Data Dependent Cells Chi-Square Test With Recurrent Events

作者：Adekpedjou Akim^*; Demel Withanage A; Zamba Gideon K D

来源：Scandinavian Journal of Statistics, 2015, 42(4): 1045-1064.

DOI：10.1111/sjos.12150

• Chi-squared test
• data dependent cells
• empirical process
• minimum chi-square estimator
• recurrent events
• Pitman efficiency

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.

• 出版日期2015-12