RLiu-short bio-112024

Abstract:
Advanced data acquisition technology nowadays has often made inferences from diverse data sources easily accessible. Fusion learning refers to fusing inferences from multiple sources or studies to make more effective overall inference. We focus on the tasks: 1) Whether/When to combine inferences? 2) How to combine inferences efficiently? 3) How to combine inference to enhance the inference for a target study? We present a general framework for nonparametric and efficient fusion learning. The main tool underlying this framework is the new notion of depth confidence distribution (depth-CD), developed by combining data depth, bootstrap and confidence distributions. We show that a depth-CD is an omnibus form of confidence regions, whose contours of level sets shrink toward the true parameter value, and thus an all-encompassing inferential tool. The approach is efficient, general and robust, and readily applies to heterogeneous studies with a broad range of complex settings. The approach is demonstrated with an aviation safety analysis application in tracking aircraft landing performance.

This is joint work with Dungang Liu (U. Cincinnati) and Minge Xie (Rutgers University).

要旨：　Diagnostic tests for regression discontinuity design face a size-control problem. We document a massive over-rejection of the identifying restriction among empirical studies in the top five economics journals. At least one diagnostic test was rejected for 21 out of 60 studies, whereas less than 5% of the collected 799 tests rejected the null hypotheses. In other words, more than one-third of the studies rejected at least one of their diagnostic tests, whereas their underlying identifying restrictions appear valid. Multiple testing causes this problem because the median number of tests per study was as high as 12. Therefore, we offer unified tests to overcome the size-control problem. Our procedure is based on the new joint asymptotic normality of local polynomial mean and density estimates. In simulation studies, our unified tests outperformed the Bonferroni correction.

プログラム2023年度official

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.

Abstract:
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.

Abstract:
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.