Related papers: Nonparametric and high-dimensional functional grap…
We consider the problem of estimating an undirected Gaussian graphical model when the underlying distribution is multivariate totally positive of order 2 (MTP2), a strong form of positive dependence. Such distributions are relevant for…
Over the last decade, nonparametric methods have gained increasing attention for modeling complex data structures due to their flexibility and minimal structural assumptions. In this paper, we study a general multivariate nonparametric…
We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…
We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…
We develop a uniform inference theory for high-dimensional slope parameters in threshold regression models, allowing for either cross-sectional or time series data. We first establish oracle inequalities for prediction errors, and L1…
This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear…
In recent years, there has been considerable interest in estimating conditional independence graphs in the high-dimensional setting. Most prior work has assumed that the variables are multivariate Gaussian, or that the conditional means of…
We consider a nonparametric additive model of a conditional mean function in which the number of variables and additive components may be larger than the sample size but the number of nonzero additive components is "small" relative to the…
We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…
Multivariate distributions often carry latent structures that are difficult to identify and estimate, and which better reflect the data generating mechanism than extrinsic structures exhibited simply by the raw data. In this paper, we…
We introduce a generalized additive model for location, scale, and shape (GAMLSS) next of kin aiming at distribution-free and parsimonious regression modelling for arbitrary outcomes. We replace the strict parametric distribution…
We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…
Additive regression provides an extension of linear regression by modeling the signal of a response as a sum of functions of covariates of relatively low complexity. We study penalized estimation in high-dimensional nonparametric additive…
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…
When predicting scalar responses in the situation where the explanatory variables are functions, it is sometimes the case that some functional variables are related to responses linearly while other variables have more complicated…
Due to the curse of dimensionality, estimation in a multidimensional nonparametric regression model is in general not feasible. Hence, additional restrictions are introduced, and the additive model takes a prominent place. The restrictions…
Graphical models are an important tool in exploring relationships between variables in complex, multivariate data. Methods for learning such graphical models are well developed in the case where all variables are either continuous or…
Factor analysis is a widely used statistical tool in many scientific disciplines, such as psychology, economics, and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor…
Gaussian process regression is a frequently used statistical method for flexible yet fully probabilistic non-linear regression modeling. A common obstacle is its computational complexity which scales poorly with the number of observations.…
In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…