Abstract
We consider the theory of R-estimation of the regression parameters of a multiple regression models with measurement errors. Using the standard linear rank statistics, R-estimators are defined and their asymptotic properties are studied as robust alternatives to the least squares estimator. This paper fills the gap of the rank theory for the estimation of regression parameters with measurement error models. Some simulation results are presented to show the effectiveness of the R-estimators.
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References
Adichie JN (1967) Estimates of regression parameters based on rank tests. Ann Math Stat 38: 894–904
Cheng C-L, Tsai C-L (1995) Estimating linear measurement error models via M-estimators. In: Mammitzsch V, Schneeweiss H (eds) Symposia Gaussiana: Proceedings of second gauss symposium, conference B: statistical sciences. Walter de Gruyter, Berlin, pp 247–259
Fuller WA (1987) Measurement error models. Wiley, New York
Guttenbrunner C, Jurečková J (1992) Regression rank scores and regression quantiles. Ann Math Stat 20: 305–330
Guttenbrunner C, Jurečková J, Koenker R, Portnoy S (1993) Test of linear hypotheses based on regression rank scores. Nonparametr Stat 2: 307–331
Hájek J, Šidák Z, Sen PK (1999) Theory of rank tests, 2nd edn. Academic Press, New York
Hodges JL, Lehmann EL (1963) Estimates of location based on ranks. Ann Math Stat 34(2): 598–611
Huber PJ (1981) Robust statistics. Wiley, New York
Jurečková J (1969) Asymptotic linearity of a rank statistic in regression parameter. Ann Math Stat 40: 1889–1900
Jurečková J, Picek J, Saleh AKMdE (2010) Rank tests and regression rank scores tests in measurement error models. Comput Stat Data Anal 54: 3108–3120
Jurečková J, Sen PK (1996) Robust statistical procedures: asymptotics and inter-relations. Wiley, New York
Koul HL (2000) Weighted empirical processes in dynamic nonlinear models. Springer, New York
Polland D (1991) Asymptotics for least absolute deviation regression estimators. Econom Theory 7: 186–199
Puri ML, Sen PK (1986) Nonparametric methods in generalized linear models. Wiley, New York
Saleh AKMdE, Sen PK (1978) Nonparametric estimation of location parameter after a preliminary test on regression. Ann Stat 6: 154–168
Saleh AKMdE, Picek J, Kalina J (2009) Nonparametric estimation of regression parameters in measurement error models. Metron 62(2): 177–200
Schneeweiss H (1976) Consistent estimation of regression with errors in variables. Metrika 23: 101–115
Zamar RH (1989) Robust estimation in the errors-in-variables models. Biometrika 76: 149–160
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Saleh, A.K.M.E., Picek, J. & Kalina, J. R-estimation of the parameters of a multiple regression model with measurement errors. Metrika 75, 311–328 (2012). https://doi.org/10.1007/s00184-010-0328-2
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DOI: https://doi.org/10.1007/s00184-010-0328-2