Finite-sample inference with monotone incomplete multivariate normal data, I

  • Authors:

  • Wan-Ying Chang;Donald St. P. Richards

  • Affiliations:

  • Washington Department of Fish and Wildlife, Olympia, WA 98501, USA;Department of Statistics, Penn State University, University Park, PA 16802, USA and The Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, NC 27709, USA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2009

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Abstract

We consider problems in finite-sample inference with two-step, monotone incomplete data drawn from N"d(@m,@S), a multivariate normal population with mean @m and covariance matrix @S. We derive a stochastic representation for the exact distribution of @m@^, the maximum likelihood estimator of @m. We obtain ellipsoidal confidence regions for @m through T^2, a generalization of Hotelling's statistic. We derive the asymptotic distribution of, and probability inequalities for, T^2 under various assumptions on the sizes of the complete and incomplete samples. Further, we establish an upper bound for the supremum distance between the probability density functions of @m@^ and @m@?, a normal approximation to @m@^.