Goodness‐of‐Fit Tests for Positive Quadrant Dependence

Summary When two random variables are positive quadrant dependent (PQD), they are more likely to assume small (or large) values simultaneously compared with when the random variables are independent. This dependence structure is of interest in many areas, including finance, actuarial science and engineering. We propose a new nonparametric goodness‐of‐fit testing procedure to assess whether PQD holds between two random variables. Our test uses empirical likelihood (EL) and is motivated by the seminal work of Owen and McKeague on this topic. We reviewed the statistics and econometrics literature and identified six nonparametric tests for the same problem, all of which estimate copula functions first. An advantage of our test is that it avoids copula estimation and can be implemented using asymptotic or finite‐sample critical values. Our comparisons reveal the EL test performs as well as or better than copula‐based approaches for a variety of dependence structures. We analyse three data sets and provide online R resources. A useful by‐product of our work is that we synthesize a complex set of existing methods and offer data analysts the ability to implement all available nonparametric goodness‐of‐fit tests at once.