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2011 | 21 | nr 3-4 | 35--55
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Rank Based Tests for Testing the Constancy of the Regression Coefficients Against Random Walk Alternatives

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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. (original abstract)
Opis fizyczny
  • University of Pune, India
  • University of Pune, India
  • University of Pune, India
  • [1] CHERNICK M., Bootstrap Methods: A Practitioner's Guide, Wiley, New York, 2007.
  • [2] COX D.R., HINKLEY D.V., Theoretical Statistics, Chapman and Hall, London, 1974.
  • [3] DAVISON A.C., HINKLEY D.V., Bootstrap Methods and Their Application, Cambridge Series in Statistical and Probabilistic Mathematics, No. 1, 1999.
  • [4] DELICADO F., ROMO J., Goodness-of-fit tests in random coefficient regression models, Annals of the Institute of Statistical Mathematics, 1999, 51, 125-148.
  • [5] DELICADO F., ROMO J., Random coefficient regressions: Parametric goodness-of-fit tests, Journal of Statistical Planning and Inference, 2004, 119 (2), 377-400.
  • [6] GARBADE K., Two methods for examining the stability of regression coefficients, Journal of American Statistical Association, 1977, 72, 54-63.
  • [7] HALL P., WILSON S.R., Two guidelines for bootstrap hypothesis testing, Biometrics, 1991, 47, 757-762.
  • [8] HAUSMAN J.A., Specification tests in econometrics, Econometrica, 1978, 46 (6), 1251-1271.
  • [9] HINKLEY D.V., Bootstrap significance tests, Bulletin of the International Statistical Institute, Proceedings of the 47th Session, 1989, 53, 65-74.
  • [10] 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.
  • [11] KOROLJUK V.S., BOROVISKICH Y.V., Theory of Statistics, [in:] Mathematics and its application, Vol. 273, Kluwer Academic Publishers Group, Dordrecht, 1994.
  • [12] LAHIRI S.N., Resampling methods for dependent data, Springer, New York, 2003.
  • [13] 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.
  • [14] LEE A.J., U-Statistics Theory and Practice, Dekker, New York, 1990.
  • [15] 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.
  • [16] 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.
  • [17] NABEYA S., TANAKA K., Acknowledgment of priority, The Annals of Statistics, 1994, 22 (1), 563.
  • [18] NEWBOLD P., BOS T., Stochastic Parameter Regression Models, Series: Quantitative Applications in Social Sciences, A Sage University Paper No. 51, 1985.
  • [19] 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.
  • [20] PRAKASA RAO B.L.S., Nonparametric Functional Estimation, Academic Press, New York, 1983.
  • [21] 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.
  • [22] 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.
  • [23] 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.
  • [24] 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.
  • [25] SHORACK G.R., Bootstrapping robust regression, Communications in Statistics: Theory and Methods, 1982, 11, 961-972.
  • [26] SHORACK G., WELLNER J.A., Empirical Processes with Applications to Statistics, Wiley, New York, 1986.
  • [27] SILVERMAN B.W., Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1996.
  • [28] SWAMY P.A.V.B., Statistical Inference in Random Coefficient Regression Model, Lecture Notes, Springer, 1971.
  • [29] ZELTERMAN D., CHEN C., Homogeneity tests against central mixture alternatives, Journal of American Statistical Association, 1988, 83, 179-182.
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