An idea of Chibisov (1969) for obtaining asymptotically optimal tests by solving a corresponding testing problem associated with the limiting Gaussian process is explored in the case of nuisance Eucledian parameters. It is shown that Neyman's C(α) test corresponds to the conditional test for the exponential family of the limiting Gaussian process. This sheds new insight into the nature of Neyman's projected scores. In addition the methodology helps suggest a one-step estimation procedure with nuisance Eucledian parameters.
All Science Journal Classification (ASJC) codes
- Statistics, Probability and Uncertainty
- Statistics and Probability