Dear all,

I’m are glad to invite you to the following seminar.

When: Thursday, September 19th, 2015, 14:30  

Where: Department of Management, Economics and quantitative Methods, Via dei Caniana n. 2 – Room 15 

Title: A stochastic maximal inequality, strict countability, and related topics

Speaker: Yoichi Nishiyama (Waseda University, Tokyo)

Abstract: As an alternative to the well-known methods of "chaining" and "bracketing" that

have been developed in the study of random fields,

a new method, which is based on a stochastic maximal inequality derived

by using It\^o's formula, is presented.

The main results are some weak convergence theorems for sequences of

separable random fields of locally square-integrable martingales

under the uniform topology with the help also of entropy methods.

As special cases, some new results for i.i.d. random sequences, including a new

Donsker theorem and a moment bound for suprema

of empirical processes indexed by classes of sets or functions, are obtained.

An application to statistical estimation in semiparametric models is presented

with an illustration to construct adaptive estimators in Cox's regression model.