The research is concerned with the development and implementation of statistical techniques by using approximations to marginal likelihood of ranks.

A brief review of rank techniques to analyse data is made.

For the problem of predicting a future response, when the data can be transformed to a standard linear model, but the transformation is unknown, a technique is introduced. The predictive probabilities for a future response, in terms.of the spacings of the order statistics of the sample of responses are found. Various estimates of the future response based on these probabilities are presented. Simulation studies are undertaken in different conditions for comparing these estimates with existing estimates based on ranks and some parametric estimates. It is shown that the new estimates do not suffer the same difficulties as the earlier estimates.

Some techniques are proposed for the two population discrimination problem. Estimates of the predictive probability of a new case being a member of one of the population given the ranks of the observations are obtained by approaching the problem in two different ways. A similarity of rank and parametric techniques and differences between the two rank methods proposed, are highlighted, error rate estimates are obtained. A medical data set is examined.

The approximation to the rank marginal likelihood is extended up to quartic terms and the scores are found where the variables are assumed to have logistic distribution. The asymptotic likelihood is considered for two sample population and trend models to compare the approximation with earlier ones.

Finally rank based techniques are developed·for making inferences for a serial correlation model. A computational model is developed to evaluate the integral for the marginal likelihood of ranks and it is used to investigate the performance of the approximation. Simulation studies are undertaken to compare the proposed technique with the earlier rank based methods and to show the effect of marginalization over the ranks of the serially correlated random variables on the curvature of the resulting likelihood function. A test of location is proposed and assessed where the observations are related by the linear model with serially correlated errors.