{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:11:33Z","timestamp":1760029893992,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T00:00:00Z","timestamp":1738886400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Zhejiang Provincial Philosophy and Social Sciences Planning Project","award":["24NDJC014YB","LY23A010013"],"award-info":[{"award-number":["24NDJC014YB","LY23A010013"]}]},{"name":"Zhejiang Provincial Natural Science Foundation of China","award":["24NDJC014YB","LY23A010013"],"award-info":[{"award-number":["24NDJC014YB","LY23A010013"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper proposes a variable selection method for a semiparametric varying coefficient spatial autoregressive panel model with fixed effects based on a penalized profile quasi-likelihood method, which can simultaneously select significant variables in parametric components and nonparametric components without estimating fixed effects. With an appropriate selection of the tuning parameters and some mild assumptions, the consistency of this procedure and the oracle property of the obtained estimators are established. Then, we conduct some Monte Carlo simulations to assess the finite sample performance of the proposed variable selection method, and finally, we analyze a real dataset for further illustration.<\/jats:p>","DOI":"10.3390\/axioms14020121","type":"journal-article","created":{"date-parts":[[2025,2,7]],"date-time":"2025-02-07T11:03:51Z","timestamp":1738926231000},"page":"121","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Penalized Profile Quasi-Likelihood Method for a Semiparametric Varying Coefficient Spatial Autoregressive Panel Model with Fixed Effects"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9163-1056","authenticated-orcid":false,"given":"Ruiqin","family":"Tian","sequence":"first","affiliation":[{"name":"School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1263-3457","authenticated-orcid":false,"given":"Miaojie","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0903-9601","authenticated-orcid":false,"given":"Dengke","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Economics, Hangzhou Dianzi University, Hangzhou 310018, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1016\/0166-0462(92)90042-Y","article-title":"Spatial econometrics in practice: A review of software options","volume":"22","author":"Anselin","year":"1992","journal-title":"Reg. Sci. Urban Econ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/j.jeconom.2006.09.001","article-title":"Testing for serial correlation, spatial autocorrelation and random effects using panel data","volume":"140","author":"Baltagi","year":"2007","journal-title":"J. Econom."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/j.jeconom.2006.09.004","article-title":"Panel data models with spatially correlated error components","volume":"140","author":"Kapoor","year":"2007","journal-title":"J. Econom."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1111\/j.1368-423X.2008.00254.x","article-title":"Asymptotic properties of estimators for the linear panel regression model with random individual effects and serially correlated errors: The case of stationary and non-stationary regressors and residuals","volume":"11","author":"Baltagi","year":"2008","journal-title":"Econom. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.jeconom.2009.08.001","article-title":"Estimation of spatial autoregressive panel data models with fixed effects","volume":"154","author":"Lee","year":"2010","journal-title":"J. Econom."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1080\/07474938.2015.1113641","article-title":"Estimation of partially specified spatial panel data models with fixed-effects","volume":"36","author":"Ai","year":"2017","journal-title":"Econom. Rev."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.regsciurbeco.2015.01.003","article-title":"Estimation of partially specified dynamic spatial panel data models with fixed-effects","volume":"51","author":"Zhang","year":"2015","journal-title":"Reg. Sci. Urban Econ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.jspi.2014.11.001","article-title":"Estimation of semi-parametric varying-coefficient spatial panel data models with random-effects","volume":"159","author":"Zhang","year":"2015","journal-title":"J. Stat. Plan. Inference"},{"doi-asserted-by":"crossref","unstructured":"Feng, S., Tong, T., and Chiu, S.N. (2023). Statistical Inference for Partially Linear Varying Coefficient Spatial Autoregressive Panel Data Model. Mathematics, 11.","key":"ref_9","DOI":"10.3390\/math11224606"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"594","DOI":"10.1007\/s11424-014-2263-1","article-title":"Estimation in a semi-varying coefficient model for panel data with fixed effects","volume":"27","author":"Hu","year":"2014","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1016\/j.jkss.2016.01.001","article-title":"Empirical likelihood for semi-varying coefficient models for panel data with fixed effects","volume":"45","author":"He","year":"2016","journal-title":"J. Korean Stat. Soc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"107054","DOI":"10.1016\/j.csda.2020.107054","article-title":"Model detection and estimation for varying coefficient panel data models with fixed effects","volume":"152","author":"Feng","year":"2020","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_13","first-page":"935","article-title":"Varying coefficient panel data model with interactive fixed effects","volume":"31","author":"Feng","year":"2021","journal-title":"Stat. Sin."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1108\/S0731-9053(2009)0000025006","article-title":"Semiparametric estimation of fixed-effects panel data varying coefficient models","volume":"25","author":"Sun","year":"2009","journal-title":"Adv. Econom."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression Shrinkage and Selection Via the Lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Stat. Soc. Ser. B (Methodol.)"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1198\/016214501753382273","article-title":"Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties","volume":"96","author":"Fan","year":"2001","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1198\/016214506000000735","article-title":"The Adaptive Lasso and Its Oracle Properties","volume":"101","author":"Zou","year":"2006","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1556","DOI":"10.1198\/016214508000000788","article-title":"Variable Selection in Nonparametric Varying-Coefficient Models for Analysis of Repeated Measurements","volume":"103","author":"Wang","year":"2008","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1214\/009053607000000604","article-title":"Variable selection in semiparametric regression modeling","volume":"36","author":"Li","year":"2008","journal-title":"Ann. Stat."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3841","DOI":"10.1214\/09-AOS695","article-title":"Quantile regression in partially linear varying coefficient models","volume":"37","author":"Wang","year":"2009","journal-title":"Ann. Stat."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2148","DOI":"10.1016\/j.spl.2009.07.004","article-title":"Variable selection for semiparametric varying coefficient partially linear models","volume":"79","author":"Zhao","year":"2009","journal-title":"Stat. Probab. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1016\/j.jmva.2014.07.015","article-title":"Penalized quadratic inference functions for semiparametric varying coefficient partially linear models with longitudinal data","volume":"132","author":"Tian","year":"2014","journal-title":"J. Multivar. Anal."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/j.jkss.2014.12.003","article-title":"Smooth-threshold GEE variable selection for varying coefficient partially linear models with longitudinal data","volume":"44","author":"Tian","year":"2015","journal-title":"J. Korean Stat. Soc."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1416","DOI":"10.1080\/03610926.2019.1651858","article-title":"Estimation and variable selection for partially linear additive models with measurement errors","volume":"50","author":"Li","year":"2021","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s10260-021-00576-4","article-title":"Model detection and variable selection for mode varying coefficient model","volume":"31","author":"Ma","year":"2022","journal-title":"Stat. Methods Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s00362-022-01383-z","article-title":"Estimation and variable selection for generalized functional partially varying coefficient hybrid models","volume":"65","author":"Liu","year":"2024","journal-title":"Stat. Pap."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1914288","article-title":"Consistent Estimates Based on Partially Consistent Observations","volume":"16","author":"Neyman","year":"1948","journal-title":"Econometrica"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.spasta.2018.05.001","article-title":"A penalized quasi-maximum likelihood method for variable selection in the spatial autoregressive model","volume":"25","author":"Liu","year":"2018","journal-title":"Spat. Stat."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1125","DOI":"10.1007\/s00362-018-0984-2","article-title":"Variable selection for spatial autoregressive models with a diverging number of parameters","volume":"61","author":"Xie","year":"2020","journal-title":"Stat. Pap."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2062","DOI":"10.1080\/03610926.2019.1659367","article-title":"Variable selection for semiparametric varying-coefficient spatial autoregressive models with a diverging number of parameters","volume":"50","author":"Luo","year":"2021","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1899","DOI":"10.1111\/j.1468-0262.2004.00558.x","article-title":"Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models","volume":"72","author":"Lee","year":"2004","journal-title":"Econometrica"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5109","DOI":"10.1007\/s00362-024-01586-6","article-title":"Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects","volume":"65","author":"Tian","year":"2024","journal-title":"Stat. Pap."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/S0304-4076(01)00064-1","article-title":"On the asymptotic distribution of the Moran I test statistic with applications","volume":"104","author":"Kelejian","year":"2001","journal-title":"J. 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USA"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"27138","DOI":"10.1007\/s11356-019-05929-x","article-title":"Analysis of influencing factors of the carbon dioxide emissions in China\u2019s commercial department based on the STIRPAT model and ridge regression","volume":"26","author":"Wen","year":"2019","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1007\/s11069-017-2932-1","article-title":"Industrial structure, technological progress and CO2 emissions in China: Analysis based on the STIRPAT framework","volume":"88","author":"Li","year":"2017","journal-title":"Nat. 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