The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requires a restrictive functional form assumption for parametric estimation or tuning parameters for nonparametric estimation. In this paper, we propose an alternative approach to estimate the conditional variance function under nonparametric monotonicity constraints by utilizing the isotonic regression method. Our GLS estimator is shown to be asymptotically equivalent to the infeasible GLS estimator with knowledge of the conditional error variance, and is free from tuning parameters, not only for point estimation but also for interval estimation or hypothesis testing. Our analysis extends the scope of the isotonic regression method by showing that the isotonic estimates, possibly with generated variables, can be employed as first stage estimates to be plugged in for semiparametric objects. Simulation studies illustrate excellent finite sample performances of the proposed method. As an empirical example, we revisit Acemoglu and Restrepo's (2017) study on the relationship between an aging population and economic growth to illustrate how our GLS estimator effectively reduces estimation errors.
翻译:通用最小方( GLS) 是回归分析的最基本工具之一 。 实施 GLS 的一个主要问题是估算错误术语的有条件差异功能, 这通常要求为非参数估计的参数估计或调整参数提供严格的功能假设, 非参数估计或调整参数。 在本文中, 我们建议了一种替代办法, 通过使用等离子回归法来估算非参数单一度限制条件下的有条件差异功能。 我们的 GLS 测量仪显示, 与了解有条件误差差异的不可行的 GLS 估计仪相比, 其随机差异功能是无差别的, 并且不受调控参数的影响, 不仅用于点估计, 而且也用于间隙估计或假设测试。 我们的分析扩大了等离子回归法的范围, 显示可使用等离子估计, 作为对半参数对象的首期估算值。 模拟研究显示了拟议方法的精细的有限样本性表现。 作为经验的例子, 我们重新审视关于正在形成的人口和经济增长之间关系的Acemoglu 和Resrepo's (2017) 研究, 以有效减少我们的人口和GLSAsestimator 的误差如何降低 GLS。