关于统一误差指数的一点注记：假设检验、数据压缩和测度集中
A remark on unified error exponents: Hypothesis testing, data compression and measure concentration
摘要：
设A是一个有限集，具有一个概率分布P，M是A上的一个“质量”函数.给出了一个最有效的方法，其中A^n可以覆盖使用一个固定半径的球体的特征。覆盖是A^n的一个子集C_n，它具有这样的性质：A^n的大多数元素与C_n的至少一个元素在某个固定距离内，“大多数元素”意味着一个概率指数地接近1的集合（相对于乘积分布P^n）。有效覆盖是具有小质量M^n（C_n）的覆盖。随着对A上几何的不同选择，这个刻画给出了各种推论作为特例，包括有损数据压缩中的Marton误差指数定理，Hoeffding最优假设检验指数，以及离散空间上某些测度集中不等式的一个新的尖锐逆.
英文摘要：
Let A be finite set equipped with a probability distribution P, and let M be a "mass" function on A. A characterization is given for the most efficient way in which A^n can be covered using spheres of a fixed radius. A covering is a subset C_n of A^n with the property that most of the elements of A^n are within some fixed distance from at least one element of C_n, and "most of the elements" means a set whose probability is exponentially close to one (with respect to the product distribution P^n). An efficient covering is one with small mass M^n(C_n). With different choices for the geometry on A, this characterization gives various corollaries as special cases, including Marton's error-exponents theorem in lossy data compression, Hoeffding's optimal hypothesis testing exponents, and a new sharp converse to some measure concentration inequalities on discrete spaces.
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