Related papers: Estimation of High-dimensional Nonlinear Vector Au…
This paper investigates the high-dimensional linear regression with highly correlated covariates. In this setup, the traditional sparsity assumption on the regression coefficients often fails to hold, and consequently many model selection…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
Vector autoregressions (VARs) are a widely used tool for modelling multivariate time-series. It is common to assume a VAR is stationary; this can be enforced by imposing the stationarity condition which restricts the parameter space of the…
In high-dimensional Bayesian statistics, various methods have been developed, including prior distributions that induce parameter sparsity to handle many parameters. Yet, these approaches often overlook the rich spectral structure of the…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
In contemporary neuroscience, a key area of interest is dynamic effective connectivity, which is crucial for understanding the dynamic interactions and causal relationships between different brain regions. Dynamic effective connectivity can…
We show that the mixed causal-noncausal Vector Autoregressive (VAR) processes satisfy the Markov property in both calendar and reverse time. Based on that property, we introduce closed-form formulas of forward and backward predictive…
We present a method of variable selection for the sparse generalized additive model. The method doesn't assume any specific functional form, and can select from a large number of candidates. It takes the form of incremental forward…
The nonlinear vector autoregressive (NVAR) model provides an appealing framework to analyze multivariate time series obtained from a nonlinear dynamical system. However, the innovation (or error), which plays a key role by driving the…
A Poisson autoregressive (PAR) model accounting for discreteness and autocorrelation of count time series data is typically estimated in the state-space modelling framework through extended Kalman filter. However, because of the complex…
This paper considers an augmented double autoregressive (DAR) model, which allows null volatility coefficients to circumvent the over-parameterization problem in the DAR model. Since the volatility coefficients might be on the boundary, the…
High-dimensional linear models have been widely studied, but the developments in high-dimensional generalized linear models, or GLMs, have been slower. In this paper, we propose an empirical or data-driven prior leading to an empirical…
This paper considers nonparametric estimation and inference in first-order autoregressive (AR(1)) models with deterministically time-varying parameters. A key feature of the proposed approach is to allow for time-varying stationarity in…
This paper proposes a new high dimensional regression method by merging Gaussian process regression into a variational autoencoder framework. In contrast to other regression methods, the proposed method focuses on the case where output…
Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…
Modern applications have made ubiquitous high-dimensional data, especially time-dependent data, with more and more complicated structures, and it also has become more frequent to encounter the scenario of hierarchical relationships among…
Among semiparametric regression models, partially linear additive models provide a useful tool to include additive nonparametric components as well as a parametric component, when explaining the relationship between the response and a set…
A threshold autoregressive (TAR) model is a powerful tool for analyzing nonlinear multivariate time series, which includes special cases like self-exciting threshold autoregressive (SETAR) models and vector autoregressive (VAR) models. In…
Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…
Bayesian non-parametric methods based on Dirichlet process mixtures have seen tremendous success in various domains and are appealing in being able to borrow information by clustering samples that share identical parameters. However, such…