Data Dependent Cells Chi-Square Test with Recurrent Events


We consider a recurrent event wherein the inter-event times are independent and identically distributed with a common absolutely continuous distribution function F. In this article, interest is in the problem of testing the null hypothesis that F belongs to some parametric family where the q-dimensional parameter is unknown. We propose a general Chi-squared test in which cell boundaries are data dependent. An estimator of the parameter obtained by minimizing a quadratic form resulting from a properly scaled vector of differences between Observed and Expected frequencies is used to construct the test. This estimator is known as the minimum chi-square estimator. Large sample properties of the proposed test statistic are established using empirical processes tools. A simulation study is conducted to assess the performance of the test under parameter misspecification, and our procedures are applied to a fleet of Boeing 720 jet planes' air conditioning system failures.


Mathematics and Statistics

Keywords and Phrases

Chi-squared test; Data dependent cells; Empirical process; Minimum chi-square estimator; Pitman efficiency; Recurrent events

International Standard Serial Number (ISSN)

0303-6898; 1467-9469

Document Type

Article - Journal

Document Version


File Type





© 2015 Board of the Foundation of the Scandinavian Journal of Statistics, All rights reserved.

Publication Date

01 Dec 2015