function and a polynomial or a sin or cos function; in such cases γ is a sum of a continuous function (that is separated from zero on bounded sets within its support) with singular functions such as the δ − function, shifted δ − function and its derivatives. The support conditions in the assumption imply that the open support set of the continuous γ$_{L}$$_{1}$ contains Λ$_{g}$. The existence of a function sequence converging in S ∗ to γ$_{g}$ with the support properties stated follows from the general properties of generalized functions; the only sub- stantive condition there is that the values of the approximating functions ( γ$_{g}$ ) n be separated from zero and from the values of γ$_{L}$$_{1}$. For example, if g included an additive constant, then γ$_{g}$ is a δ − function, and ( γ$_{g}$ ) n could be selected as a sequence of step functions. These approximating functions need not be specified, only their existence is required for the proof. 

The next assumption is on the stochastic properties of the data generating process, the sampling and on the kernel and bandwidth. 

Assumption 7. Moments of order q > d +1 of 1 (1+ z $^{2}$) $_{m}$y, 1 (1+ z $^{2}$) $_{m}$xy con- ditional on z are bounded; { x$_{i}$, y$_{i}$, z$_{i}$ } n i =1 is a random sample from { x, y, z } ; the kernel K is the indicator function of the unit sphere; the bandwidth h is such that h → 0 and satisfies n 1 − d q$_{−}$ 1 h d → ∞ . 

Note that Assumption 6(b) implies boundedness of first conditional mo- ments (functions w$_{·}$ ) of 1 (1+ z $^{2}$) $_{m}$y, 1 (1+ z $^{2}$) $_{m}$xy. 

Define the estimators (denoting by ( x$_{k}$ )$_{i}$ the ith observation on the kth 

