On nonparametric inference for spatial regression models under domain expanding and infill asymptotics

Kurisu, Daisuke

doi:10.1016/j.spl.2019.06.019

Cited by 7 publications

(5 citation statements)

References 31 publications

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“…Another stream of literature uses kernel-based methods to estimate the processes that are nonanticipative smooth functions with unknown structures (e.g., [23]) and make forecasts through conditional density estimation (e.g., [19,20,29,30]). It has been shown, however, that traditional kernel estimators can become inconsistent as the sampling density grows despite the underlying processes becoming further revealed [18,31], and the infill asymptotics (i.e., the asymptotic properties achieved as the sample becomes increasingly dense [32]) require the careful consideration of the dependence among observations, which is substantial work [33].…”

Section: Introductionmentioning

confidence: 99%

A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics

Chen,

Li,

Tian

2023

Mathematics

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Parametric continuous-time analysis often entails derivations of continuous-time models from predefined discrete formulations. However, undetermined convergence rates of frequency-dependent parameters can result in ill-defined continuous-time limits, leading to modeling discrepancy, which impairs the reliability of fitting and forecasting. To circumvent this issue, we propose a simple solution based on functional data analysis (FDA) and truncated Taylor series expansions. It is demonstrated through a simulation study that our proposed method is superior—compared with misspecified parametric methods—in fitting and forecasting continuous-time stochastic processes, while the parametric method slightly dominates under correct specification, with comparable forecast errors to the FDA-based method. Due to its generally consistent and more robust performance against possible misspecification, the proposed FDA-based method is recommended in the presence of modeling discrepancy. Further, we apply the proposed method to predict the future return of the S&P 500, utilizing observations extracted from a latent continuous-time process, and show the practical efficacy of our approach in accurately discerning the underlying dynamics.

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Section: Introductionmentioning

confidence: 99%

A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics

Chen,

Li,

Tian

2023

Mathematics

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“…Modeling strategies for such non-uniformly spaced spatial data have been discussed in [10,11]. Kernel estimation for locally stationary random fields defined over such irregularly spaced locations has been proposed in [12,13] while autoregressive estimation of similarly defined locally stationary random fields has been proposed in [14]. In the other style of modeling the random field {Y t , t ∈ S} is defined over a regularly spaced grid S ⊂ Z d .…”

Section: Introductionmentioning

confidence: 99%

Model-Based and Model-Free Point Prediction Algorithms for Locally Stationary Random Fields

Das,

Zhang,

Politis

2023

Applied Sciences

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The Model-Free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper, we demonstrate how Model-Free Prediction can be applied to handle random fields that are only locally stationary such as pixel values over an image or satellite data observed on an ocean surface, i.e., they can be assumed to be stationary only across a limited part over their entire region of definition. We construct novel one-step-ahead Model-Based and Model-Free point predictors and compare their performance using synthetic data as well as images from the CIFAR-10 dataset. In the latter case, we demonstrate that our best Model-Free point prediction results outperform those obtained using Model-Based prediction.

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“…As such, assuming independence in the latent variables across units was a reasonable foundation on which to base developments. By contrast, with spatial data such theory does not carry over directly: one requires alternative asymptotic frameworks, for example, increasing domain, fixed domain infill, and it is not guaranteed that properties such as consistency can be necessarily achieved within all these frameworks The asymptotics of spatial and spatio‐temporal modeling remains an active area of research (e.g., Lu and Tjostheim, 2014; Kurisu, 2019), and to our knowledge there has been no theoretical research into the large sample effects of misspecifying the correlation structure in spatial GLLVMs (although related empirical work has been done on this by Shirota et al ., 2019).…”

Section: Introductionmentioning

confidence: 99%

Assuming independence in spatial latent variable models: Consequences and implications of misspecification

2021

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Multivariate spatial data, where multiple responses are simultaneously recorded across spatially indexed observational units, are routinely collected in a wide variety of disciplines. For example, the Southern Ocean Continuous Plankton Recorder survey collects records of zooplankton communities in the Indian sector of the Southern Ocean, with the aim of identifying and quantifying spatial patterns in biodiversity in response to environmental change. One increasingly popular method for modeling such data is spatial generalized linear latent variable models (GLLVMs), where the correlation across sites is captured by a spatial covariance function in the latent variables. However, little is known about the impact of misspecifying the latent variable correlation structure on inference of various parameters in such models. To address this gap in the literature, we investigate how misspecifying and assuming independence for the latent variables' correlation structure impacts estimation and inference in spatial GLLVMs. Through both theory and numerical studies, we show that performance of maximum likelihood estimation and inference on regression coefficients under misspecification depends on a combination of the response type, the magnitude of true regression coefficient and the corresponding loadings, and, most importantly, whether the corresponding covariate is (also) spatially correlated. On the other hand, estimation and inference of truly non-zero loadings and prediction of latent variables is consistently not robust to misspecification of the latent variable correlation structure.

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On nonparametric inference for spatial regression models under domain expanding and infill asymptotics

Cited by 7 publications

References 31 publications

A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics

A Functional Data Approach for Continuous-Time Analysis Subject to Modeling Discrepancy under Infill Asymptotics

Model-Based and Model-Free Point Prediction Algorithms for Locally Stationary Random Fields

Assuming independence in spatial latent variable models: Consequences and implications of misspecification

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