{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:09:18Z","timestamp":1760144958908,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T00:00:00Z","timestamp":1717459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China\u2019s General Program","award":["72073079","19YJC790163"],"award-info":[{"award-number":["72073079","19YJC790163"]}]},{"name":"MOE (Ministry of Education in China) Project of Humanities and Social Science","award":["72073079","19YJC790163"],"award-info":[{"award-number":["72073079","19YJC790163"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Under the condition of non-classical distributed errors, the test for spatial dependence in spatial panel data models is still a problem waiting to be solved. In this paper, we apply the FDB (Fast Double Bootstrap) method to spatial panel data models to test spatial dependence. In order to research the validity of the Bootstrap LM-Error test in spatial random effect models under the condition that the error term obeys a normal distribution, heteroscedasticity, or time-series correlation, we construct Bootstrap LM-Error statistics and make use of Monte Carlo simulation from size distortion and power aspects to carry out our research. The Monte Carlo simulation results show that the asymptotic LM-Error test in the spatial random effects model has a large size of distortion when the error term disobeys classical distribution. However, the FDB LM-Error test can effectively correct the size distortion of the asymptotic test with the precondition that there is nearly no loss of power in the FDB test. Obviously, compared to the asymptotic LM-Error test, the FDB LM-Error test is a more valid method to test spatial dependence in a spatial random effects model.<\/jats:p>","DOI":"10.3390\/axioms13060378","type":"journal-article","created":{"date-parts":[[2024,6,4]],"date-time":"2024-06-04T05:17:30Z","timestamp":1717478250000},"page":"378","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Research on the Validity of Bootstrap LM-Error Test in Spatial Random Effect Models"],"prefix":"10.3390","volume":"13","author":[{"given":"Tongxian","family":"Ren","sequence":"first","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Economics and Finance, South China University of Technology, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengliang","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Economics and Statistics, Guangzhou University, Guangzhou 510006, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1111\/j.1435-5957.2010.00279.x","article-title":"Thirty years of spatial econometrics","volume":"89","author":"Anselin","year":"2010","journal-title":"Pap. Reg. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1214\/aos\/1176344552","article-title":"Bootstrap methods: Another look at the jackknife","volume":"7","author":"Efron","year":"1979","journal-title":"Ann. Stat."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3259","DOI":"10.1016\/j.csda.2006.04.001","article-title":"Improving the reliability of bootstrap tests with the fast double bootstrap","volume":"51","author":"Davidson","year":"2007","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_4","first-page":"263","article-title":"Bootstrap unit root tests in Panels with cross-sectional dependence","volume":"110","author":"Chang","year":"2003","journal-title":"J. Econom."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4028","DOI":"10.1016\/j.csda.2006.12.025","article-title":"Bootstrap Panel unit root test under cross-sectional dependence with an application to PPP","volume":"51","author":"Cerrato","year":"2007","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Godfrey, L. (2009). Bootstrap Tests for Regression Models, Palgrave Macmillan.","DOI":"10.1057\/9780230233737"},{"key":"ref_7","unstructured":"Warren, D.E. (2008, January 27\u201329). Bootstrap Methods for Inference with Spatial Panel Data Models. Proceedings of the Moriarty Graduate Paper Competition at the 47th Annual Meeting of the Southern Regional Science Association, Arlington, VA, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/j.regsciurbeco.2009.10.001","article-title":"A robust LM test for spatial error components","volume":"40","author":"Yang","year":"2010","journal-title":"Reg. Sci. Urban Econ."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/s10614-010-9224-0","article-title":"The size and power of bootstrap tests for spatial dependence in a linear regression model","volume":"38","author":"Lin","year":"2011","journal-title":"Comput. Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.econmod.2014.04.022","article-title":"Moran\u2019s I Test of Spatial Panel Data Model Based on Bootstrap Method","volume":"41","author":"Ren","year":"2014","journal-title":"Econ. Model."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.jeconom.2014.10.005","article-title":"LM tests of spatial dependence based on bootstrap critical values","volume":"185","author":"Yang","year":"2015","journal-title":"J. Econom."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/j.jeconom.2014.09.005","article-title":"On the bootstrap for Moran\u2019s I test for spatial dependence","volume":"184","author":"Jin","year":"2015","journal-title":"J. Econom."},{"key":"ref_13","first-page":"127","article-title":"Testing Random Effect for Panel Data Model with Spatial Error Correlation","volume":"10","year":"2012","journal-title":"J. Quant. Tech. Econ."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0304-4076(03)00120-9","article-title":"Testing panel data regression models with spatial error correlation","volume":"117","author":"Baltagi","year":"2003","journal-title":"J. Econom."},{"key":"ref_15","first-page":"98","article-title":"Study on the validity of robust LM test for time-varying spatial weight matrix panel data model","volume":"10","author":"Ling","year":"2015","journal-title":"Stat. Res."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"687","DOI":"10.1080\/01621459.1988.10478649","article-title":"Prepivoting test statistics: A bootstrap view of asymptotic refinements","volume":"83","author":"Beran","year":"1988","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_17","first-page":"417","article-title":"Fast double bootstrap tests of nonnested linear regression models","volume":"21","author":"Davidson","year":"2022","journal-title":"Econom. Rev."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/j.jeconom.2005.06.002","article-title":"The power of bootstrap and asymptotic tests","volume":"133","author":"Davidson","year":"2006","journal-title":"J. Econom."},{"key":"ref_19","first-page":"947","article-title":"Spatial effect test of fixed effect variable coefficient spatial autoregressive panel data model","volume":"4","author":"Shufen","year":"2022","journal-title":"Appl. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1080\/17421770903511346","article-title":"Bootstrap inference in spatial econometrics: The J-test","volume":"5","author":"Burridge","year":"2010","journal-title":"Spat. Econ. Anal."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/6\/378\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:53:23Z","timestamp":1760108003000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/6\/378"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,4]]},"references-count":20,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2024,6]]}},"alternative-id":["axioms13060378"],"URL":"https:\/\/doi.org\/10.3390\/axioms13060378","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2024,6,4]]}}}