Nolan and Pollard obtained the central limit theorems for U-processes.In this note, we will study the Bootstrap approximation of generalized U-processes by using the Bootstrap method of Efront.
In this paper, we study bootstrap approximation for generalized U-processes (GUP) indexedby a class of functions. Under mild conditions we obtain that the asymptotic distributions ofbootstrapping generalized U-process...In this paper, we study bootstrap approximation for generalized U-processes (GUP) indexedby a class of functions. Under mild conditions we obtain that the asymptotic distributions ofbootstrapping generalized U-processes (BGUP) are the same as those of GUP almost surely. Asa result, the asymptotic properties of bootstrap approximation for PP generalized U-processes(BPPGUP) are obtained. In addition we have derived bootstrap approximation for generalizedV-processes (GVP). Thus, we can use BGUP or bootstrapping GVP (BGVP) to simulate GUPand GVP.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘Nolan and Pollard obtained the central limit theorems for U-processes.In this note, we will study the Bootstrap approximation of generalized U-processes by using the Bootstrap method of Efront.
文摘In this paper, we study bootstrap approximation for generalized U-processes (GUP) indexedby a class of functions. Under mild conditions we obtain that the asymptotic distributions ofbootstrapping generalized U-processes (BGUP) are the same as those of GUP almost surely. Asa result, the asymptotic properties of bootstrap approximation for PP generalized U-processes(BPPGUP) are obtained. In addition we have derived bootstrap approximation for generalizedV-processes (GVP). Thus, we can use BGUP or bootstrapping GVP (BGVP) to simulate GUPand GVP.
