Semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices

We consider a new class of semiparametric spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a type of sparse structure in order to include as many panels as possible. We apply the local linear method and least squares method for Yule-Walker equation to estimate trend function and spatio-temporal autoregressive coefficient matrices respectively. We also balance the over-determined and under-determined phenomena in part by adjusting the order of extracting sample information. Both the asymptotic normality and convergence rates of the proposed estimators are established. The proposed methods are further illustrated using both simulation and case studies, the results also show that our estimator is stable among different sample size, and it performs better than the traditional method with known spatial weight matrices.

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Estimation of the trend function for spatio-temporal models

Journal of Nonparametric Statistics ◽

10.1080/10485250902783608 ◽

2009 ◽

Vol 21 (5) ◽

pp. 567-588 ◽

Cited By ~ 7

Author(s):

Hongxia Wang ◽

Jinde Wang

Keyword(s):

Trend Function ◽

Temporal Models ◽

Spatio Temporal

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On the accuracy and convergence of the hybrid FE-meshfree Q4-CNS element in surface fitting problems

MATEC Web of Conferences ◽

10.1051/matecconf/201814701002 ◽

2018 ◽

Vol 147 ◽

pp. 01002

Author(s):

Foek Tjong Wong ◽

Richo Soetanto ◽

Januar Budiman

Keyword(s):

Convergence Rates ◽

Least Squares Method ◽

Hybrid Methods ◽

Numerical Study ◽

Surface Fitting ◽

Shape Functions ◽

Distorted Mesh ◽

Gradient Fields ◽

Elasticity Problems ◽

Better Than

In the last decade, several hybrid methods combining the finite element and meshfree methods have been proposed for solving elasticity problems. Among these methods, a novel quadrilateral four-node element with continuous nodal stress (Q4-CNS) is of our interest. In this method, the shape functions are constructed using the combination of the ‘non-conforming’ shape functions for the Kirchhoff’s plate rectangular element and the shape functions obtained using an orthonormalized and constrained least-squares method. The key advantage of the Q4-CNS element is that it provides the continuity of the gradients at the element nodes so that the global gradient fields are smooth and highly accurate. This paper presents a numerical study on the accuracy and convergence of the Q4-CNS interpolation and its gradients in surface fitting problems. Several functions of two variables were employed to examine the accuracy and convergence. Furthermore, the consistency property of the Q4-CNS interpolation was also examined. The results show that the Q4-CNS interpolation possess a bi-linier order of consistency even in a distorted mesh. The Q4-CNS gives highly accurate surface fittings and possess excellent convergence characteristics. The accuracy and convergence rates are better than those of the standard Q4 element.

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Semiparametric spatio‐temporal models with unknown and banded autoregressive coefficient matrices

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.8053 ◽

2021 ◽

Author(s):

Hongxia Wang ◽

Xuehong Luo ◽

Long Ling

Keyword(s):

Autoregressive Coefficient ◽

Temporal Models ◽

Spatio Temporal

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Pyramidal Framework: Guidance for the Next Generation of GIS Spatial-Temporal Models

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi10030188 ◽

2021 ◽

Vol 10 (3) ◽

pp. 188

Author(s):

Cyril Carré ◽

Younes Hamdani

Keyword(s):

Conceptual Models ◽

Future Generations ◽

Temporal Data ◽

Temporal Modeling ◽

Temporal Models ◽

Gis Data ◽

Spatio Temporal ◽

New Interpretation ◽

Conventional Literature

Over the last decade, innovative computer technologies and the multiplication of geospatial data acquisition solutions have transformed the geographic information systems (GIS) landscape and opened up new opportunities to close the gap between GIS and the dynamics of geographic phenomena. There is a demand to further develop spatio-temporal conceptual models to comprehensively represent the nature of the evolution of geographic objects. The latter involves a set of considerations like those related to managing changes and object identities, modeling possible causal relations, and integrating multiple interpretations. While conventional literature generally presents these concepts separately and rarely approaches them from a holistic perspective, they are in fact interrelated. Therefore, we believe that the semantics of modeling would be improved by considering these concepts jointly. In this work, we propose to represent these interrelationships in the form of a hierarchical pyramidal framework and to further explore this set of concepts. The objective of this framework is to provide a guideline to orient the design of future generations of GIS data models, enabling them to achieve a better representation of available spatio-temporal data. In addition, this framework aims at providing keys for a new interpretation and classification of spatio-temporal conceptual models. This work can be beneficial for researchers, students, and developers interested in advanced spatio-temporal modeling.

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An analytics-based heuristic decomposition of a bilevel multiple-follower cutting stock problem

OR Spectrum ◽

10.1007/s00291-021-00638-9 ◽

2021 ◽

Author(s):

Adejuyigbe O. Fajemisin ◽

Laura Climent ◽

Steven D. Prestwich

Keyword(s):

Real Life ◽

Forest Harvesting ◽

Cutting Stock Problem ◽

Cutting Stock ◽

Decomposition Approach ◽

New Class ◽

Bilevel Problem ◽

Programming Techniques ◽

Bilevel Problems ◽

Better Than

AbstractThis paper presents a new class of multiple-follower bilevel problems and a heuristic approach to solving them. In this new class of problems, the followers may be nonlinear, do not share constraints or variables, and are at most weakly constrained. This allows the leader variables to be partitioned among the followers. We show that current approaches for solving multiple-follower problems are unsuitable for our new class of problems and instead we propose a novel analytics-based heuristic decomposition approach. This approach uses Monte Carlo simulation and k-medoids clustering to reduce the bilevel problem to a single level, which can then be solved using integer programming techniques. The examples presented show that our approach produces better solutions and scales up better than the other approaches in the literature. Furthermore, for large problems, we combine our approach with the use of self-organising maps in place of k-medoids clustering, which significantly reduces the clustering times. Finally, we apply our approach to a real-life cutting stock problem. Here a forest harvesting problem is reformulated as a multiple-follower bilevel problem and solved using our approach.

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Reinforcement learning versus swarm intelligence for autonomous multi-HAPS coordination

SN Applied Sciences ◽

10.1007/s42452-021-04658-6 ◽

2021 ◽

Vol 3 (6) ◽

Author(s):

Ogbonnaya Anicho ◽

Philip B. Charlesworth ◽

Gurvinder S. Baicher ◽

Atulya K. Nagar

Keyword(s):

Reinforcement Learning ◽

State Space ◽

Swarm Intelligence ◽

Performance Indicators ◽

Convergence Rates ◽

Tuning Parameters ◽

Continuous State Space ◽

Continuous State ◽

User Coverage ◽

Better Than

AbstractThis work analyses the performance of Reinforcement Learning (RL) versus Swarm Intelligence (SI) for coordinating multiple unmanned High Altitude Platform Stations (HAPS) for communications area coverage. It builds upon previous work which looked at various elements of both algorithms. The main aim of this paper is to address the continuous state-space challenge within this work by using partitioning to manage the high dimensionality problem. This enabled comparing the performance of the classical cases of both RL and SI establishing a baseline for future comparisons of improved versions. From previous work, SI was observed to perform better across various key performance indicators. However, after tuning parameters and empirically choosing suitable partitioning ratio for the RL state space, it was observed that the SI algorithm still maintained superior coordination capability by achieving higher mean overall user coverage (about 20% better than the RL algorithm), in addition to faster convergence rates. Though the RL technique showed better average peak user coverage, the unpredictable coverage dip was a key weakness, making SI a more suitable algorithm within the context of this work.

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Spatio-temporal expectile regression models

Statistical Modelling ◽

10.1177/1471082x19829945 ◽

2019 ◽

Vol 20 (4) ◽

pp. 386-409

Author(s):

Elmar Spiegel ◽

Thomas Kneib ◽

Fabian Otto-Sobotka

Keyword(s):

Tensor Product ◽

Least Squares Regression ◽

Expectile Regression ◽

Specific Distribution ◽

Weighted Means ◽

Temporal Models ◽

Error Terms ◽

Spatio Temporal ◽

Set Up ◽

Main Effects

Spatio-temporal models are becoming increasingly popular in recent regression research. However, they usually rely on the assumption of a specific parametric distribution for the response and/or homoscedastic error terms. In this article, we propose to apply semiparametric expectile regression to model spatio-temporal effects beyond the mean. Besides the removal of the assumption of a specific distribution and homoscedasticity, with expectile regression the whole distribution of the response can be estimated. For the use of expectiles, we interpret them as weighted means and estimate them by established tools of (penalized) least squares regression. The spatio-temporal effect is set up as an interaction between time and space either based on trivariate tensor product P-splines or the tensor product of a Gaussian Markov random field and a univariate P-spline. Importantly, the model can easily be split up into main effects and interactions to facilitate interpretation. The method is presented along the analysis of spatio-temporal variation of temperatures in Germany from 1980 to 2014.

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Evaluation of IMERG Level-3 Products in Depicting the July to October Rainfall over Taiwan: Typhoon Versus Non-Typhoon

Remote Sensing ◽

10.3390/rs13040622 ◽

2021 ◽

Vol 13 (4) ◽

pp. 622

Author(s):

Wan-Ru Huang ◽

Pin-Yi Liu ◽

Ya-Hui Chang ◽

Cheng-An Lee

Keyword(s):

Real Time ◽

Tropical Rainfall Measuring Mission ◽

Temporal Variations ◽

Rain Gauge ◽

Advantages And Disadvantages ◽

Level 3 ◽

Spatio Temporal ◽

Typhoon Season ◽

Early Late ◽

Better Than

This study assesses the performance of satellite precipitation products (SPPs) from the latest version, V06B, Integrated Multi-satellitE Retrievals for Global Precipitation Mission (IMERG) Level-3 (including early, late, and final runs), in depicting the characteristics of typhoon season (July to October) rainfall over Taiwan within the period of 2000–2018. The early and late runs are near-real-time SPPs, while final run is post-real-time SPP adjusted by monthly rain gauge data. The latency of early, late, and final runs is approximately 4 h, 14 h, and 3.5 months, respectively, after the observation. Analyses focus on the seasonal mean, daily variation, and interannual variation of typhoon-related (TC) and non-typhoon-related (non-TC) rainfall. Using local rain-gauge observations as a reference for evaluation, our results show that all IMERG products capture the spatio-temporal variations of TC rainfall better than those of non-TC rainfall. Among SPPs, the final run performs better than the late run, which is slightly better than the early run for most of the features assessed for both TC and non-TC rainfall. Despite these differences, all IMERG products outperform the frequently used Tropical Rainfall Measuring Mission 3B42 v7 (TRMM7) for the illustration of the spatio-temporal characteristics of TC rainfall in Taiwan. In contrast, for the non-TC rainfall, the final run performs notably better relative to TRMM7, while the early and late runs showed only slight improvement. These findings highlight the advantages and disadvantages of using IMERG products for studying or monitoring typhoon season rainfall in Taiwan.

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