Implicit Alternatives and the Local Power of Test Statistics
分析检验统计量的局部功效，考虑趋近原假设但不一定满足备择假设的数据生成过程序列，发现LR、Wald和LM三个经典统计量在所有这些序列下渐近趋于同一随机变量，并指出每个渐近卡方统计量都存在一个“隐式备择假设”使其功效最高。
The local power of test statistics is analyzed by considering sequences of data-generating processes (DGPs) that approach the null hypothesis without necessarily satisfying the alternative. The three classical test statistics-LR, Wald, and LM-are shown to tend asymptot ically to the same random variable under all such sequences. The powe r of these statistics depends on the null, the alternative, and the sequence of DGPs in a geometrically intuitive way. This implies that, for any statistic that is asymptotically chi-squared under the null, there exists an "implicit alternative hypothesis" against which that statistic will have highest power. Copyright 1987 by The Econometric Society.