content_image/319693.jpg content_image/319695.jpg content_image/319696.jpg
Represent ( − 1) d$_{x}$ ∫ ˆ F$_{x,y}$ ( x, y ) ∂ $^{d$_{x}$}$ψ ( ˆ F$_{x}$ ( x ) ) d ( ˆ F$_{x}$ ( x ) ) as 

<img src='content_image/319693.jpg'>

where ˜ F$_{x}$ represents an intermediate value and takes values in (0 , 1) d$_{x}$ ; by properties of ψ ∈ D ( W ) the function ( ∂ $^{d$_{x}$}$∂$^{d$_{x}$}$ψ ) ( ˜ F$_{x}$ ) is bounded. Then √$_{n}$ ( ˆ F$_{y}$$_{|}$$_{x}$ − F$_{y}$$_{|}$$_{x}$, ψ ) can be expressed as 

<img src='content_image/319695.jpg'>

where 

<img src='content_image/319696.jpg'>

and R ( ., . ) is a bounded function. 

Since the limit process of √$_{n}$ ( ˆ F$_{.}$ − F$_{.}$ ) is U$_{.}$, a Brownian bridge, and the 

