部分线性可加分位数回归模型的多项式形式检验

Specification Test of Polynomials under Partially Linear Additive Quantile Regression

部分线性可加模型是半/非参数统计中的常见模型.目前大多数研究围绕着模型参数的估计与推断以及变量选择问题,却对模型的特定参数形式的检验研究较少.然而在实际应用场景中,模型设定的错误有可能带来后续分析的谬误.本文关注于部分线性可加分位数回归模型中的多项式形式检验.我们首先提出基于B样条的两步估计法,并给出了相应估计量的渐近性质;接着我们研究了该模型中可加非参数成分的多项式形式与对应B样条基函数系数之间的联系,并基于这种关系创新性地提出了一种新的假设检验.数值模拟展现了该检验的优越表现,而实际案例的分析也给出了与社会观察颇为一致的结果.

There exists rich literature on partially linear additive models,while most of them focus on estimation,inference and variable selection.Relatively less efforts have been made in specification tests on models,which is important because model misspecification may lead to unpersuasive analysis.In this paper,we consider the specification test of polynomial forms for nonparametric components under partially linear additive quantile regression,which has not been touched in the current literature.A two-step estimation procedure is proposed based on B-spline approximation,and we novally connect the null hypothesis to a specific structure of the B-spline coefficient matrix.Our simulation study has demonstrated the superior performance of the proposed method,and the real case study indicates that the proposed method has given some results that are consistent with previous social studies.