Related papers: The Debiased Spatial Whittle Likelihood
We consider the problem of estimating a low-dimensional parameter in high-dimensional linear regression. Constructing an approximately unbiased estimate of the parameter of interest is a crucial step towards performing statistical…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
Sparse inducing points have long been a standard method to fit Gaussian processes to big data. In the last few years, spectral methods that exploit approximations of the covariance kernel have shown to be competitive. In this work we…
Many high-dimensional data sets suffer from hidden confounding which affects both the predictors and the response of interest. In such situations, standard regression methods or algorithms lead to biased estimates. This paper substantially…
Completely randomized experiment is the gold standard for causal inference. When the covariate information for each experimental candidate is available, one typical way is to include them in covariate adjustments for more accurate treatment…
Debiasing is a fundamental concept in high-dimensional statistics. While degrees-of-freedom adjustment is the state-of-the-art technique in high-dimensional linear regression, it is limited to i.i.d. samples and sub-Gaussian covariates.…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
Stochastic differential equations provide a powerful tool for modelling dynamic phenomena affected by random noise. In case of repeated observations of time series for several experimental units, it is often the case that some of the…
This paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain empirical likelihood (FDEL) methodology for time series (on a regular grid), the formulation of…
Inferring causal relationships or related associations from observational data can be invalidated by the existence of hidden confounding. We focus on a high-dimensional linear regression setting, where the measured covariates are affected…
We introduce methods for estimating the spectral density of a random field on a $d$-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance…
In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require…
We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of…
This paper provides estimation and inference methods for an identified set's boundary (i.e., support function) where the selection among a very large number of covariates is based on modern regularized tools. I characterize the boundary…
In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…
Statistical inferences for high-dimensional regression models have been extensively studied for their wide applications ranging from genomics, neuroscience, to economics. However, in practice, there are often potential unmeasured…
Stochastic spectral methods have achieved great success in the uncertainty quantification of many engineering problems, including electronic and photonic integrated circuits influenced by fabrication process variations. Existing techniques…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…