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首页> 外文期刊>Statistics >RENYI STATISTICS FOR TESTING COMPOSITE HYPOTHESES IN GENERAL EXPONENTIAL MODELS
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RENYI STATISTICS FOR TESTING COMPOSITE HYPOTHESES IN GENERAL EXPONENTIAL MODELS

机译：在一般指数模型中测试复合假设的仁义统计

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摘要

We introduce a family of Renyi statistics of orders r ∈ R for testing composite hypotheses in general exponential models, as alternatives to the previously considered generalized likelihood ratio (GLR) statistic and generalized Wald statistic. If appropriately normalized exponential models converge in a specific sense when the sample size (observation window) tends to infinity, and if the hypothesis is regular, then these statistics are shown to be χ~2-distributed under the hypothesis. The corresponding Renyi tests are shown to be consistent. The exact sizes and powers of asymptotically α-size Renyi, GLR and generalized Wald tests are evaluated for a concrete hypothesis about a bivariate Levy process and moderate observation windows. In this concrete situation the exact sizes of the Renyi test of the order r = 2 practically coincide with those of the GLR and generalized Wald tests but the exact powers of the Renyi test are on average somewhat better.
机译：为了介绍一般指数模型中的复合假设，我们引入了r∈R阶的Renyi统计族，以替代先前考虑的广义似然比（GLR）统计和广义Wald统计。如果当样本量（观察窗）趋于无穷大时，如果适当归一化的指数模型在特定意义上收敛，并且如果假设是规则的，则这些统计量在假设下显示为χ〜2分布。相应的人意测验显示是一致的。评估了渐近α大小的Renyi，GLR和广义Wald检验的确切大小和功效，以得出关于二元征税过程和中等观察窗的具体假设。在这种具体情况下，r = 2阶的Renyi检验的确切大小实际上与GLR和广义Wald检验的大小一致，但Renyi检验的确切功效平均而言要好一些。

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