For (23) we obtain where ˜ R combines the remaining terms. Analogously to the proof of Theorem 3 √$_{n}$$_{( ˆ}$ m − m, ψψ$_{v}$ ) is represented as The limit process for the first functional is expressed via a value of the func- tional for Brownian bridges, Q$_{ψψ}$$_{v}$ ( U$_{x}$, U$_{xy}$ ) = ∫ ∫ U$_{x,y}$ [ yψ ′ $_{v}$( y ) + ψ$_{v}$ ( y )] ∂ $^{d$_{x}$}$ψ ( F$_{x}$ ( x )) d ( F$_{x}$ ( x )) dy (28) + ∫ F$_{x,y}$ ( x, y ) ( ∂ d$_{x}$ ) $^{2}$ψ ( F$_{x}$ ( x )) U$_{x}$ [ yψ ′ $_{v}$( y ) + ψ$_{v}$ ( y )] d ( F$_{x}$ ( x )) dy + ∫ F$_{x,y}$ ( x, y ) ∂ $^{d$_{x}$}$ψ ( F$_{x}$ ( x )) [ yψ ′ $_{v}$( y ) + ψ$_{v}$ ( y )] d ( U$_{x}$ ) dy. This process is Gaussian with mean zero; summing over v we get a 40 ( − 1) d$_{x}$ +1 ∫ ∫ ˆ F$_{x,y}$ ( x, y ) ∂ $^{d$_{x}$}$ψ ( ˆ F$_{x}$ ( x ) ) [ yψ ′ $_{v}$( y ) + ψ$_{v}$ ( y )] d ( ˆ F$_{x}$ ( x ) ) dy = ( − 1) d$_{x}$ $^{+1}${ F$_{x,y}$ ( x, y ) ∂ $^{d$_{x}$}$ψ ( F$_{x}$ ( x )) [ yψ ′ $_{v}$( y ) + ψ$_{v}$ ( y )] d ( F$_{x}$ ( x )) dy + ∫ ∫ [ ˆ F$_{x,y}$ ( x, y ) − F$_{x,y}$ ( x, y )][ yψ ′ $_{v}$( y ) + ψ$_{v}$ ( y )] ∂ $^{d$_{x}$}$ψ ( F$_{x}$ ( x )) d ( F$_{x}$ ( x )) dy + F$_{x,y}$ ( x, y ) ( ∂ d$_{x}$ ) $^{2}$ψ ( F$_{x}$ ( x )) [ ˆ F$_{x}$ ( x ) − F$_{x}$ ( x )][ yψ ′ $_{v}$( y ) + ψ$_{v}$ ( y )] d ( F$_{x}$ ( x )) dy + ∫ ∫ F$_{x,y}$ ( x, y ) ∂ $^{d$_{x}$}$ψ ( F$_{x}$ ( x )) [ yψ ′ $_{v}$( y ) + ψ$_{v}$ ( y )] d ( ˆ F$_{x}$ ( x ) − F$_{x}$ ( x ) ) dy + ˜ R } , Q$_{ψψ}$$_{v}$ ( √$_{n}$ ( ˆ F$_{x}$ − F$_{x}$ ) $_{,}$√$_{n}$ ( ˆ F$_{xy}$ − F$_{xy}$ )) + n − 1 2 R ( √$_{n}$$_{(}$ ˆ F$_{x}$ − F$_{x}$ ) $_{,}$√$_{n}$ ( ˆ F$_{xy}$ − F$_{xy}$ )) .