要旨：In this study, we test for a bubble in a model with a random
explosive autoregressive coefficient. We consider two local
alternatives and find that versions of recursive stochastic unit root
tests are more powerful when facing a randomly explosive process than
the recursive right-tailed ADF tests, whereas the latter performs
better in a model with a nonstochastic coefficient. We then propose
the union of rejections strategy using the recursive right-tailed ADF
and stochastic unit root tests. We examine the finite sample
properties of the proposed tests using Monte Carlo simulations and
observe that the test based on the union of rejections strategy is the
second-best, and its power is close to the best one in most cases.
Self-normalization if a tuning free inference method for time series that avoids long-run variance estimation. This talk will introduce the basic idea behind self-normalization and give intuition on when this method is applicable. We will also discuss the usage of self-normalization in two specific settings: change-point detection in the mean of high-dimensional time series and testing relevant hypotheses in functional time series.
Abstract. We propose confidence regions for the parameters of incomplete models
with exact coverage of the true parameter in finite samples. Our confidence region
inverts a test, which generalizes Monte Carlo tests to incomplete models. The test
statistic is a discrete analogue of a new optimal transport characterization of the
sharp identified region. Both test statistic and critical values rely on simulation
drawn from the distribution of latent variables and are computed using solutions
to discrete optimal transport, hence linear programming problems. We also pro-
pose a fast preliminary search in the parameter space with an alternative, more
conservative yet consistent test, based on a parameter free critical value.
We show that the identification problem for a class of dynamic panel logit models with fixed effects has a connection to the truncated moment problem in mathematics. We use this connection to show that the sharp identified set of the structural parameters is characterized by a set of moment equality and inequality conditions. This result provides sharp bounds in models where moment equality conditions do not exist or do not point identify the parameters. We also show that the sharp identified set of the non-parametric latent distribution of the fixed effects is characterized by a vector of its generalized moments, and that the number of moments grows linearly in T. This final result lets us point identify, or sharply bound specific classes of functionals, without solving an optimization problem with respect to the latent distribution. We illustrate our identification result with several examples, and an empirical application on modeling children’s respiratory conditions.
Quantile regression is a method that allows to access the effect of predictors on the conditional quantile of the response in a regression framework. In this talk, we will present some recent theoretical and methodology developments for quantile regression in a panel data setting where repeated observations on individuals are available. On the theory side, we will discuss conditions that guarantee unbiased asymptotic normality of quantile regression with individual-specific intercepts and common slopes. From a methodological standpoint, we will discuss approaches to relax the common slope assumption and allow for groups of individuals that share the same slopes while leaving the intercepts unrestricted.
2) Counterfactual Identification and Latent Space Enumeration
Jiaying Gu (University of Toronto)
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.