Asymptotic properties of a goodness-of-fit test based on maximum correlations

作者：Grane Aurea^*; Tchirina Anna V

来源：Statistics, 2013, 47(1): 202-215.

DOI：10.1080/02331888.2011.588709

• Bahadur asymptotic relative efficiency
• goodness-of-fit
• local asymptotic optimality
• L-statistics
• maximum correlation

We study the efficiency properties of the goodness-of-fit test based on the Q n statistic introduced in Fortiana and Grane [Goodness-of-fit tests based on maximum correlations and their orthogonal decompositions, J. R. Stat. Soc. B 65 (2003), pp. 115126] using the concepts of Bahadur asymptotic relative efficiency and Bahadur asymptotic optimality. We compare the test based on this statistic with those based on the KolmogorovSmirnov, the Cramer-von Mises criterion and the AndersonDarling statistics. We also describe the distribution families for which the test based on Q n is locally asymptotically optimal in the Bahadur sense and, as an application, we use this test to detect the presence of hidden periodicities in a stationary time series.

• 出版日期2013-2-1