# Joint Statistics and Econometrics Seminar Series

## PLEASE NOTE THAT THESE SEMINARS ARE POSTPONED UNTIL FURTHER NOTICE

Statistics takes the numbers that you have and summarises them into fewer numbers which are easily digestible by the human brain

This seminar series is a joint partnership with the STICERD Econometrics programme.

All joint Statistics and Econometrics seminars during Lent Term 2019 will take place from 12.00pm to 1.00pm and will be preceded by refreshments from 11.45am. Unless otherwise specified, the seminars will take place in COL 6.15 (Leverhulme Library), 6th Floor of Columbia House.

## Friday 7th February, 12pm in COL 6.15 - Peter Orbanz (UCL)

Asymptotically normal estimation in random graphs and random structures

Consider a large random structure -- a stochastic process on the line, a random graph, a random field on the grid -- and a function that depends only on a small part of the structure. Now use a family of transformations to ‘move’ the domain of the function over the structure, and average over the collected function values. It has only been clarified fairly recently, by results in ergodic theory, that there are precise conditions under which such averages have a law of large numbers: By collecting values at different locations, we can consistently estimate (conditional) expectations. I will explain under what conditions the estimates are also asymptotically normal. Several known central limit theorems for stationary random fields, graphon models of networks, etc emerge as special cases.

## Friday 21st February, 12pm in COL 6.15 - Dennis Kristensen (UCL)

Bayesian Indirect Inference and the ABC of GMM

Approximate Bayesian Computation (ABC) is a Bayesian technique for estimation of parametric models where the likelihood is not available on closed form. We extend ABC in two directions: First, we demonstrate how one easily can incorporate parameter-dependent moments/statistics into the method. Second, we propose a semiparametric version that allows for the usage of ABC in the context of generalized method of moments (GMM). The two extensions are special cases of what we refer to as generalized ABC (GABC) - a general class of ABC-type estimators. We derive the large-sample properties of GABC estimators and analyze the effect of simulations and smoothing on the estimators.

## Friday 6th March, 12pm in COL 6.15 (Haolei Weng, Michigan State University)

Optimal estimation of functionals of high-dimensional mean and covariance matrix

Motivated by portfolio allocation and linear discriminant analysis, we consider estimating a functional involving both the mean vector and covariance matrix. We study the minimax estimation of the functional in the high-dimensional sparse setting. Akin to past works on functional estimation, we show that the optimal rate for estimating the functional undergoes a phase transition between regular parametric rate and some form of high-dimensional estimation rate. We further show that the optimal rate is attained by a carefully designed plug-in estimator based on de-biasing, while a family of naive plug-in estimators are proved to fall short. We further generalize the estimation problem and techniques that allow robust inputs of mean and covariance matrix estimators. Extensive numerical experiments lend further supports to our theoretical results.