A1152
Title: A multisample rank test based on Hermite polynomials
Authors: Yuta Sato - Tokyo University of Science (Japan) [presenting]
Hidetoshi Murakami - Tokyo University of Science (Japan)
Amitava Mukherjee - XLRI - Xavier School of Management (India)
Abstract: Multiple aspects involving location, scale, and skewness of statistical distributions should be compared among different samples in practice, instead of only location or scale aspects. While rank statistics based on Legendre polynomials have been studied to this end, a new multisample rank-based test statistic that replaces Legendre polynomials with Hermite polynomials is proposed. The proposed statistic is constructed using the Gram-Schmidt orthonormalization process. The limiting distribution of the proposed test statistic is derived. In addition, simulations are conducted to investigate the convergence of the statistic to its limiting distribution and to compare the power with existing test statistics. Power performances of the proposed test are highly encouraging in various situations compared to some of its competitors. A practical illustration is provided with real data. Some conclusions and future research problems are suggested.
