Testing for structural changes in factor models via a nonparametric regression

Ministry of Education, Singapore under its Academic Research Funding Tier

Identifying latent group structures in nonlinear panels

Ministry of Education, Singapore under its Academic Research Funding Tier

A constrained mean curvature flow and Alexandrov-Fenchel inequalities

In this article, we study a locally constrained mean curvature flow for star-shaped hypersurfaces with capillary boundary in the half-space. We prove its long-time existence and the global convergence to a spherical cap. Furthermore, the capillary quermassintegrals defined in \cite{WWX2022} evolve monotonically along the flow, and hence we establish a class of new Alexandrov-Fenchel inequalities for convex hypersurfaces with capillary boundary in the half-space.Comment: Final version, to appear in Int. Math. Res. Not. IMR

The relative isoperimetric inequality for minimal submanifolds in the Euclidean space

In this paper, we mainly consider the relative isoperimetric inequalities for minimal submanifolds in $\mathbb{R}^{n+m}$. We first provide, following Cabr\'e \cite{Cabre2008}, an ABP proof of the relative isoperimetric inequality proved in Choe-Ghomi-Ritor\'e \cite{CGR07}, by generalizing ideas of restricted normal cones given in \cite{CGR06}. Then we prove a relative isoperimetric inequalities for minimal submanifolds in $\mathbb{R}^{n+m}$, which is optimal when the codimension $m\le 2$. In other words we obtain a relative version of isoperimetric inequalities for minimal submanifolds proved recently by Brendle \cite{Brendle2019}. When the codimension $m\le 2$, our result gives an affirmative answer to an open problem proposed by Choe in \cite{Choe2005}, Open Problem 12.6. As another application we prove an optimal logarithmic Sobolev inequality for free boundary submanifolds in the Euclidean space following a trick of Brendle in \cite{Brendle2019b}.Comment: 18 page

Homogeneity Pursuit in Panel Data Models: Theory and Applications

This paper studies estimation of a panel data model with latent structures where individuals can be classified into different groups where slope parameters are homogeneous within the same group but heterogeneous across groups. To identify the unknown group structure of vector parameters, we design an algorithm called Panel-CARDS which is a systematic extension of the CARDS procedure proposed by Ke, Fan, and Wu (2015) in a cross section framework. The extension addresses the problem of comparing vector coefficients in a panel model for homogeneity and introduces a new concept of controlled classification of multidimensional quantities called the segmentation net. We show that the Panel-CARDS method identifies group structure asymptotically and consistently estimates model parameters at the same time. External information on the minimum number of elements within each group is not required but can be used to improve the accuracy of classification and estimation in finite samples. Simulations evaluate performance and corroborate the asymptotic theory in several practical design settings. Two empirical economic applications are considered: one explores the effect of income on democracy by using cross-country data over the period 1961-2000; the other examines the effect of minimum wage legislation on unemployment in 50 states of the United States over the period 1988-2014. Both applications reveal the presence of latent groupings in these panel data

Panel Data Models with Time-Varying Latent Group Structures

This paper considers a linear panel model with interactive fixed effects and unobserved individual and time heterogeneities that are captured by some latent group structures and an unknown structural break, respectively. To enhance realism the model may have different numbers of groups and/or different group memberships before and after the break. With the preliminary nuclear-norm-regularized estimation followed by row- and column-wise linear regressions, we estimate the break point based on the idea of binary segmentation and the latent group structures together with the number of groups before and after the break by sequential testing K-means algorithm simultaneously. It is shown that the break point, the number of groups and the group memberships can each be estimated correctly with probability approaching one. Asymptotic distributions of the estimators of the slope coefficients are established. Monte Carlo simulations demonstrate excellent finite sample performance for the proposed estimation algorithm. An empirical application to real house price data across 377 Metropolitan Statistical Areas in the US from 1975 to 2014 suggests the presence both of structural breaks and of changes in group membership