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/Co-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.