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摘要翻译：
提出了条件均值函数的线性估计和逼近的同时均值-方差回归。在存在未知形式的异方差的情况下，我们的方法通过使用与平均回归参数共同确定的权值来说明在条件变量支持下回归结果的变化离散性。同时生成结果预测，保证比普通的最小二乘预测误差改进，相应的参数标准误差自动有效。在条件均值和方差函数的形状不规范下，我们建立了所得到的近似的存在唯一性，并刻画了它们的形式解释和鲁棒性。特别地，我们证明了相应的均值-方差回归位置尺度模型在Kullback-Leibler散度测度下弱地支配普通最小二乘位置模型，并在异方差存在时严格改进。同时均值-方差回归损失函数是全局凸的，相应的估计量易于实现。我们建立了它在错误规格下的相合性和渐近正态性，给出了鲁棒的推理方法，并给出了数值模拟，表明在有限样本下的估计和推理方面比普通最小二乘和加权最小二乘有很大的改进。我们进一步用两个实证应用来说明我们的方法，以估计1500年和今天的经济繁荣与美国汽油需求之间的关系。
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英文标题：
《Simultaneous Mean-Variance Regression》
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作者：
Richard Spady, Sami Stouli
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最新提交年份：
2019
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
We propose simultaneous mean-variance regression for the linear estimation and approximation of conditional mean functions. In the presence of heteroskedasticity of unknown form, our method accounts for varying dispersion in the regression outcome across the support of conditioning variables by using weights that are jointly determined with the mean regression parameters. Simultaneity generates outcome predictions that are guaranteed to improve over ordinary least-squares prediction error, with corresponding parameter standard errors that are automatically valid. Under shape misspecification of the conditional mean and variance functions, we establish existence and uniqueness of the resulting approximations and characterize their formal interpretation and robustness properties. In particular, we show that the corresponding mean-variance regression location-scale model weakly dominates the ordinary least-squares location model under a Kullback-Leibler measure of divergence, with strict improvement in the presence of heteroskedasticity. The simultaneous mean-variance regression loss function is globally convex and the corresponding estimator is easy to implement. We establish its consistency and asymptotic normality under misspecification, provide robust inference methods, and present numerical simulations that show large improvements over ordinary and weighted least-squares in terms of estimation and inference in finite samples. We further illustrate our method with two empirical applications to the estimation of the relationship between economic prosperity in 1500 and today, and demand for gasoline in the United States.
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PDF链接：
https://arxiv.org/pdf/1804.01631
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