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摘要翻译：
在数据随机缺失(MAR)的假设下，研究了正态分布和多项式分布的二元缺失数据一般模式的极大似然估计问题。对于正常数据，分数方程有九个复杂的解，其中至少有一个是真实的和统计显著的。我们的计算表明，实解的个数与是否满足MAR假设有关。在多项式情况下，得分方程的所有解都是实解，实解的数目随潜在随机变量的状态数目呈指数增长，尽管总是精确地存在一个统计上显著的局部极大值。
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英文标题：
《The Algebraic Complexity of Maximum Likelihood Estimation for Bivariate
Missing Data》
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作者：
Serkan Hosten and Seth Sullivant
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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：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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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 study the problem of maximum likelihood estimation for general patterns of bivariate missing data for normal and multinomial random variables, under the assumption that the data is missing at random (MAR). For normal data, the score equations have nine complex solutions, at least one of which is real and statistically significant. Our computations suggest that the number of real solutions is related to whether or not the MAR assumption is satisfied. In the multinomial case, all solutions to the score equations are real and the number of real solutions grows exponentially in the number of states of the underlying random variables, though there is always precisely one statistically significant local maxima.
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PDF链接：
https://arxiv.org/pdf/0709.0935
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