Related papers: Simultaneous Inference for Non-Stationary Random F…

This paper investigates Gaussian Markov random field approximations to nonstationary Gaussian fields using graph representations of stochastic partial differential equations. We establish approximation error guarantees building on the…

Focusing on a high dimensional linear model $y = X\beta + \epsilon$ with dependent, non-stationary, and heteroskedastic errors, this paper applies the debiased and threshold ridge regression method that gives a consistent estimator for…

Many real-world phenomena are naturally bivariate. This includes blood pressure, which comprises systolic and diastolic levels. Here, we develop a Bayesian hierarchical model that estimates these values and their interactions…

Gaussian Markov random fields (GMRFs) are popular for modeling dependence in large areal datasets due to their ease of interpretation and computational convenience afforded by the sparse precision matrices needed for random variable…

This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series. The procedure is based on a novel frequency-domain factor model that provides a flexible yet parsimonious…

Tests for structural breaks in time series should ideally be sensitive to breaks in the parameter of interest, while being robust to nuisance changes. Statistical analysis thus needs to allow for some form of nonstationarity under the null…

An important task in the statistical analysis of inhomogeneous point processes is to investigate the influence of a set of covariates on the point-generating mechanism. In this article, we consider the nonparametric Bayesian approach to…

We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

Gaussian process state-space models (GPSSMs) provide a principled and flexible approach to modeling the dynamics of a latent state, which is observed at discrete-time points via a likelihood model. However, inference in GPSSMs is…

Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…

Several new methods have been proposed for performing valid inference after model selection. An older method is sampling splitting: use part of the data for model selection and part for inference. In this paper we revisit sample splitting…

Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…

Many machine learning problems can be framed in the context of estimating functions, and often these are time-dependent functions that are estimated in real-time as observations arrive. Gaussian processes (GPs) are an attractive choice for…

Structured additive distributional regression models offer a versatile framework for estimating complete conditional distributions by relating all parameters of a parametric distribution to covariates. Although these models efficiently…

The existing theory of penalized quantile regression for longitudinal data has focused primarily on point estimation. In this work, we investigate statistical inference. We propose a wild residual bootstrap procedure and show that it is…

Modern statistical inference tasks often require iterative optimization methods to compute the solution. Convergence analysis from an optimization viewpoint only informs us how well the solution is approximated numerically but overlooks the…

This paper is mainly concerned with asymptotic studies of weighted bootstrap for u- and v-statistics. We derive the consistency of the weighted bootstrap u- and v-statistics, based on i.i.d. and non i.i.d. observations, from some more…

Inference for functional linear models in the presence of heteroscedastic errors has received insufficient attention given its practical importance; in fact, even a central limit theorem has not been studied in this case. At issue,…

We consider the problem of approximating sums of high-dimensional stationary time series by Gaussian vectors, using the framework of functional dependence measure. The validity of the Gaussian approximation depends on the sample size $n$,…

Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…