Venue

  • DATE: 2023-12-21 (Thu) TIME SLOT: 20:00 - 22:00 ROOM: my office

  • Presentation: WYZ: Chernzhukov, Chetverikov, and Kato (2014): “Gaussian approximations of suprema of empirical processes”

Contents

Proofs

已经发表出来的证明,是从起点(假设)到终点(结论)的行走过程。这跟走迷宫游戏差不多。一开始首先看懂别人是如何走通迷宫,这要花时间。然后要体会别人走迷宫的心路历程。 初学者以可能以为起点和终点都是固定的,然后去走路。其实做到更高级的阶段,自己写文章,起点和终点都由自己定。 一个办法是从结论出发。我知道一些可以行走的路径。比如说工具箱里的大数定律或者中心极限定理。我先就使用这些东西,把结论证了。然后回头看,在证明的过程中,我需要哪些假设,再把假设补上。 另一种可能是从假设出发。在一些我认为是合理的假设下,我能推出些什么东西。太难的结论证不出来,需要知道什么时候停步。

Lee, Shi and Gao (2022): start from the setting and see how far we can go.

Shi, Su and Xie (2023): convert primal problem to dual problem, and use something familiar. Create some “group seminorm” for the context.

LMNS (2023): 先知道结论再做证明。target: show consistency. Eliminate the variance. Bai and Yin (1993). 从结论倒推。

Extra Reading

Isaac Newton:

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.