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摘要翻译：
我们提出并研究了一种在可能是间接的、损坏的或部分可用的观测的基础上构造一致性统计检验的一般方法。本文设计的测试类包括Neyman平滑测试、数据驱动分数测试和一些类型的多样本测试作为基本示例。我们的测试是数据驱动的，并且还与模型选择规则结合在一起。该方法允许使用基于惩罚思想的广泛的模型选择规则。特别是，在统计文献中导出的许多最优惩罚可以用于我们的测试。我们建立了模型选择规则和数据驱动测试在零假设和替代假设下的行为，导出了替代假设的显式可检测性规则，并从类中证明了测试的主一致性定理。本文表明，这些检验适用于许多问题，包括统计逆问题的假设检验、多样本问题的假设检验和非参数假设检验。
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英文标题：
《Data-driven goodness-of-fit tests》
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作者：
Mikhail Langovoy
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最新提交年份：
2017
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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：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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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 and study a general method for construction of consistent statistical tests on the basis of possibly indirect, corrupted, or partially available observations. The class of tests devised in the paper contains Neyman's smooth tests, data-driven score tests, and some types of multi-sample tests as basic examples. Our tests are data-driven and are additionally incorporated with model selection rules. The method allows to use a wide class of model selection rules that are based on the penalization idea. In particular, many of the optimal penalties, derived in statistical literature, can be used in our tests. We establish the behavior of model selection rules and data-driven tests under both the null hypothesis and the alternative hypothesis, derive an explicit detectability rule for alternative hypotheses, and prove a master consistency theorem for the tests from the class. The paper shows that the tests are applicable to a wide range of problems, including hypothesis testing in statistical inverse problems, multi-sample problems, and nonparametric hypothesis testing.
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PDF链接：
https://arxiv.org/pdf/708.0169
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