This paper characterizes the precision of index estimation as it carries over into precision of matching. In a model assuming Gaussian covariates and making best-case assumptions about matching quality, it sharply characterizes average and worst-case discrepancies between paired differences of true versus estimated index values. In this optimistic setting, worst-case true and estimated index differences decline to zero if $p=o[n/(\log n)]$, the same restriction on model size that is needed for consistency of common index models. This remains so as the Gaussian assumption is relaxed to sub-gaussian, if in that case the characterization of paired index errors is less sharp. The formula derived under Gaussian assumptions is used as the basis for a matching caliper. Matching such that paired differences on the estimated index fall below this caliper brings the benefit that after matching, worst-case differences onan underlying index tend to 0 if $p = o\{[n/(\log n)]^{2/3}\}$. (With a linear index model, $p=o[n/(\log n)]$ suffices.) A proposed refinement of the caliper condition brings the same benefits without the sub-gaussian condition on covariates. When strong ignorability holds and the index is a well-specified propensity or prognostic score, ensuring in this way that worst-case matched discrepancies on it tend to 0 with increasing $n$ also ensures the consistency of matched estimators of the treatment effect.

翻译：本文描述指数估计的精确性, 因为它会传递到匹配的精确性。 在假设高斯系数的模型中, 并且对匹配质量做出最佳假设时, 它将真实值和估计指数值的对齐差异之间的平均和最坏差异特征。 在这种乐观的环境下, 最坏情况的真实和估计指数差异会下降到零, 如果美元=o[n/ (log n)] 美元, 对共同指数模型一致性所需要的模型规模的限制也是一样的。 这仍然是高斯的假设会放松到下加西南, 如果在这种情况下对齐指数错误的定性不那么尖锐。 高斯假设下的公式衍生值被用来作为匹配卡利伯尔的对等差异。 匹配后, 对一个基本指数的最坏情况的差异会达到0, 如果美元=o ⁇ [n/(log n)] ⁇ 2/3 ⁇ 美元。 (如果直线性指数模型, $p=o [n/ n] 最坏的对准指数错误的定性, 高斯的公式将用作匹配卡利普尔尼差的计算方法。 提议的卡利比亚的精确性( ) 的精确性, 的精确性状况的精确性, 的精确性, 的精确性, 的精确性, 的精确性将保持该状况的精确性, 的精确性, 。