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首页> 外文期刊>Econometric Reviews >Finite-sample generalized confidence distributions and sign-based robust estimators in median regressions with heterogeneous dependent errors
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Finite-sample generalized confidence distributions and sign-based robust estimators in median regressions with heterogeneous dependent errors

机译：具有异构依赖误差的中位数回归中的有限样本广义置信分布和符号的鲁棒估算

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摘要

We study the problem of estimating the parameters of a linear median regression without any assumption on the shape of the error distribution - including no condition on the existence of moments - allowing for heterogeneity (or heteroskedasticity) of unknown form, noncontinuous distributions, and very general serial dependence (linear and nonlinear). This is done through areverse inference approach, based on a distribution-free sign-based testing theory, from which confidence sets and point estimators are subsequently generated. We propose point estimators, which have a natural association with confidence distributions. These estimators are based on maximizing testp-values and inherit robustness properties from the generating distribution-free tests. Both finite-sample and large-sample properties of the proposed estimators are established under weak regularity conditions. We show that they are median-unbiased (under symmetry and estimator unicity) and possess equivariance properties. Consistency and asymptotic normality are established without any moment existence assumption on the errors. A Monte Carlo study of bias and RMSE shows sign-based estimators perform better than LAD-type estimators in various heteroskedastic settings. We illustrate the use of sign-based estimators on an example of beta-convergence of output levels across U.S. states.
机译：我们研究了估计线性中值回归参数的问题，而不是错误分布形状的任何假设 - 包括瞬间存在的条件 - 允许未知形式，非连续分布的异质性（或异源性）和非常一般序列依赖（线性和非线性）。这是通过基于无分布的符号的基于符号的测试理论来完成的，从中生成置信集和点估计值。我们提出了与置信分布的自然关联的点估计。这些估算器基于最大化Testp-Values并从生成的无分布测试中继承稳健性属性。在弱规律条件下建立了建议估算率的有限样本和大样本性质。我们表明它们是中位数 - 无偏见（在对称性和估计机构单性下）并具有标准性质。在错误的情况下没有任何时刻存在假设，建立了一致性和渐近性常态。偏置和RMSE的蒙特卡罗研究显示了基于符号的估计比各种异源性设置中的LAD型估算更好。我们说明了在U.S.状态的β-收敛的示例上使用了基于符号的估计。

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