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Data Dependent Cells Chi‐Square Test With Recurrent Events
Author(s) -
Adekpedjou Akim,
De Mel WITHANAGE A.,
Zamba Gideon KD
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12150
Subject(s) - mathematics , chi square test , estimator , test statistic , independent and identically distributed random variables , kolmogorov–smirnov test , statistics , statistical hypothesis testing , event (particle physics) , parametric statistics , null hypothesis , pearson's chi squared test , null distribution , exact test , statistic , random variable , physics , quantum mechanics
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.