Asymptotics for minimisers of convex processes
Asymptotics for minimisers of convex processes
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发表时间：
2011-07
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通讯作者：
N. Hjort;D. Pollard
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作者：
N. Hjort;D. Pollard
通过两个简单的凸性论证，我们能够开发一种通用方法来证明由凸准则函数的最小化定义的估计量的一致性和渐近正态性。然后将该方法应用于一系列不同的统计估计问题，包括 Cox 回归、逻辑回归和泊松回归、模型条件外的最小绝对偏差回归以及马尔可夫链的伪似然估计。我们的论文有两个目标。首先是阐述方法本身，在许多情况下，在合理的规律性条件下，会产生比传统证明更简单的新证明。我们的第二个目标是利用该方法的逻辑回归和 Cox 回归的极限，在尽可能弱的正则性条件下寻求渐近结果。特别是对于 Cox 回归，我们能够大幅削弱之前发布的正则性条件。
By means of two simple convexity arguments we are able to develop a gen- eral method for proving consistency and asymptotic normality of estimators that are deflned by minimisation of convex criterion functions. This method is then applied to a fair range of difierent statistical estimation problems, including Cox regression, logistic and Poisson regression, least absolute deviation regression outside model conditions, and pseudo-likelihood estimation for Markov chains. Our paper has two aims. The flrst is to exposit the method itself, which in many cases, under reasonable regularity conditions, leads to new proofs that are simpler than the traditional proofs. Our second aim is to exploit the method to its limits for logistic regression and Cox regression, where we seek asymptotic results under as weak regularity conditions as possible. For Cox regression in particular we are able to weaken previously published regularity conditions substantially.