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摘要翻译：
Behrens-Fisher问题涉及检验两个方差可能不同的正态总体均值的相等性。该问题中的零假设导出了一个统计模型，该模型的似然函数可能具有一个以上的局部极大值。我们证明了这种多模态与零假设相矛盾，因为如果这个假设为真，那么当两个样本量都趋于无穷大时，多模态的概率收敛到零。另外的结果还包括零点下多模态概率的有限样本界和交替下多模态概率的渐近性。
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英文标题：
《Multiple solutions to the likelihood equations in the Behrens-Fisher
problem》
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作者：
Mathias Drton
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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：
The Behrens-Fisher problem concerns testing the equality of the means of two normal populations with possibly different variances. The null hypothesis in this problem induces a statistical model for which the likelihood function may have more than one local maximum. We show that such multimodality contradicts the null hypothesis in the sense that if this hypothesis is true then the probability of multimodality converges to zero when both sample sizes tend to infinity. Additional results include a finite-sample bound on the probability of multimodality under the null and asymptotics for the probability of multimodality under the alternative.
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PDF链接：
https://arxiv.org/pdf/705.4516
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