Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bickel PJ (1978) Using residuals robustly I: Tests for heteroscedasticity, nonlinearity. Ann Statist 6:266–291
Breusch TS, Pagan AR (1979) A simple test for heteroscedasticity and random coefficient variation. Econometrica 47:1287–1294
Cox DR, Hinkley DV (1974) Theoretical Statistics. Chapman and Hall, London
Dielman TE (1989) Pooled Cross-Sectional and Time Series Data Analysis. Marcel Dekker, New York
Newbold, P, Bos T (1985) Stochastic Parameter Regression Models. Series: Quantitative Applications in Social Sciences, A Sage University Paper: No 51. London
Shorack GR (1984) Empirical and rank processes of observations and residuals. Can J Statist 12:319–332
Shorack GR, Wellner JA (1986) Empirical Processes with Applications to Statistics. Wiley, New York
Swamy PAVB (1971) Statistical Inference for Random Coefficient Regression Models. Springer-Verlag, New York
Author information
Authors and Affiliations
Additional information
Research was supported by the University Grants Commission, India.
Rights and permissions
About this article
Cite this article
Ramanathan, T.V., Rajarshi, M.B. Rank tests for testing randomness of a regression coefficient in a linear regression model. Metrika 39, 113–124 (1992). https://doi.org/10.1007/BF02613990
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02613990