Adaptive confidence intervals for regression functions under shape constraints
Adaptive confidence intervals for regression functions under shape constraints
复制标题
形状约束下回归函数的自适应置信区间
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Yin Xia
中科院分区：
文献类型：
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作者：
T. Cai;Mark G. Low;Yin Xia
回归函数的自适应置信区间是在单调性和凸性的形状约束下构造的。根据分析量（局部连续性模量），为给定函数的置信区间的最小预期长度建立自然基准。该界限不仅取决于函数，还取决于假定的函数类。这些基准表明，构建的置信区间对于每个单独的函数具有接近最小预期长度，同时保持类内函数的给定覆盖概率。这种自适应性比大参数空间集合上的自适应极小极大值强得多。
Adaptive confidence intervals for regression functions are constructed under shape constraints of monotonicity and convexity. A natural benchmark is established for the minimum expected length of confidence intervals at a given function in terms of an analytic quantity, the local modulus of continuity. This bound depends not only on the function but also the assumed function class. These benchmarks show that the constructed confidence intervals have near minimum expected length for each individual function, while maintaining a given coverage probability for functions within the class. Such adaptivity is much stronger than adaptive minimaxity over a collection of large parameter spaces.