Contributions to the study of sequential covariance analysis

The use of concomitant information in multivariate sequential tests of statistical hypotheses

“…One such extension is based on Wald's method of weight functions, which seems particularly well suited for composite hypotheses concerning ranges of parameters. Some relevant sequential tests based on Waldian weight functions are Wald's (1947) sequential t-test and the sequential t-tests developed by Sampson (1968). For further discussion of the theory of weight functions in sequential analysis, the reader is referred to Wald (1947) or Wetherill (1966).…”

“…As described in Chapter I, statistical analyses utilizing concomitant information have been used in fixed-sample-size experimentation for the multivariate case (see, for example, Rao, 1966) , as well as for the univariate case (see, for example, Cochran, 1957); and, as noted therein, at least one purpose for the utilization of concomitant information is to remove the effects of disturbing variables in observational studies. With this purpose in mind, Roseberry (1965), Cox and Roseberry (1966), and Sampson (1968) where X = a" Z a.…”

“…Roseberry (1965) and Cox and Roseberry (1966) developed and investigated empirically some sequential tests that utilize one covariate. Sampson (1968), using a different approach, subsequently developed univariate sequential test procedures that utilize a vector of covariates.…”

“…The sequential test of the mean vector adjusted for covariates, which we develop in Chapter IV, is also a singlesample test procedure with obvious application to the pairedcomparison experimental design. Hajnal (1961) and Sampson (1968) developed two-sample univariate sequential t-test procedures for the case of unpaired observations. Further, Sampson (1968) we have developed sequential tests utilizing a type of information that has seemingly been ignored in previous sequential test procedures, that is, the information in a preliminary independent estimate of nuisance parameters.…”

“…Hajnal (1961) and Sampson (1968) developed two-sample univariate sequential t-test procedures for the case of unpaired observations. Further, Sampson (1968) we have developed sequential tests utilizing a type of information that has seemingly been ignored in previous sequential test procedures, that is, the information in a preliminary independent estimate of nuisance parameters. The advantages of incorporating this type of information into the sequential tests will become apparent in subsequent chapters.…”