for ψ ∈ G is and consider e$_{nh}$ = 1 n ∑ n j $_{=1}$e$_{nhj}$ ; this generalized function provides ̂ f − f. The expectation functional Ee$_{hn}$ gives the generalized bias of the estima- tor ˆ f, Bias ( ˆ f ) , see (8) . Next to derive the variance functional consider T$_{lj}$ = E ( e$_{nhl}$, ψ$_{1}$ )( e$_{hnj}$, ψ$_{2}$ )) . For l = j by independence For l = j where 33 T 1 jj = ∫ (∫ 1 Π h$_{i}$ K ( x$_{j}$ − x h ) ψ$_{1}$ ( x ) dx ) (∫ 1 Π h$_{i}$ K ( x$_{j}$ − x h ) ψ$_{2}$ ( x ) dx ) dF ( x$_{j}$ ) T$_{jj}$ = E ( e$_{nhj}$ ( x ) , ψ$_{1}$ )( e$_{nhj}$ ( x ) , ψ$_{2}$ ) = ∫ [∫ 1 Π h$_{i}$ K ( x$_{j}$ − x h ) ψ$_{1}$ ( x ) dx − ( f, ψ$_{1}$ ) ] × [∫ 1 Π h$_{i}$ K ( x$_{j}$ − x h ) ψ$_{2}$ ( x ) dx − ( f, ψ$_{2}$ ) ] dF ( x$_{j}$ ) = T 1 jj + T 2 $_{jj}$, T$_{lj}$ = E ( e$_{nhl}$, ψ$_{1}$ )( e$_{nhj}$, ψ$_{2}$ ) = E ( e$_{nhl}$, ψ$_{1}$ ) E ( e$_{nhj}$, ψ$_{2}$ ) = ( Bias ( ˆ f ) , ψ$_{1}$ ) ( Bias ( ˆ f ) , ψ$_{2}$ ) . ( e$_{nhj}$, ψ ) = ∫ 1 Π h$_{i}$ K ( x − x$_{j}$ h ) ψ ( x ) dx − ( f, ψ )