Averaged shifted chi-square test

Abstract

A simple procedure based on the average of shifted chi-square statistics (ASCS) is proposed to improve the classical chi-square procedure for testing whether a random sample has been drawn from a specified continuous distribution. We repeatedly partition the sample space, say, ℓ times to obtain ℓ respective chi-square statistics. The proposed test statistic is defined as the average value of the resultant ℓ shifted chi-square statistics. We prove that the ASCS is asymptotically distributed as a weighted sum of a finite number of chi-square variables by the theory of U-statistics. The proposed procedure is shown to be markedly less sensitive to the choice of the anchor position and Monte Carlo experiments demonstrate that it leads to noticeable gains in power.

Keywords:

• averaged shifted chi-square statistics
• goodness-of-fit test
• anchor point
• U-statistics
• overlapping ells

AMS Subject Classifications :

• 62G10
• 62G07
• 62G20

Acknowledgements

We thank the editor, an associate editor and two referees for their valuable comments and suggestions, which substantially improved the quality of the article. The work of J.-S. Wu was supported by NSC-98-2118-M032-001.