含单调约束的广义回归估计量

Generalized Regression Estimators with Monotonic Constraints

传统广义回归估计量的假设是域与域相互独立。实践中,域值通常呈现特定的顺序和形状,使得域间变量的相关性广泛存在。例如,给定地区,信息传输、计算及服务和软件业、金融业等服务业较纺织业、农副产品加工业等制造业的行业内学历为本科及以上的人员占比、行业平均工资等更高。域间相关性的充分利用有助于提高传统广义回归估计量的精度。对此,在辅助变量域值和目标变量域值变化趋势一致的情况下,首先,引入广义回归估计量的保序回归,构建含单调约束的广义回归估计量,满足目标变量和辅助变量的单调性约束。其次,证明了含单调约束的广义回归估计量在一定条件下具有一致性,均方误差更小。最后,利用数值模拟验证含单调约束的广义回归估计量的估计效果。结果显示,在目标变量域值和辅助变量域值变化趋势一致的情况下,含单调约束的广义回归估计量较传统广义回归估计量,估计精度更高。实证部分采用中国健康与营养调查数据进行分析,进一步说明在对多个域进行估计的情况下,考虑域间相关性的影响,采用含单调约束的广义回归估计量,估计效果更好。

The traditional generalized regression estimators assume that the domains are independent with each other.In practice,the variables of domain are frequently expected to respect shape or order constraints,the correlation of variables inter-domain often exists.The correlation inter-domain should be used to improve the precision of generalized regression estimators.When the auxiliary variable and the target variable have common trend,in order to satisfy the monotonicity constraint of the target variable and the auxiliary variable,the isotonic regression is introduced,and the generalized regression estimator with monotonic constraints is constructed.Moreover,it is proved that,under mild conditions,the new estimator is consistent,and its mean square error is smaller.Again,numerical simulation is used to demonstrate the statistical property of the new estimator.It shows that when two domain values of the target variable and the auxiliary variable have the common trend,the generalized regression estimator with monotonic constraints has higher accuracy.Finally,the empirical part uses the China Health and Nutrition Survey data,which further indicates that,in the case of estimate the variables of multiple domains,considering the influence of the correlation inter-domain,the generalized regression estimators with monotone constraint is more efficient.