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首页> 外文期刊>Scandinavian journal of statistics >How Many Iterations are Sufficient for Efficient Semiparametric Estimation?
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How Many Iterations are Sufficient for Efficient Semiparametric Estimation?

机译：有效的半参数估计需要多少个迭代？

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摘要

A common practice in obtaining an efficient semiparametric estimate is through iter-atively maximizing the (penalized) full log-likelihood w.r.t. its Euclidean parameter and functional nuisance parameter. A rigorous theoretical study of this semiparametric iterative estimation approach is the main purpose of this study. We first show that the grid search algorithm produces an initial estimate with the proper convergence rate. Our second contribution is to provide a formula in calculating the minimal number of iterations k* needed to produce an efficient estimate θ_n~((k*)), We discover that (ⅰ) k* depends on the convergence rates of the initial estimate and the nuisance functional estimate, and (ⅱ) k* iterations are also sufficient for recovering the estimation sparsity in high dimensional data. The last contribution is the novel construction of θ_n~((k)) which does not require knowing the explicit expression of the efficient score function. The above general conclusions apply to semiparametric models estimated under various regularizations, for example, kernel or penalized estimation. As far as we are aware, this study provides a first general theoretical justification for the 'one-/two-step iteration' phenomena observed in the semiparametric literature.
机译：获得有效的半参数估计值的一种常见做法是通过迭代最大化（惩罚后的）全对数似然比w.r.t。其欧几里得参数和功能干扰参数。对该半参数迭代估计方法进行严格的理论研究是本研究的主要目的。我们首先表明，网格搜索算法以适当的收敛速度产生初始估计。我们的第二个贡献是在计算产生有效估计θ_n〜（（k *））所需的最小迭代次数k *时提供一个公式。我们发现（ⅰ）k *取决于初始估计的收敛速度，并且讨厌的功能估计和（*）k *次迭代也足以恢复高维数据中的估计稀疏性。最后一个贡献是θ_n〜（（k））的新颖构造，它不需要知道有效得分函数的显式表达式。以上一般结论适用于在各种正则化条件下估计的半参数模型，例如核或惩罚估计。据我们所知，这项研究为半参数文献中观察到的“单步/两步迭代”现象提供了第一个一般的理论依据。

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