Based on the empirical likelihood method, the subset selection and hypothesis test for parameters in a partially linear autoregressive model are investigated. We show that the empirical log-likelihood ratio at the tru...Based on the empirical likelihood method, the subset selection and hypothesis test for parameters in a partially linear autoregressive model are investigated. We show that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. We then present the definitions of the empirical likelihood-based Bayes information criteria （EBIC） and Akaike information criteria （EAIC）. The results show that EBIC is consistent at selecting subset variables while EAIC is not. Simulation studies demonstrate that the proposed empirical likelihood confidence regions have better coverage probabilities than the least square method, while EBIC has a higher chance to select the true model than EAIC.展开更多
In many application fields of regression analysis,prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficien...In many application fields of regression analysis,prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients.In this paper,the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions.By combining series approximation method,twostage least squares method and Lagrange multiplier method,the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties.Furthermore,the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions,and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses.Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples.Furthermore,a real example is provided to illustrate the application of the proposed estimation and testing methods.展开更多
基金Supported by the National Natural Science Foundation of China(No.10871188,10801123)
文摘Based on the empirical likelihood method, the subset selection and hypothesis test for parameters in a partially linear autoregressive model are investigated. We show that the empirical log-likelihood ratio at the true parameters converges to the standard chi-square distribution. We then present the definitions of the empirical likelihood-based Bayes information criteria （EBIC） and Akaike information criteria （EAIC）. The results show that EBIC is consistent at selecting subset variables while EAIC is not. Simulation studies demonstrate that the proposed empirical likelihood confidence regions have better coverage probabilities than the least square method, while EBIC has a higher chance to select the true model than EAIC.
基金supported by the Natural Science Foundation of Shaanxi Province under Grant No.2021JM349the Natural Science Foundation of China under Grant Nos.11972273 and 52170172。
文摘In many application fields of regression analysis,prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients.In this paper,the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions.By combining series approximation method,twostage least squares method and Lagrange multiplier method,the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties.Furthermore,the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions,and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses.Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples.Furthermore,a real example is provided to illustrate the application of the proposed estimation and testing methods.
