Ignoring　potential　spatial　autocorrelation　in　georeferenced　data　may　cause　biased　estimators.　Furthermore,　existing　studies　assume　insufficiently　flexible　structure　of　spatial　lag　model　for　some　practical　applications,　which　makes　it　difficult　to　portray　the　complex　relationship　between　responses　and　covariates.　Thus,　we　propose　a　novel　garrotized　kernel　machine　estimation　method　for　the　nonparametric　spatial　lag　model　and　develop　an　eigenvector　spatial　filtering　algorithm　with　sparse　regression　to　filter　spatial　autocorrelation　out　of　the　residuals.　The　“one-group-at-a-time”　cyclical　coordinate　descent　algorithm　is　introduced　for　a　solution　path　of　tuning　parameters.　Our　method　can　better　describe　the　potential　nonlinear　relationship　between　responses　and　covariates,　making　it　possible　to　model　high-order　interaction　effects　among　covariates.　Numerical　results　and　the　analysis　of　commodity　residential　house　prices　in　large　and　medium-sized　Chinese　cities　indicate　that　the　proposed　method　achieves　better　prediction　performance　compared　with　competing　ones.　The　result　of　real　data　analysis　can　provide　guidance　for　the　government　to　take　targeted　suppression　measures　of　house　prices　for　different　areas.　©　2023　Elsevier　B.V.