Indeed, where ˜ w = αw for some 0 ≤ α ≤ 1 and since h$_{i}$ ≤ ¯ h and | w | < 1 on support of K holds and the right-hand side is uniformly bounded by some B$_{ψ}$$_{s}$ < ∞ since ψ$_{s}$ ∈ D$_{l}$$_{+}$$_{k}$ ( U ) . Thus Similarly, | R$_{2}$ | < ∞ . Combining we get that T$_{jj}$ = cov ( ψ$_{1}$, ψ$_{2}$ ) + O ( ¯ h ) as ¯ h → 0 . Consider now Note that here η$_{nhj}$ = n 1 2 ( e$_{nhj}$ − Bias ( ˆ f ) ) . This generalized random function 35 η$_{nhj}$ = n 1 2 [ e$_{nhj}$ − E ( e$_{nhj}$ )]; η$_{nh}$ = 1 n ∑ η$_{nhj}$. (25) | R$_{1}$ | ≤ B$_{ψ}$$_{1}$ sup ψ$_{2}$ + B$_{ψ}$$_{2}$ sup ψ$_{1}$ + ¯ hB$_{ψ}$$_{1}$B$_{ψ}$$_{2}$. ∣ Σ k i =1 ∂ψ$_{s}$ ∂x$_{i}$ ( x − h ˜ w ) w$_{j}$ h$_{j}$ ¯ h ∣ ≤ ∣ Σ k i =1 ∂ψ$_{s}$ ∂x$_{i}$ ( x − h ˜ w ) ∣ ψ$_{s}$ ( x − hw ) = ψ$_{s}$ ( x ) − ¯ h Σ k i =1 ∂ψ$_{s}$ ∂x$_{i}$ ( x − h ˜ w ) w$_{i}$ h$_{i}$ ¯ h , s = 1 , 2 , (24)