摘要翻译：
非参数回归实验的渐近等价性结果总是假定观测的方差是已知的。然而，在实践中，每个观测量的方差通常被认为是一个未知的干扰参数。当方差值是待估计或检验的附加参数时，我们建立了非参数回归实验的渐近逼近。这个渐近等价实验有两个部分：第一部分包含关于方差的全部信息，第二部分包含关于均值的全部信息。该结果可推广到方差随观测量变化缓慢的回归问题。
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英文标题：
《Asymptotic approximation of nonparametric regression experiments with
  unknown variances》
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作者：
Andrew V. Carter
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最新提交年份：
2007
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分类信息：

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：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：
  Asymptotic equivalence results for nonparametric regression experiments have always assumed that the variances of the observations are known. In practice, however the variance of each observation is generally considered to be an unknown nuisance parameter. We establish an asymptotic approximation to the nonparametric regression experiment when the value of the variance is an additional parameter to be estimated or tested. This asymptotically equivalent experiment has two components: the first contains all the information about the variance and the second has all the information about the mean. The result can be extended to regression problems where the variance varies slowly from observation to observation.
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PDF链接：
https://arxiv.org/pdf/710.3647