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This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…
The main object of investigation in this paper is a very general regression model in optional setting - when an observed process is an optional semimartingale depending on an unknown parameter. It is well-known that statistical data may…
This work develops non-asymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including…
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…
In this paper, we propose a new semiparametric regression estimator by using a hybrid technique of a parametric approach and a nonparametric penalized spline method. The overall shape of the true regression function is captured by the…
In this paper we propose a semiparametric spatial autoregressive model that combines a linear covariate component with a nonparametrically estimated spatial term, allowing flexible dependence modeling without restrictive covariance…
Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization…
We study the behavior of high-dimensional robust regression estimators in the asymptotic regime where $p/n$ tends to a finite non-zero limit. More specifically, we study ridge-regularized estimators, i.e…
Functional data present as functions or curves possessing a spatial or temporal component. These components by nature have a fixed observational domain. Consequently, any asymptotic investigation requires modelling the increased correlation…
Statistical modeling of a nonstationary spatial extremal dependence structure is challenging. Max-stable processes are common choices for modeling spatially-indexed block maxima, where an assumption of stationarity is usual to make…
In this paper we study the asymptotic theory for spectral analysis of stationary random fields, including linear and nonlinear fields. Asymptotic properties of Fourier coefficients and periodograms, including limiting distributions of…
The issue of spatial confounding between the spatial random effect and the fixed effects in regression analyses has been identified as a concern in the statistical literature. Multiple authors have offered perspectives and potential…
This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to…
Regression adjustments are often considered by investigators to improve the estimation efficiency of causal effect in randomized experiments when there exists many pre-experiment covariates. In this paper, we provide conditions that…
We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On…
This paper considers an estimation of semiparametric functional (varying)-coefficient quantile regression with spatial data. A general robust framework is developed that treats quantile regression for spatial data in a natural…
The analysis of continuously spatially varying processes usually considers two sources of variation, namely, the large-scale variation collected by the trend of the process, and the small-scale variation. Parametric trend models on latitude…
This paper deals with variable selection in multivariate linear regression model when the data are observations on a spatial domain being a grid of sites in $\mathbb{Z}^d$ with $d\geqslant 2$. We use a criterion that allows to characterize…
Central limit theorems are established for the sum, over a spatial region, of observations from a linear process on a $d$-dimensional lattice. This region need not be rectangular, but can be irregularly-shaped. Separate results are…
This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…