{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T02:49:42Z","timestamp":1771469382590,"version":"3.50.1"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T00:00:00Z","timestamp":1752624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["81860605"],"award-info":[{"award-number":["81860605"]}]},{"name":"National Natural Science Foundation of China","award":["2023MS01001"],"award-info":[{"award-number":["2023MS01001"]}]},{"name":"National Natural Science Foundation of China","award":["2020MS01005"],"award-info":[{"award-number":["2020MS01005"]}]},{"name":"National Natural Science Foundation of China","award":["JY20220087"],"award-info":[{"award-number":["JY20220087"]}]},{"name":"the Natural Science Foundation of Inner Mongolia","award":["81860605"],"award-info":[{"award-number":["81860605"]}]},{"name":"the Natural Science Foundation of Inner Mongolia","award":["2023MS01001"],"award-info":[{"award-number":["2023MS01001"]}]},{"name":"the Natural Science Foundation of Inner Mongolia","award":["2020MS01005"],"award-info":[{"award-number":["2020MS01005"]}]},{"name":"the Natural Science Foundation of Inner Mongolia","award":["JY20220087"],"award-info":[{"award-number":["JY20220087"]}]},{"name":"Basic Scientific Research Business Expense Project of Colleges and Universities Directly under Inner Mongolia","award":["81860605"],"award-info":[{"award-number":["81860605"]}]},{"name":"Basic Scientific Research Business Expense Project of Colleges and Universities Directly under Inner Mongolia","award":["2023MS01001"],"award-info":[{"award-number":["2023MS01001"]}]},{"name":"Basic Scientific Research Business Expense Project of Colleges and Universities Directly under Inner Mongolia","award":["2020MS01005"],"award-info":[{"award-number":["2020MS01005"]}]},{"name":"Basic Scientific Research Business Expense Project of Colleges and Universities Directly under Inner Mongolia","award":["JY20220087"],"award-info":[{"award-number":["JY20220087"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJGI"],"abstract":"<jats:p>A geographically and temporally weighted regression (GTWR) model is an effective tool for dealing with spatial heterogeneity and temporal non-stationarity simultaneously. As an important characteristic of spatiotemporal data, spatiotemporal autocorrelation should be considered when constructing spatiotemporally varying coefficient models. The proposed local autoregressive geographically and temporally weighted regression (GTWRLAR) model can simultaneously handle spatiotemporal autocorrelations among response variables and the spatiotemporal heterogeneity of regression relationships. The two-stage weighted least squares (2SLS) estimation can effectively reduce computational complexity. However, the weighted least squares estimation is essentially a Nadaraya\u2013Watson kernel-smoothing approach for nonparametric regression models, and it suffers from a boundary effect. For spatiotemporally varying coefficient models, the three-dimensional spatiotemporal coefficients (longitude, latitude, and time) inherently exhibit larger boundaries than one-dimensional intervals. Therefore, the boundary effect of the 2SLS estimation of GTWRLAR will be more serious. A local\u2013linear geographically and temporally weighted 2SLS (GTWRLAR-L) estimation is proposed to correct the boundary effect in both the spatial and temporal dimensions of GTWRLAR and simultaneously improve parameter estimation accuracy. The simulation experiment shows that the GTWRLAR-L method reduces the root mean square error (RMSE) of parameter estimates compared to the standard GTWRLAR approach. Empirical analyses of carbon emissions in China\u2019s Yellow River Basin (2017\u20132021) show that GTWRLAR-L enhances the adjusted R2 from 0.888 to 0.893.<\/jats:p>","DOI":"10.3390\/ijgi14070276","type":"journal-article","created":{"date-parts":[[2025,7,16]],"date-time":"2025-07-16T12:55:00Z","timestamp":1752670500000},"page":"276","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Local\u2013Linear Two-Stage Estimation of Local Autoregressive Geographically and Temporally Weighted Regression Model"],"prefix":"10.3390","volume":"14","author":[{"given":"Dan","family":"Xiang","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8189-527X","authenticated-orcid":false,"given":"Zhimin","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1111\/j.1477-9552.2003.tb00047.x","article-title":"Spatial Effects within the Agricultural Land Market in Northern Ireland","volume":"54","author":"Mcerlean","year":"2003","journal-title":"J. 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