Title: Hypothesis testing for a parabolic linear SPDE with a small perturbation
Authors: Yusuke Kaino - Kobe University (Japan) [presenting]
Masayuki Uchida - Osaka University (Japan)
Abstract: A statistical hypothesis test is considered for a parabolic linear second-order stochastic partial differential equation (SPDE) in one space dimension with a small perturbation from high-frequency data which are observed in time and space. We aim to test whether a parameter of the SPDE model is zero. We propose three kinds of test statistics based on the high-frequency data: likelihood ratio type test statistic, Wald type test statistic and Rao's score type test statistic. It is shown that under some regularity conditions, these test statistics converge in distribution to a chi-squared random variable with one degree of freedom under the null hypothesis, and the tests are consistent. Moreover, we give some simulation results of the test statistics and examine the asymptotic behavior of the test statistics under the null and alternative hypotheses.