Rank based tests for testing the constancy of the regression coefficients against random walk alternatives

• Authors: Manohar B. RAJARSHI , Thekke V. RAMANATHAN , Chanchala A. GHADGE
• Languages of publication: EN

Abstracts

EN

A class of approximately locally most powerful type tests based on ranks of residuals is suggested for testing the hypothesis that the regression coefficient is constant in a standard regression model against the alternatives that a random walk process generates the successive regression coefficients. We derive the asymptotic null distribution of such a rank test. This distribution can be described as a generalization of the asymptotic distribution of the Cramer-von Mises test statistic. However, this distribution is quite complex and involves eigen values and eigen functions of a known positive definite kernel, as well as the unknown density function of the error term. It is then natural to apply bootstrap procedures. Extending a result due to Shorack in [25], we have shown that the weighted empirical process of residuals can be bootstrapped, which solves the problem of finding the null distribution of a rank test statistic. A simulation study is reported in order to judge performance of the suggested test statistic and the bootstrap procedure.

Keywords

EN

bootstrap; random coefficient regression models; random walk alternative models; rank tests; weighted empirical and rank processes

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2011
• Volume: 21
• Issue: 3-4
• Pages: 35-55

Contributors

author

Manohar B. RAJARSHI

• Department of Statistics, University of Pune, Pune 411 007, India

author

Thekke V. RAMANATHAN

• Department of Statistics, University of Pune, Pune 411 007, India

author

Chanchala A. GHADGE

References

• CHERNICK M., Bootstrap Methods: A Practitioner’s Guide, Wiley, New York, 2007.
• COX D.R., HINKLEY D.V., Theoretical Statistics, Chapman and Hall, London, 1974.
• DAVISON A.C., HINKLEY D.V., Bootstrap Methods and Their Application, Cambridge Series in Statistical and Probabilistic Mathematics, No. 1, 1999.
• DELICADO F., ROMO J., Goodness-of-fit tests in random coeffient regression models, Annals of the Institute of Statistical Mathematics, 1999, 51, 125–148.
• DELICADO F., ROMO J., Random coefficient regressions: Parametric goodness-of-fit tests, Journal of Statistical Planning and Inference, 2004, 119 (2), 377–400.
• GARBADE K., Two methods for examining the stability of regression coefficients, Journal of American Statistical Association, 1977, 72, 54–63.
• HALL P., WILSON S.R., Two guidelines for bootstrap hypothesis testing, Biometrics, 1991, 47, 757–762.
• HAUSMAN J.A., Specification tests in econometrics, Econometrica, 1978, 46 (6), 1251–1271.
• HINKLEY D.V., Bootstrap significance tests, Bulletin of the International Statistical Institute, Proceedings of the 47th Session, 1989, 53, 65–74.
• JANDHYALA V.K., MACNEILL I.B., On testing for the constancy of regression coefficients under random walk and change-point alternatives, Econometric Theory, 1992, 8 (4), 501–517.
• KOROLJUK V.S., BOROVISKICH Y.V., Theory of Statistics, [in:] Mathematics and its application, Vol. 273, Kluwer Academic Publishers Group, Dordrecht, 1994.
• LAHIRI S.N., Resampling methods for dependent data, Springer, New York, 2003.
• LAMOTTE, L.R., MCWHORTER A., An exact test for the presence of random walk coefficients in a linear model, Journal of American Statistical Association, 1978, 73, 816–820.
• LEE A.J., U-Statistics Theory and Practice, Dekker, New York, 1990.
• NABEYA S., Asymptotic distributions of the test statistics for the constancy of regression coefficients under a sequence of random walk alternatives, Journal of the Japan Statistical Society, 1989, 19, 13–33.
• NABEYA S., TANAKA K., Asymptotic theory of a test for the constancy of regression coefficients against the random walk alternative, Annals of Statistics, 1988, 16, 218–235.
• NABEYA S., TANAKA K., Acknowledgment of priority, The Annals of Statistics, 1994, 22 (1), 563.
• NEWBOLD P., BOS T., Stochastic Parameter Regression Models, Series: Quantitative Applications in Social Sciences, A Sage University Paper No. 51, 1985.
• NYBLOM S., MAAKELAAINEN T., Comparison of tests for the presence of random walk coefficients in a simple linear model, Journal of American Statistical Association, 1983, 78, 856–864.
• PRAKASA RAO B.L.S., Nonparametric Functional Estimation, Academic Press, New York, 1983.
• RAJARSHI M.B., RAMANATHAN T.V., Testing constancy of a Markovian parameter against random walk alternatives, Journal of Indian Statistical Association, 2000, 38, 23–44.
• RAMANATHAN T.V., RAJARSHI M.B., Rank tests for testing randomness of a regression coefficient in a linear regression model, Metrika, 1992, 39, 113–124.
• RAMSEY J.B., Tests for specification errors in classical linear least squares regression analysis, Journal of the Royal Statistical Society B, 1969, 31 (2), 350–371.
• SHIVELY T.S., An exact test for a stochastic coefficient in a time series regression model, Journal of Time Series Analysis, 1988, 9, 81–88.
• SHORACK G.R., Bootstrapping robust regression, Communications in Statistics: Theory and Methods, 1982, 11, 961–972.
• SHORACK G., WELLNER J.A., Empirical Processes with Applications to Statistics, Wiley, New York, 1986.
• SILVERMAN B.W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1996.
• SWAMY P.A.V.B., Statistical Inference in Random Coeffcient Regression Model, Lecture Notes, Springer, 1971.
• ZELTERMAN D., CHEN C., Homogeneity tests against central mixture alternatives, Journal of American Statistical Association, 1988, 83, 179–182.

Identifiers

DOI

10.5277/ord1203-0403