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摘要翻译：
我们考虑了基于有色高斯噪声的测量值估计未知的确定性参数向量的线性回归问题。提出并分析了盲极大极小估计(BMEs)，它是由一个有界参数集的极大极小估计组成的，其参数集本身是由测量值估计出来的。因此，不需要任何先验假设或知识，所提出的估计量可以应用于任何线性回归问题。我们解析地证明了BMEs严格支配最小二乘估计量，即对于参数向量的任意值，它们都能获得较低的均方误差。Stein的估计量及其正部分校正量都可以在盲极小极大框架内导出。此外，我们的方法可以很容易地扩展到比Stein的估计更广泛的估计问题，它只定义为白噪声和未变换的测量。我们通过仿真表明，BMEs通常优于Stein技术的先前扩展。
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英文标题：
《Blind Minimax Estimation》
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作者：
Zvika Ben-Haim and Yonina C. Eldar
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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：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 consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded parameter set minimax estimator, whose parameter set is itself estimated from measurements. Thus, one does not require any prior assumption or knowledge, and the proposed estimator can be applied to any linear regression problem. We demonstrate analytically that the BMEs strictly dominate the least-squares estimator, i.e., they achieve lower mean-squared error for any value of the parameter vector. Both Stein's estimator and its positive-part correction can be derived within the blind minimax framework. Furthermore, our approach can be readily extended to a wider class of estimation problems than Stein's estimator, which is defined only for white noise and non-transformed measurements. We show through simulations that the BMEs generally outperform previous extensions of Stein's technique.
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PDF链接：
https://arxiv.org/pdf/709.392
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