THE EMPIRICAL CHARACTERISTIC FUNCTION AND LARGE SAMPLE HYPOTHESIS TESTING
DOI:
https://doi.org/10.5281/zenodo.14506988Keywords:
empirical characteristic function, characteristic function, probability space, independent and identically distributed random variables.Abstract
Many properties of distribution functions can be characterized in terms of their characteristic functions. This suggests that statistical inference about such properties might utilize the characteristic function. This requires that some means be found to gather information about the characteristic function from a random sample. In this investigation, the empirical characteristic function is proposed to do this.
References
Billingsley, P., Convergence of Probability Measures, Wiley, New York, 1968.
Cramér, H., Mathematical Methods of Statistics, Princeton Univ. Press, Princeton, New Jersey, 1946.
Csurgo, S., The empirical characteristic process when parameters are estimated, 1979 (to appear).
Feuerverger, A., and Mureika, R. A., The empirical characteristic function and its applications, Ann. Statis., 5(1977).
