Foundations of Multivariate Inference Using Modern Computers
نویسنده
چکیده
Fisher analytically structured pivot functions (PFs) whose distribution does not suggested in 1930's depend on unknown parameters. These pivots provided a foundation for (asymptotic) statistical inference. Anderson (1958, p. 116) introduced the concept of a critical function of observables, which finds the rejection probability of a test for Fisher's pivot. Vinod (1998) shows that Godambe's (1985) pivot function (GPF) based on Godambe-Durbin “estimating functions” (EFs) from 1960 are particularly robust compared to pivots by Efron and Hinkley (1978) and Royall (1986). Vinod argues that numerically computed roots of GPFs based on scaled score functions can fill a long-standing need of the bootstrap literature for robust pivots. This paper considers Cox's example in detail and reports on a simulation for it. This paper also discusses new pivots for Poisson mean, Binomial probability and Normal standard deviation. we propose and discuss a second In the context of regression problems multivariate pivot 2) and robust choices of error (denoted by GPF which is asymptotically ;2 covariances to allow for heteroscedasticity and autocorrelation.
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