Omnibus goodness of fit test based on quadratic distance

This study considers a goodness of fit test based on the quadratic distance (QD) in composite hypotheses. Lindsay et al. [Quadratic distances on probabilities: a unified approach. Ann Statist. 2008;36:983-1006] established a general theory of QD measures for the goodnees of fit test. Using the spectral decomposition of centred kernels, they verified that the QD test asymptotically follows a sum of weighed chi-square distributions. In this study special attention is paid to a smoothing kernel-based QD test and its bootstrap version. Their performances are compared via Monte Carlo simulations with those of the Bickel-Rosenblatt test and those of the Fisher's dispersion test for the normality and the testing for the Poisson distribution in IID samples and AR(1) models. The comparison results demonstrate the validity of our method.

Automated summary

This study examines a goodness of fit test based on quadratic distance (QD) in composite hypotheses, focusing on a smoothing kernel-based QD test and its bootstrap version. Through Monte Carlo simulations, the performance of these tests is compared with others, demonstrating the validity of the proposed method.