POWER MAXIMIZATION AND SIZE CONTROL IN HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS WITH EXPONENTIATED KERNELS
研究了指数化核在异方差自相关稳健t检验中的渐近性质，提出一种选择最优功率参数的新方法，在控制第一类错误的同时最小化第二类错误，模拟显示新检验在规模精度上不逊于Kiefer-Vogelsang检验且避免了其功率损失。
Using the power kernels of Phillips, Sun, and Jin (2006, 2007), we examine the large sample asymptotic properties of the t -test for different choices of power parameter ( ρ ). We show that the nonstandard fixed- ρ limit distributions of the t -statistic provide more accurate approximations to the finite sample distributions than the conventional large- ρ limit distribution. We prove that the second-order corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also second-order correct under the large- ρ asymptotics. As a further contribution, we propose a new practical procedure for selecting the test-optimal power parameter that addresses the central concern of hypothesis testing: The selected power parameter is test-optimal in the sense that it minimizes the type II error while controlling for the type I error. A plug-in procedure for implementing the test-optimal power parameter is suggested. Simulations indicate that the new test is as accurate in size as the nonstandard test of Kiefer and Vogelsang (2002a, 2002b), and yet it does not incur the power loss that often hurts the performance of the latter test. The results complement recent work by Sun, Phillips, and Jin (2008) on conventional and b T HAC testing.