CONTENTS -- PREFACE -- A BIT OF HISTORY -- PH.D. STUDENTS SUPERVISED BY THOMAS P. HETTMANSPERGER -- Estimation of Location and Scale Parameters Based on Kernel Functional Estimators -- 1. Introduction -- 2. The Location Estimator and its Properties -- 3. The Scale Estimator and its Properties -- 4. Simulations -- References -- Bandwidth Selection in an EM-Like Algorithm for Nonparametric Multivariate Mixtures -- 1. Introduction -- 2. The Nonparametric EM Algorithm -- 3. Bandwidth Selection -- 4. An Example -- 5. Further Extensions -- 6. Summary -- Acknowledgments -- Appendix A. Computer code -- References -- Dealing with More Variables than the Sample Size: An Application to Shape Analysis -- 1. Introduction -- 2. An NPC solution to multivariate small-sample problems -- 3. Motivation -- 4. A simulation study and results -- 5. Application -- 6. Discussion -- Acknowledgements -- References -- A Non-Parametric Cramér-von Mises Penalty Function Smoother -- 1. Introduction -- 2. The Cramér-von Mises formulation -- 3. A computation method -- 4. Updating the functional estimates -- 5. Choosing the central Cramér-von Mises value -- 6. An example and simulations -- 7. Remarks -- References -- Statistical Models for Globular Cluster Luminosity Distribution -- 1. Introduction -- 2. The Bayesian Information Criterion -- 3. Models for GCLF Distribution in the Milky Way and in M31 -- 4. Concluding Remarks -- Acknowledgments -- References -- A Likelihood-Tuned Density Estimator Via a Nonparametric Mixture Model -- 1. Introduction -- 2. Methodology -- 2.1. Background -- 2.2. Likelihood-tuning Procedure -- 3. Asymptotic Properties -- 4. Simulation Comparison -- 5. Discussion -- Appendix A. Outline proof of Theorem 1 -- References -- Shock Models for Defaults: Parametric and Nonparametric Approaches -- 1. Introduction.

2. Extreme shock models with varying threshold -- 3. Distribution for ν -- 3.1. Exact distribution -- 3.2. Asymptotic distribution -- 4. A nonparametric urn-based generalized extreme shock model -- 5. Using the UbGESM to study firms' defaults -- 5.1. The Data -- 5.2. Initialization of the process -- 5.3. The benchmark: the Z*-score -- 5.4. Results -- Acknowledgments -- References -- Kernel Density Estimation with Missing Data: Misspecifying the Missing Data Mechanism -- 1. Introduction -- 2. Propensity Score Estimation -- 3. Misspecifying the Missing Data Mechanism -- 4. Augmenting the Kernel Density Estimator -- 5. Simulation Study -- 6. Summary -- References -- On the Non-Gaussian Asymptotics of the Likelihood Ratio Test Statistic for Homogeneity of Covariance -- 1. Introduction -- 2. A generalization of a result by Yanagihara et al. (2005) -- 3. The homokurtic case -- Appendix A. Proof of Proposition 1 -- Acknowledgments -- References -- Deconvolution Density Estimation on the Space of Positive Definite Symmetric Matrices -- 1. Introduction -- 2. Preliminaries -- 2.1. The Helgason-Fourier Transform -- 2.2. The Inversion Formula for the Helgason-Fourier Transform -- 2.3. The Convolution Property of the Helgason-Fourier Transform -- 2.4. Eigenvalues, the Laplacian, and Sobolev Spaces -- 2.5. The Plancherel Formula for the Helgason-Fourier Transform -- 3. Deconvolution Density Estimation on Pm -- 4. The Wishart Distribution -- 5. Proofs -- 5.1. The Integrated Bias -- 5.2. The Integrated Variance -- 5.3. Proof of Theorem 3.1 -- 5.4. Proof of Theorem 3.2 -- 5.5. Proof of Lemma 4.1 -- Acknowledgments -- References -- Recent History Functional Linear Models -- 1. Introduction -- 2. Estimation in Recent History Functional Linear Models -- 3. The Choice of Model Parameters: The Number of Basis Functions and Lags -- 4. Simulation Study.

4.1. Data generation -- 4.2. Simulation results -- 5. Data Analysis -- 6. Concluding Remarks -- Acknowledgments -- References -- Rank-Based Estimation for Arnold-Transformed Data -- 1. Introduction -- 2. Rank Estimation in Linear Models -- 2.1. Regression through the origin -- 2.2. Asymptotic results -- 3. Estimation Based on Arnold-Transformed Data -- 3.1. The model and the Arnold transformation -- 3.2. Least Squares Estimates Based on the Transformed Data -- 3.3. Rank-Based Estimates Based on the Transformed Data -- 4. Studentized Residuals -- 4.1. AT Least Squares Studentized Residuals -- 4.2. AT Rank-Based Studentized Residuals -- 5. Simulation Study -- 6. Example -- 6.1. Studentized Residuals -- 6.2. Sensitivity Analysis -- 7. Conclusion -- Acknowledgments -- References -- QQ Plots for Assessing Symmetry Models -- 1. Introduction -- 2. Multivariate spatial quantiles -- 3. Symmetry models -- 4. Examples -- 4.1. Plus/minus symmetry in two dimensions -- 4.2. Compound symmetry -- 4.3. Spherical symmetry -- 5. Comparing rotations -- 6. Calculating the ranks for symmetrized distributions -- Acknowledgments -- References -- A Comparison of Estimators for the Variance of Cross-Validation Estimators of the Generalization Error of Computer Algorithms -- 1. Introduction -- 2. The Estimators of Variance of Cross-Validation Estimators of the Generalization Error -- 2.1. The Framework and Relevant Definitions -- 2.2. The Variance Estimators -- 3. Bias Calculation -- 4. A Simulation Study -- 4.1. Normal distribution -- 4.2. Other distributions -- 4.3. Linear Regression -- 5. Conclusions -- Acknowledgments -- References -- Estimation of Hazard Functions with Shape Restrictions Using Regression Splines -- 1. Introduction and Statement of the Problem -- 2. Constrained Maximum Likelihood Estimation of h -- 3. Smoothed Constrained Maximum Likelihood Estimation.

4. Knot Choices -- 5. Comparing with Kernel Methods -- 6. Right Censoring and Examples -- References -- Multivariate Models and the First Four Moments -- 1. Introduction -- 2. Moments and multivariate descriptive statistics -- 3. The moments in some multivariate statistical models -- 3.1. General structures for models -- 3.2. Elliptical Model -- 3.3. Other symmetric models -- 3.4. Models with skew distributions -- 3.5. Model selection -- 4. Examples -- 4.1. Examples with simulated data -- 4.2. Examples with real data sets -- 5. Discussion -- Appendix A. Technical details -- Appendix B. Tables -- References -- An Empirical Study of Indirect Cross-Validation -- 1. Introduction -- 2. Description of indirect cross-validation -- 2.1. Notation and definitions -- 2.2. The basic method -- 2.3. Selection kernels -- 3. Practical issues -- 3.1. Large sample theory -- 3.2. MSE-optimal α and σ -- 3.3. Model for the ICV parameters -- 4. Simulation study -- 5. Real data examples -- 5.1. PGA data -- 5.2. Local ICV example -- 6. Summary -- References -- Extensions of Reliability Theory -- 1. Introduction -- 2. Classical Theory for a Fixed Individual with T = t -- 3. Proposed Model -- 3.1. Difference scores -- 3.2. Normal mixture model for the difference -- 3.3. Posterior probability weights wi and the weighted correlation rw -- 4. Estimation and Application Example -- 4.1. Example: Infant Habituation -- 5. Discussion -- Acknowledgments -- References -- Rank Regression under Possible Model Misspecification -- 1. Introduction -- 2. Asymptotic Normality of the Wilcoxon Rank Regression Estimator under Possible Model Misspecification -- 2.1. Preliminaries and Notation -- 2.2. Three steps toward asymptotic normality -- 2.3. The asymptotic normality -- 3. Omitted Variables Bias -- 4. Discussions -- Acknowledgments -- References.

Iterative Conditional Maximization Algorithm for Nonconcave Penalized Likelihood -- 1. Introduction -- 2. Nonconcave Penalized Likelihood for Variable Selection -- 2.1. Some Preliminaries -- 2.2. Optimization -- 2.3. Tuning Parameter Selection -- 3. An Iterative Conditional Maximization (ICM) Algorithm -- 3.1. Characterizations of the Penalized Likelihood Estimates -- 3.2. The ICM Algorithm -- 4. Numerical Studies -- 4.1. Model Fitting and Model Sparsity -- 4.2. Tests of Convergence and Computing Time -- 4.3. A Real Data Application -- 5. Conclusion -- Appendix A. Proof of Theorem 3.1 -- Acknowledgments -- References -- AUTHOR INDEX.