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This paper introduces unit-specific heterogeneity in panel data threshold regression. We develop the asymptotic theory for models with heterogeneous thresholds, heterogeneous slope coefficients, and interactive fixed effects. The estimation…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
In this paper, we propose a general subgroup analysis framework based on semiparametric additive mixed effect models in longitudinal analysis, which can identify subgroups on each covariate and estimate the corresponding regression…
For the high-dimensional covariance estimation problem, when $\lim_{n\to \infty}p/n=c \in (0,1)$ the orthogonally equivariant estimator of the population covariance matrix proposed by Tsai and Tsai (2024b) enjoys some optimal properties.…
This paper studies new tests for the number of latent factors in a large cross-sectional factor model with small time dimension. These tests are based on the eigenvalues of variance-covariance matrices of (possibly weighted) asset returns,…
Estimation models from connected vehicles often assume low level parameters such as arrival rates and market penetration rates as known or estimate them in real-time. At low market penetration rates, such parameter estimators produce large…
Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in…
In this paper, the use of partitioned linear multistep methods (PLMM) as time integrators for the numerical approximation of some partial differential equations (pdes) is studied. We consider the periodic initial-value problem of two…
In this article, we study a partially linear single-index model for longitudinal data under a general framework which includes both the sparse and dense longitudinal data cases. A semiparametric estimation method based on a combination of…
This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as massive MIMO, where there are hundreds of antennas at one side of the link. Motivated by the fact…
Multivariate time series data appear often as realizations of non-stationary processes where the covariance matrix or spectral matrix smoothly evolve over time. Most of the current approaches estimate the time-varying spectral properties…
In this paper, we define an underlying data generating process that allows for different magnitudes of cross-sectional dependence, along with time series autocorrelation. This is achieved via high-dimensional moving average processes of…
This article reviews recent advances in fixed effect estimation of panel data models for long panels, where the number of time periods is relatively large. We focus on semiparametric models with unobserved individual and time effects, where…
A standard approach for assessing the performance of partition models is to create synthetic data sets with a prespecified clustering structure, and assess how well the model reveals this structure. A common format is that subjects are…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
We study the sample complexity of estimating the covariance matrix $T$ of a distribution $\mathcal{D}$ over $d$-dimensional vectors, under the assumption that $T$ is Toeplitz. This assumption arises in many signal processing problems, where…
We review our recent results on pseudo-hermitian random matrix theory which were hitherto presented in various conferences and talks. (Detailed accounts of our work will appear soon in separate publications.) Following an introduction of…
Motivated by normalizing DNA microarray data and by predicting the interest rates, we explore nonparametric estimation of additive models with highly correlated covariates. We introduce two novel approaches for estimating the additive…
Complex dynamic systems can be investigated by fitting mechanistic stochastic dynamic models to time series data. In this context, commonly used Monte Carlo inference procedures for model selection and parameter estimation quickly become…
In this paper we consider two closely related problems : estimation of eigenvalues and eigenfunctions of the covariance kernel of functional data based on (possibly) irregular measurements, and the problem of estimating the eigenvalues and…