EXTENSION OF FACTORING LIKELIHOOD APPROACH TO NON-MONOTONE MISSING DATA

  • Kim, Jae-Kwang (Department of Applied Statistics, Yonsei University)
  • Published : 2004.12.01

Abstract

We address the problem of parameter estimation in multivariate distributions under ignorable non-monotone missing data. The factoring likelihood method for monotone missing data, termed by Rubin (1974), is extended to a more general case of non-monotone missing data. The proposed method is algebraically equivalent to the Newton-Raphson method for the observed likelihood, but avoids the burden of computing the first and the second partial derivatives of the observed likelihood. Instead, the maximum likelihood estimates and their information matrices for each partition of the data set are computed separately and combined naturally using the generalized least squares method.

Keywords

References

  1. ANDERSON, T. W. (1957). 'Maximum likelihood estimates for a multivariate normal distribution when some observations are missing', Journal of the American Statistical Association, 52, 200-203 https://doi.org/10.2307/2280845
  2. Cox, D. R. AND REID, N. (1987). 'Parameter orthogonality and approximate conditional inference (with discussion)', Journal of the Royal Statistical Society, B49, 1-39
  3. DEMPSTER, A. P., LAIRD, N. M. AND RUBIN, D. B. (1977). 'Maximum likelihood from incomplete data via the EM algorithm (with discussion)', Journal of the Royal Statistical Society, B39, 1-38
  4. FULLER, W. A. (1996). Introduction to Statistical Times Series, 2nd ed., John Wiley & Sons, New York
  5. GROVES, R. M., DILLMAN, D. A., ELTINGE, J. L. AND LITTLE, R. J. A. (2001). Survey Nonresponse, John Wiley & Sons, New York
  6. LEHMANN, E. L. (1983). Theory of Point Estimation, John Wiley & Sons, New York
  7. LITTLE, R. J. A. (1982). 'Models for nonresponse in sample surveys', Journal of the American Statistical Association, 77, 237-250 https://doi.org/10.2307/2287227
  8. LITTLE, R. J. A. AND RUBIN, D. B. (2002). Statistical Analysis with Missing Data, 2nd ed., John Wiley & Sons, New York
  9. RUBIN, D. B. (1974). 'Characterizing the estimation of parameters in incomplete-data problems', Journal of the American Statistical Association, 69, 467-474 https://doi.org/10.2307/2285680
  10. RUBIN, D. B. (1976). 'Inference and missing data', Biometrika, 63, 581-592 https://doi.org/10.1093/biomet/63.3.581