Omnibus goodness of fit test based on quadratic distance

Abstract

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.

Keywords:

• Goodness of fit test
• quadratic distance test
• spectral decomposition of kernel
• Bickel-Rosenblatt test
• bootstrap
• AR models

2010 Mathematics Subject Classification:

• 62E20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Sangyeol Lee and Byungtae Seo's research are supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (No. NRF-2021R1A2C1004009) and (No. NRF-2019R1F1A1059959), respectively.