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The additive model affected by missing completely at random in the covariate

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Summary

The main purpose of this paper is a comparison of several imputation methods within the simple additive model ty =f(x) + ε where the independent variable X is affected by missing completely at random. Besides the well-known complete case analysis, mean imputation plus random noise, single imputation and two kinds of nearest neighbor imputations are used. A short introduction to the model, the missing mechanism, the inference, the imputation methods and their implementation is followed by the main focus—the simulation experiment. The methods are compared within the experiment based on the sample mean squared error, estimated variances and estimated biases of f(x) at the knots.

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References

  • Chen, J., & Shao, J. (2001). Jackknife variance estimation for nearest-neighbor imputation,Journal of the American Statistical Association 96(453): 260–269.

    Article  MathSciNet  Google Scholar 

  • Fahrmeir, L., & Tutz, G. (2001).Multivariate Statistical Modelling Based on Generalized Linear Models, 2 edn, Springer-Verlag, New York.

    Book  Google Scholar 

  • Green, P., & Silverman, B. (1994).Nonparametric Regression and Generalized Linear Models, Chapman and Hall, London.

    Book  Google Scholar 

  • Hastie, T., & Tibshirani, R. J. (1990).Generalized Additive Models, Chapman and Hall, London.

    MATH  Google Scholar 

  • Ibrahim, J. G., Lipsitz, S. R., & Chen, M.-H. (1999). Missing covariates in generalized linear models when the missing data mechanism is nonignorable,Journal of the Royal Statistical Society, Series B 61(1): 173–190.

    Article  MathSciNet  Google Scholar 

  • Little, R. J. A. (1992). Regression with missingX’s: A review,Journal of the American Statistical Association 87(420): 1227–1237.

    Google Scholar 

  • Little, R. J. A., & Rubin, D. B. (1987).Statistical Analysis with Missing Data, Wiley, New York.

    MATH  Google Scholar 

  • Nittner, T. (2002). Missing at, Random MAR in Nonparametric Regression - A Simulation Experiment,SFB386-Discussion Paper 284, Ludwig-Maximilians-Universität München.

    Google Scholar 

  • Rubin, D. B. (1987).Multiple Imputation for Nonresponse in Sample Surveys, Wiley, New York.

    Book  Google Scholar 

  • Schafer, J. L. (1997).Analysis of Incomplete Multivariate Data, Chapman and Hall, London.

    Book  Google Scholar 

  • Toutenburg, H., Fieger, A., & Srivastava, V. K. (1999). Weighted modified first order regression procedures for estimation in linear models with missingX-observations,Statistical Papers 40: 351–361.

    Article  MathSciNet  Google Scholar 

  • Toutenburg, H., & Nittner, T. (2002). Linear regression models with incomplete categorical covariates,Computational Statistic 17(2): 215–232.

    Article  MathSciNet  Google Scholar 

  • Vach, W. (1994).Logistic Regression with Missing Values and Covariates, Vol. 86 ofLecture Notes in Statistics, Springer-Verlag, Berlin.

    MATH  Google Scholar 

  • Venables, W., & Smith, D. (2001).An Introduction to R.

  • Wilks, S. S. (1932). Moments and distributions of estimates of population parameters from fragmentary samples,Annals of Mathematical Statistics 3: 163–195.

    Article  Google Scholar 

  • Wood, S. (2000). Modelling and smoothing parameter estimation with multiple quadratic penalties,Journal of the Royal Statistical Society, Series B 62(2): 413–428.

    Article  MathSciNet  Google Scholar 

  • Wood, S. (2001).mgcv: GAMs and Generalized Ridge Regression for R.

Download references

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Nittner, T. The additive model affected by missing completely at random in the covariate. Computational Statistics 19, 261–282 (2004). https://doi.org/10.1007/BF02892060

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