel density estimate of $$f(x)$$ and local polynomial kernel estimators of $$m(x) = E(Y|X = x)$$ depend on quantities of the form

$$\hat{s}_k(x) = \sum_{i=1}^n(X_i - x)^kK_h^P(X_i-x)$$ (and similar for $$\hat{t_k}$$)

where $$k=(k_1, ..., k_d)$$, and for a $$d$$-vector $$u=(u_1, ..., u_d)$$ the convention $$u_k=(u_1^{k_1} ... u_d^{k_d})$$ is used.

Then $$k$$ is used to calculate the kernel weights $$\kappa$$ which depend on $$k, K$$ and $$h$$ (the kernel and bandwidth), and $$l$$ (which is introduced later).

What do $$k$$ and $$u$$ mean here? It seems like it is something the reader is supposed to know because it comes out of nowhere.