Thispaperstudiesestimationandserialcorrelationtestofasemiparametricvarying-coefficientpartiallylinearEVmodeloftheformY=Xτβ+Zτα(T)+ε,ξ=X+ηwiththeidentifyingconditionE[(ε,ητ)τ]=0,Cov[(ε,ητ)η]=σ2Ip+1.Theestimatorsofinterestedregressionparametersβ,andthemodelerrorvarianceσ2,aswellasthenonparametriccomponentsα(T),areconstructed.Undersomeregularconditions,weshowthattheestimatorsoftheunknownvectorβandtheunknownparameterσ2arestronglyconsistentandasymptoticallynormalandthattheestimatorofα(T)achievestheoptimalstrongconvergencerateoftheusualnonparametricregression.Basedontheseestimatorsandasymptoticproperties,weproposetheVN,pteststatisticandempiricallog-likelihoodratiostatisticfortestingserialcorrelationinthemodel.Theproposedstatisticsareshowntohaveasymptoticnormalorchi-squaredistributionsunderthenullhypothesisofnoserialcorrelation.Somesimulationstudiesareconductedtoillustratethefinitesampleperformanceoftheproposedtests.
