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摘要翻译：
在多项式抽样方案下，我们定义了代表分层对数线性模型的指数分布族的自然参数的群-拉索估计。这种估计量是基于group-lasso惩罚的凸惩罚似然优化问题的解。我们说明了如何利用由group-lasso过程恢复的非零系数块来构造潜在对数线性模型的估计量。在样本容量和模型复杂度同时增长的双渐近框架下，研究了群-拉索估计作为模型选择方法的渐近性质。我们给出了保证group-lasso估计是模型选择一致的条件，即随着样本容量的增加，它以压倒性的概率正确地识别变量之间的所有非零相互作用集。如果真正的底层模型的序列足够稀疏，即使细胞数量增长大于样本量，恢复也是可能的。最后，我们给出了对数线性群Lasso估计的一些中心极限类型的结果。
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英文标题：
《The log-linear group-lasso estimator and its asymptotic properties》
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作者：
Yuval Nardi, Alessandro Rinaldo
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最新提交年份：
2012
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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：
We define the group-lasso estimator for the natural parameters of the exponential families of distributions representing hierarchical log-linear models under multinomial sampling scheme. Such estimator arises as the solution of a convex penalized likelihood optimization problem based on the group-lasso penalty. We illustrate how it is possible to construct an estimator of the underlying log-linear model using the blocks of nonzero coefficients recovered by the group-lasso procedure. We investigate the asymptotic properties of the group-lasso estimator as a model selection method in a double-asymptotic framework, in which both the sample size and the model complexity grow simultaneously. We provide conditions guaranteeing that the group-lasso estimator is model selection consistent, in the sense that, with overwhelming probability as the sample size increases, it correctly identifies all the sets of nonzero interactions among the variables. Provided the sequences of true underlying models is sparse enough, recovery is possible even if the number of cells grows larger than the sample size. Finally, we derive some central limit type of results for the log-linear group-lasso estimator.
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PDF链接：
https://arxiv.org/pdf/709.3526
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