Rank tests for testing randomness of a regression coefficient in a linear regression model

We propose a class of nonparametric tests for testing non-stochasticity of the regression parameterβ in the regression modely _i =βx _i +ɛ _i ,i=1, ...,n. We prove that the test statistics are asymptotically normally distributed both underH ₀ and under contiguous alternatives. The asymptotic relative efficiencies (in the Pitman sense) with respect to the best parametric test have also been computed and they are quite high. Some simulation studies are carried out to illustrate the results. Research was supported by the University Grants Commission, India.