We are concerned with partial dimension reduction for the conditional mean function in the presence of controlling variables.We suggest a profile least squares approach to perform partial dimension reduction for a gen...We are concerned with partial dimension reduction for the conditional mean function in the presence of controlling variables.We suggest a profile least squares approach to perform partial dimension reduction for a general class of semi-parametric models.The asymptotic properties of the resulting estimates for the central partial mean subspace and the mean function are provided.In addition,a Wald-type test is proposed to evaluate a linear hypothesis of the central partial mean subspace,and a generalized likelihood ratio test is constructed to check whether the nonparametric mean function has a specific parametric form.These tests can be used to evaluate whether there exist interactions between the covariates and the controlling variables,and if any,in what form.A Bayesian information criterion(BIC)-type criterion is applied to determine the structural dimension of the central partial mean subspace.Its consistency is also established.Numerical studies through simulations and real data examples are conducted to demonstrate the power and utility of the proposed semi-parametric approaches.展开更多
基金supported by Humanities and Social Science Foundation of Ministry of Education(Grant No.20YJC910003)Natural Science Foundation of Shanghai(Grant No.20ZR1423000)+1 种基金supported by Natural Science Foundation of Beijing(Grant No.Z19J0002)National Natural Science Foundation of China(Grant Nos.11731011 and 11931014)。
文摘We are concerned with partial dimension reduction for the conditional mean function in the presence of controlling variables.We suggest a profile least squares approach to perform partial dimension reduction for a general class of semi-parametric models.The asymptotic properties of the resulting estimates for the central partial mean subspace and the mean function are provided.In addition,a Wald-type test is proposed to evaluate a linear hypothesis of the central partial mean subspace,and a generalized likelihood ratio test is constructed to check whether the nonparametric mean function has a specific parametric form.These tests can be used to evaluate whether there exist interactions between the covariates and the controlling variables,and if any,in what form.A Bayesian information criterion(BIC)-type criterion is applied to determine the structural dimension of the central partial mean subspace.Its consistency is also established.Numerical studies through simulations and real data examples are conducted to demonstrate the power and utility of the proposed semi-parametric approaches.
