受控多元回归的序列非参数估计

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
S. Efromovich
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引用次数: 0

摘要

摘要本文考虑了一个具有分配均方积分误差(MISE)和最小最大平均停止时间的多元回归的自适应序列非参数估计,当估计量匹配已知所有干扰参数和函数的预言机的性能时。众所周知,如果回归属于可微函数的Sobolev类,则问题没有解。如果一个潜在的回归是更平滑的,比如说,分析的呢?结果表明,在这种情况下,可以匹配oracle的性能。此外,类似于参数估计的经典Stein解,两阶段序列过程解决了这个问题。第一阶段提出的基于固定样本量样本的回归估计器本身就很有意义,并且利用厌氧消化系统减少温室气体排放的发人深省的环境示例来讨论小样本的一些重要主题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sequential nonparametric estimation of controlled multivariate regression
Abstract The article considers an adaptive sequential nonparametric estimation of a multivariate regression with assigned mean integrated squared error (MISE) and minimax mean stopping time when the estimator matches performance of an oracle knowing all nuisance parameters and functions. It is known that the problem has no solution if regression belongs to a Sobolev class of differentiable functions. What if an underlying regression is smoother, say, analytic? It is shown that in this case it is possible to match performance of the oracle. Furthermore, similar to the classical Stein solution for a parameter estimation, a two-stage sequential procedure solves the problem. The proposed regression estimator for the first stage, based on a sample with fixed sample size, is of interest on its own, and a thought-provoking environmental example of reducing potent greenhouse gas emission by an anaerobic digestion system is used to discuss a number of important topics for small samples.
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来源期刊
CiteScore
1.40
自引率
12.50%
发文量
20
期刊介绍: The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches. Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.
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