1) Daisuke Kurisu (U of Tokyo) 15:10 – 16:25

Title: Prediction and nonparametric inference on random objects
Abstract: In this presentation, I will talk about two topics on statistical analysis of non-Euclidean data.
Firstly, we extend the notion of model averaging for conventional regression models to Frechet regression, which has Euclidean predictors and a non-Euclidean output.
Specifically, we will introduce a cross-validation (CV) criterion for selecting model averaging weights and demonstrate its optimality in terms of the final prediction error.
Through simulation results, we will illustrate that CV outperforms AIC and BIC-type model averaging estimators.

Secondly, we consider statistical inference on the Frechet mean, which is a generalization of the conventional population mean.
In particular, we introduce empirical likelihood (EL) methods for the inference on Frechet means of Manifold-valued data and study asymptotic properties of the EL statistics.
We also discuss some extensions of our main results.
Simulation and real data analysis illustrate the usefulness of the proposed method.

2) Jiaying Gu (U of Toronto) 16:40 – 17:55

Title: Counterfactual Identification and Latent Space Enumeration (joint work with Thomas Russell and Thomas Stringham).

Abstract: This paper provides a unified framework for partial identification of counterfactual parameters in a general class of discrete outcome models allowing for endogenous regressors and multidimensional latent variables, all without parametric distributional assumptions. Our main theoretical result is that, when the covariates are discrete, the infinite-dimensional latent variable distribution can be replaced with a finite-dimensional version that is equivalent from an identification perspective. The finite-dimensional latent variable distribution is constructed in practice by enumerating regions of the latent variable space with a new and efficient cell enumeration algorithm for hyperplane arrangements. We then show that bounds on a certain class of counterfactual parameters can be computed by solving a sequence of linear programming problems, and show how the researcher can introduce additional assumptions as constraints in the linear programs. Finally, we apply the method to a mobile phone choice example with heterogeneous choice sets, as well as an airline entry game example.