Semiparametric Minimax Rates.
Semiparametric Minimax Rates.
复制标题
DOI：
10.1214/09-ejs479
复制
发表时间：
2009
影响因子：
1.1
通讯作者：
van der Vaart A
中科院分区：
文献类型：
--
作者：
Robins J;Tchetgen Tchetgen E;Li L;van der Vaart A
我们考虑半参数模型上定义的非线性泛函的极小极大检验率（或估计率）。现有的方法似乎不能确定一个下界的极小极大率的测试（或估计）的某些功能的利益。特别是，如果半参数模型由几个无限维参数索引。为了涵盖这些例子，我们扩展的方法，这是基于比较一个“真实的分布”的扰动分布的凸混合比较两个凸混合。通过扰动模型的第一参数获得第一混合物，并且通过另外扰动第二参数获得第二混合物。我们将新的结果应用到两个例子的半参数泛函：估计的平均响应时，响应数据随机缺失，估计的预期条件协方差函数。
We consider the minimax rate of testing (or estimation) of non-linear functionals defined on semiparametric models. Existing methods appear not capable of determining a lower bound on the minimax rate of testing (or estimation) for certain functionals of interest. In particular, if the semiparametric model is indexed by several infinite-dimensional parameters. To cover these examples we extend the approach of, which is based on comparing a “true distribution” to a convex mixture of perturbed distributions to a comparison of two convex mixtures. The first mixture is obtained by perturbing a first parameter of the model, and the second by perturbing in addition a second parameter. We apply the new result to two examples of semiparametric functionals:the estimation of a mean response when response data are missing at random, and the estimation of an expected conditional covariance functional.