Abstract
In this paper, hypotheses testing based on a corrected score function are considered. Five different testing statistics are proposed and their asymptotic distributions are investigated. It is shown that the statistics are asymptotically distributed according to the chisquare distribution or can be written as a linear combination of chisquare random variables with one degree of freedom. A small scale numerical Monte Carlo study is presented in order to compare the empirical size and power of the proposed tests. A comparative calibration example is used to illustrate the results obtained.
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References
Barnett, V. D. (1969). Simultaneous pairwise linear structural relationship, Biometrics, 25, 129–142.
Bolfarine, H. and Galea-Rojas, M. (1995). Comment on “Functional comparative calibration using an EM algorithm” (by D. K. Kimura), Biometrics, 51, 1579–1580.
Carroll, R. J. and Stefanski, L. A. (1990). Approximate quasi-likelihood estimation in models with surrogate predictors, J. Amer. Statist. Assoc., 85, 652–663.
Carroll, R. J., Ruppert, D. and Stefanski, L. A. (1995). Measurement Error in Nonlinear Models, Chapman and Hall, London.
Fuller, W. A. (1987). Measurement Error Models, Wiley, New York.
Gimenez, P. and Bolfarine, H. (1997). Corrected score functions in classical error in variables and incidental parameter estimation, Austral. J. Statist., 39, 325–344.
Gordon, T. and Kannel, W. E. (1968). Introduction and General Background in the Framinghan Study-The Framinghan Study, Sections 1 and 2, National Heart, Lung and Blood Institute, Betheesda, MD.
Griffiths, P. and Hill, I. D. (1985). Applied Statistics Algorithms, Horwood, London.
Hauck, W. W. and Donner, A. (1977). Wald's test as applied to hypothesis in logit analysis, J. Amer. Statist. Assoc., 72, 851–853.
Jaech, J. L. (1985). Statistical Analysis of Measurement Errors, Wiley, New York.
Kimura, D. K. (1992). Functional comparative calibration using an EM algorithm, Biometrics, 48, 1263–1271.
Lagakos, S. A. (1988). Effects of mismodelling and mismeasuring explanatory variables on tests of their association with a response variable, Statistics in Medicine, 7, 257–274.
Lawless, J. F. (1982). Statistical Models and Methods for Lifetime Data, Wiley, New York.
Marazzi, A. (1980). ROBETH, a subroutine library for robust statistical procedures. COMPSTAT 1980, Proc. Computational Statistics, Physical, Vienna, No.4, 577–583.
Nakamura, T. (1990). Corrected score function for errors in variables models: Methodology and application to generalized linear models, Biometrika, 77, 127–137.
Okajima, S., Mine, M. and Nakamura, T. (1985). Mortality of registered A-bomb survivors in Nagasaki, Japan, 1970–1984. Radiation Research, 103, 419–431.
Pierce, D. A., Stram, D. O., Vaeth, M., Schafer, D. (1992). Some insights into the errors in variables problem provided by consideration of radiation dose-response analysis for the A-bomb survivors, J. Amer. Statist. Assoc., 87, 351–359.
Rao, C. R. (1973). Linear Statistical Inference and Its Applications, 2nd ed., Wiley, New York.
Stefanski, L. A. (1985). The effects of measurement error on parameter estimation, Biometrika, 72, 583–592.
Stefanski, L. A. (1989). Unbiased estimation of a nonlinear function of a normal mean with application to measurement error models. Comm. Statist. Theory Methods, 18, 4335–4358.
Stefanski, L. A. and Carroll, R. J. (1990). Score tests in generalized linear measurement error models, J. Roy. Statist. Soc. B, 52, 345–359.
Tosteson, T. D. and Tsiatis, A. A. (1988). The asymptotic relative efficiency of score tests in a generalized linear model with surrogate covariates, Biometrika, 75, 507–514.
Whittemore, A. S. (1989). Error-in-variables regression using Stein estimates, Amer. Statist., 43, 226–228.
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Gimenez, P., Bolfarine, H. & Colosimo, E.A. Hypotheses Testing for Error-in-Variables Models. Annals of the Institute of Statistical Mathematics 52, 698–711 (2000). https://doi.org/10.1023/A:1017525326525
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DOI: https://doi.org/10.1023/A:1017525326525