COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1749 Power Maximization and Size Control in Heteroskedasticity Yixiao Sun, Peter C.B. Phillips and Sainan Jin January 2010 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
(rho). We show that the nonstandard fixed-rho limit distributions of the t-statistic
provide more accurate approximations to the finite sample distributions than the
conventional large-rho 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-rho 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; KV), and yet it does
not incur the power loss that often hurts the performance of the latter test. The new test
therefore combines the advantages of the KV test and the standard (MSE optimal) HAC test
while avoiding their main disadvantages (power loss and size distortion, respectively).
The results complement recent work by Sun, Phillips and Jin (2008) on conventional and bT
HAC testing. |
