Foundations of multivariate inference using modern computers

摘要: Abstract Fisher suggested in 1930s algebraically structured pivot functions (PFs) whose distribution does not depend on unknown parameters. These pivots provided a foundation for (asymptotic) statistical inference. T.W. Anderson [Introduction to Multivariate Statistical Analysis, Wiley, New York, 1958, p. 116] introduced the concept of critical function observables, which finds rejection probability test Fisher's pivot. H.D. Vinod [J. Econometrics 86 (1998) 387] shows that V.P. Godambe's [Biometrika 78 (1985) 419] (GPF) based Godambe–Durbin `estimating funtions' (EFs) from [Ann. Math. Statist. 31 (1960) 1208] are particularly robust compared by B. Efron and D.V. Hinkley [Biometrica 65 (1978) 457] R.M. Royall [Internat. Rev. 54 (2) (1986) 221]. argues numerically computed algebraic roots GPFs scaled score can fill long-standing need bootstrap literature pivots. This paper considers D.R. Cox's 62 (1975) 269] example detail reports simulation it. also discusses new Poisson mean, binomial normal standard deviation. We propose inference methods modified deviation designed represent financial risk. In context regression problems, we discuss Godambe-type multivariate (denoted GPF 2 ) asymptotically χ .