NONPARAMETRIC IMPUTATION AND (MID-) RANK TESTS FOR MIXED EFFECTS MODELS WITH MISSING DATA

Open Access
Author:
Antoniou, Efi Savvas
Graduate Program:
Statistics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
April 20, 2004
Committee Members:
  • Michael G Akritas, Committee Chair
  • Thomas P Hettmansperger, Committee Member
  • Runze Li, Committee Member
  • Linda Marie Collins, Committee Member
Keywords:
  • Kernel estimation
  • Nonparametric tests
  • Marginal nonparametric model
  • Nonparametric imputation
  • Missingness conditionally at random
  • Analysis of covariance
  • Nearest neighbor windows
Abstract:
The first part of this thesis deals with factorial designs where each subject is observed at several time points with part of the data missing. A nonparametric approach for estimating the marginal cumulative distribution function at each time point is proposed and used to test for factor effects and interactions. Estimation uses more general and flexible donor sets which leads to a new type of nonparametric imputation. In particular, the donor sets allow use of univariate kernel methods even with higher dimensional data, avoiding thus the curse of dimensionality. The classical missing at random assumption is not tailored for the present nonparametric analysis. The notion of the missingness conditionally at random Comparisons with ML indicate that the proposed method fares well when the data are normal and homoscedastic, and outperforms it in other cases. The second part of this thesis considers testing for covariate-adjusted main effects and interactions in the context of the fully nonparametric ANCOVA model. The test procedures of Akritas, Arnold and Du (2000) are based on consistent estimation of the conditional distributions and as such they involve the cumbersome task of bandwidth determination. The proposed methodology does not require such consistent estimation. Asymptotic theory and numerical results, indicate that nearest neighbor windows of fixed(small) size perform well. This makes the applicability of the fully nonparametric methodology in real-life situations easily feasible.