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Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
This paper presents a general framework for the estimation of regression models with circular covariates, where the conditional distribution of the response given the covariate can be specified through a parametric model. The estimation of…
This paper presents a study on an $\ell_1$-penalized covariance regression method. Conventional approaches in high-dimensional covariance estimation often lack the flexibility to integrate external information. As a remedy, we adopt the…
This article develops direct and inverse estimates for certain finite dimensional spaces arising in kernel approximation. Both the direct and inverse estimates are based on approximation spaces spanned by local Lagrange functions which are…
In this paper we propose and study local linear and polynomial based estimators for implementing Approximate Bayesian Computation (ABC) style indirect inference and GMM estimators. This method makes use of nonparametric regression in the…
We aim at finding the value of an explanatory variable, through its expression in a large data-vector, without knowing the link function between the explanatory variable and the data-space. Sliced Inverse Regression (SIR) method allows for…
With multiple outcomes in empirical research, a common strategy is to define a composite outcome as a weighted average of the original outcomes. However, the choices of weights are often subjective and can be controversial. We propose an…
We propose a new class of estimators of the multivariate response linear regression coefficient matrix that exploits the assumption that the response and predictors have a joint multivariate Normal distribution. This allows us to indirectly…
Practical inference procedures for quantile regression models of panel data have been a pervasive concern in empirical work, and can be especially challenging when the panel is observed over many time periods and temporal dependence needs…
This article describes a multivariate polynomial regression method where the uncertainty of the input parameters are approximated with Gaussian distributions, derived from the central limit theorem for large weighted sums, directly from the…
We consider a class of inverse problems defined by a nonlinear map from parameter or model functions to the data. We assume that solutions exist. The space of model functions is a Banach space which is smooth and uniformly convex; however,…
Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital…
This paper studies the problem of testing whether a system of linear equality and inequality constraints admits a solution when the coefficients of that system may have to be estimated. We show that a wide range of inferential questions in…
To deal with non-linear relations between the predictors and the response, we can use transformations to make the data look linear or approximately linear. In practice, however, transformation methods may be ineffective, and it may be more…
The numerical availability of statistical inference methods for a modern and robust analysis of longitudinal- and multivariate data in factorial experiments is an essential element in research and education. While existing approaches that…
Due to manufacturing defects or wear and tear, industrial components may have uncertainties. In order to evaluate the performance of machined components, it is crucial to quantify the uncertainty of the scattering surface. This brings up an…
Most high-dimensional estimation and prediction methods propose to minimize a cost function (empirical risk) that is written as a sum of losses associated to each data point. In this paper we focus on the case of non-convex losses, which is…
In this paper, a downlink intelligent reflecting surface (IRS) enhanced millimeter-wave (mmWave) non-orthogonal multiple access (NOMA) system is considered. A joint optimization problem over active beamforming, passive beamforming and power…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…