Properties of the Empirical Characteristic Function and Its Application to Testing for Independence

@inproceedings{Murata2001PropertiesOT,
  title={Properties of the Empirical Characteristic Function and Its Application to Testing for Independence},
  author={Noboru Murata},
  year={2001}
}
In this article, the asymptotic properties of the empirical characteristic function are discussed. The residual of the joint and marginal empirical characteristic functions is studied and the uniform convergence of the residual in the wider sense and the weak convergence of the scaled residual to a Gaussian process are investigated. Taking into account of the result, a statistical test for independence against alternatives is considered. 
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