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Sequential Procedures for Aggregating Arbitrary Estimators of a Conditional Mean

机译：汇总条件均值的任意估计量的顺序过程

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摘要

In this correspondence, a sequential procedure for aggregating linear combinations of a finite family of regression estimates is described and analyzed. Particular attention is given to linear combinations having coefficients in the generalized simplex. The procedure is based on exponential weighting, and has a computationally tractable approximation. Analysis of the procedure is based in part on techniques from the sequential prediction of nonrandom sequences. Here these techniques are applied in a stochastic setting to obtain cumulative loss bounds for the aggregation procedure. From the cumulative loss bounds we derive an oracle inequality for the aggregate estimator for an unbounded response having a suitable moment-generating function. The inequality shows that the risk of the aggregate estimator is less than the risk of the best candidate linear combination in the generalized simplex, plus a complexity term that depends on the size of the coefficient set. The inequality readily yields convergence rates for aggregation over the unit simplex that are within logarithmic factors of known minimax bounds. Some preliminary results on model selection are also presented.
机译：在这种对应关系中，描述并分析了用于聚合有限系列回归估计的线性组合的顺序过程。特别注意具有广义单形中的系数的线性组合。该过程基于指数加权，并具有可计算的近似值。该过程的分析部分基于非随机序列的顺序预测中的技术。在这里，将这些技术应用于随机设置中以获取聚合过程的累积损耗范围。从累积损耗边界中，我们推导出具有合适的矩生成函数的无界响应的合计估计量的oracle不等式。不等式表明，总估计量的风险小于广义单纯形法中最佳候选线性组合的风险，再加上取决于系数集大小的复杂度项。不等式很容易产生在单个极小值上聚合的收敛速度，该收敛速度在已知最小极大范围的对数因子之内。还提供了一些关于模型选择的初步结果。

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