Contents -- Preface -- Review Papers -- 1. On the Scholarly Work of P. K. Bhattacharya P. Hall and F. J. Samaniego -- 1. Introduction -- 2. Early work and foundations for the future -- 3. Forays into decision theory -- 4. Work on density estimation and related problems -- 5. Special explorations -- 6. Work on statistical quality control -- 7. Work of cosmic significance -- 8. Inference about change points -- 9. Discussion -- References -- 2. The Propensity Score and Its Role in Causal Inference C. Drake and T. Loux -- 1. Introduction -- The Rubin Causal Model (RCM) -- 2. The propensity score -- 3. Propensity score estimation -- 4. Applications of propensity scores -- 5. Summary -- References -- 3. Recent Tests for Symmetry with Multivariate and Structured Data: A Review S. G. Meintanis and J. Ngatchou-Wandji -- 1. Introduction -- 2. Notions of and testing for multivariate symmetry -- 2.1. Diagonal symmetry -- 2.2. Spherical symmetry -- 2.3. Elliptical symmetry -- 3. Testing symmetry with structured data -- 3.1. Linear regression -- 3.2. Nonparametric regression -- 3.3. Conditional symmetry in time series -- 4. Testing for symmetry in random effect models -- 4.1. Model and tests -- 4.2. Specification of estimation and test statistics -- 4.3. Simulations -- 5. Other procedures for testing symmetry and conclusion -- References -- Papers on General Nonparametric Inference -- 4. On Robust Versions of Classical Tests with Dependent Data J. Jiang -- 1. Introduction -- 2. Robust Tests -- 2.1. Basic idea, assumptions, and examples -- 2.2. The W-, S-, and L- test statistics -- 3. Asymptotic theory -- 4. Application to mixed linear models -- Acknowledgments -- Appendix A. Proofs -- References -- 5. Density Estimation by Sampling from Stationary Continuous Time Parameter Associated Processes G. G. Roussas and D. Bhattacharya -- 1. Introduction.

2. Asymptotic unbiasedness and representation of the bias -- 3. Asymptotic behavior of the variance of the estimate and consistency in quadratic mean -- 4. Asymptotically uncorrelated -- 5. Uniform strong convergence of the estimates -- References -- 6. A Short Proof of the Feigin-Tweedie Theorem on the Existence of the Mean Functional of a Dirichlet Process J. Sethuraman -- 1. Introduction -- 2. Dirichlet processes -- 3. Two-parameter Dirichlet processes -- References -- 7. Max-Min Bernstein Polynomial Estimation of a Discontinuity in Distribution K.-S. Song -- 1. Introduction -- 2. Max-Min Bernstein Polynomial Estimation Method -- 3. Main Result -- 4. Proofs -- 5. Numerical Experiments -- Acknowledgments -- References -- 8. U-Statistics Based on Higher-Order Spacings D. D. Tung and S. R. Jammalamadaka -- 1. Introduction -- 2. The Asymptotic Null Distribution -- 3. The Asymptotic Distribution Under a Sequence of Close Alternatives -- 4. The Asymptotically Locally Most Powerful Test -- 5. Conclusion -- References -- 9. Nonparametric Models for Non-Gaussian Longitudinal Data N. Zhang, H.-G. M ller and J.-L. Wang -- 1. Introduction -- 2. Functional Principal Component Analysis via Quasilikelihood Maximization (FPCA-Q) -- 2.1. Model and notation -- 2.2. FPCA-Q Model -- 2.3. Estimation of Model Components -- 2.3.1. Estimation of mean and covariance function -- 2.3.2. Estimation of overdispersion and error variance -- 2.3.3. Estimation of eigenfunctions and functional principal components -- 2.3.4. Selection of the number of eigenfunctions -- 3. Other Modeling Approaches -- 3.1. The Character Process Model (CPM) -- 3.2. Cubic B-spline Models (BS) -- 3.3. Estimation for Character Process and spline models -- 3.3.1. Markov chain Monte Carlo EM algorithm (MCEM) -- 3.3.2. Simulated Maximum Likelihood Algorithm (SML) -- 4. Simulation Studies.

4.1. Design of the simulations -- 4.2. Simulation results and discussion -- Acknowledgments -- References -- Papers on Aspects of Linear or Generalized Linear Models -- 10. Better Residuals R. Beran -- 1. Introduction -- 2. An Experiment -- 3. Theoretical Framework -- 3.1. Candidate Linear Predictors of Error -- 3.2. Some Classes of Candidate Symmetric Linear Predictors -- 4. Adaptive Symmetric Linear Predictors -- 4.1. Estimating risk -- 4.2. Asymptotic Convergence of Loss, Risk, and Estimated Risk -- 4.3. Successful Adaptation -- 5. Case Studies -- 5.1. Losses and Estimated Losses in the Experiment -- 5.2. Canadian Earnings Data -- 5.3. Plasma Citrate Data -- References -- 11. The Use of Peters-Belson Regression in Legal Cases E. Bura, J. L. Gastwirth and H. Hikawa -- 1. Introduction -- 2. Parametric Peters-Belson Regression -- 2.1. Review of the method -- 3. Local Linear Peters-Belson Regression -- 3.1. Description of Local Linear PB -- 4. Application: Reanalysis of Data from EEOC v. Shelby County Government -- 5. The Suitability of Peters-Belson Regression for Studying the Class Certification Issue -- 5.1. Statistical Properties of the two Regression Approaches when the Data are Stratified -- 6. Concluding Remarks -- 7. Appendix: The Distribution of (21) when the Variances are Unequal -- References -- 12. On a Hybrid Approach to Parametric and Nonparametric Regression P. Burman and P. Chaudhuri -- 1. Introduction -- 2. Hybridization of the parametric and the nonparametric estimation procedures -- 3. Properties of the hybrid estimate -- 4. Effects of mis-specification in the parametric model and related asymptotics -- 5. Remarks and discussion -- 6. Some technical results -- Appendix A. The proofs -- Acknowledgments -- References -- 13. Nonparametric Regression Models with Integrated Covariates Z. Cai -- 1. Introduction.

2. Statistical Properties -- 2.1. Local Linear Estimation -- 2.2. Notation and Assumptions -- 2.3. Asymptotic Results -- 2.4. Nadaraya-Watson Estimation -- 3. An Illustrative Empirical Application -- 4. Discussion -- Appendix A. Proofs -- Acknowledgments -- References -- 14. A Dynamic Test for Misspecification of a Linear Model M. P. McAssey and F. Hsieh -- 1. Introduction: Modeling the linear trend in real bivariate data -- 2. Illustration: Slope underestimation with the SLM -- 3. A test for misspecification of a linear model for real data -- 4. Discussion -- Acknowledgments -- References -- 15. The Principal Component Decomposition of the Basic Martingale W. Stute -- 1. Introduction -- 2. Main Results -- 3. Limit Distribution of the CvM Test Statistic -- References -- Papers on Time Series Analysis -- 16. Fast Scatterplot Smoothing Using Blockwise Least Squares Fitting A. Aue and T. C. M. Lee -- 1. Introduction -- 2. Automatic Curve Estimation Using Blocking -- 2.1. Background -- 2.2. Automatic Selection of Number of Blocks Using MDL -- 2.3. Complexity Regularization -- 3. Pilot Estimation in Local Linear Regression -- 4. Simulation -- 4.1. Experimental Setup -- 4.2. Results -- 5. Real Data Example -- 6. Concluding Remarks -- Appendix A. Derivation of MDL(k) -- References -- 17. Some Recent Advances in Semiparametric Estimation of the GARCH Model J. Di and A. Gangopadhyay -- 1. The GARCH Model and Its Parameter Estimation -- 1.1. Parametric GARCH Estimators -- 1.2. Semiparametric GARCH Estimators -- 2. Likelihood Based Semiparametric GARCH Estimation -- 2.1. Two-step Semiparametric Estimators -- 2.2. One-step Semiparametric Estimation -- 2.3. Two-step SMLE vs. One-step SMLE -- 3. Efficiency of the Semiparametric GARCH Estimators -- 3.1. The Bias-variance Trade-off of the Semiparametric GARCH Estimators.

3.2. Adaptive Semiparametric GARCH Estimators -- 3.3. Factors that Impact the Efficiency -- 3.3.1. Selections of Kernel and Bandwidth -- 3.3.2. Trimming the Semiparametric Likelihood -- 3.3.3. Maximizing the Semiparametric Likelihood -- 4. Future Developments in Semiparametric GARCH Estimation -- Acknowledgment -- References -- 18. Extreme Dependence in Multivariate Time Series: A Review R. Sen and Z. Tan -- 1. Introduction -- 2. A brief background on Multivariate Extreme Value Theory (IID case) -- 3. Extremes of stationary time series -- 3.1. The extremal limit theorem -- 3.2. The multivariate extremal index -- 3.3. The extremal coefficient -- 3.4. The extremal correlation -- 4. Some special stationary time series -- 4.1. Multivariate maxima of moving maxima -- 4.2. Markov chains -- 5. Discussion -- References -- 19. Dynamic Mixed Models for Irregularly Observed Water Quality Data R. H. Shumway -- 1. Introduction: The Dynamic Mixed Model -- 2. Signal Extraction and Interpolation -- 2.1. Signal Extraction -- 2.2. Interpolation -- 3. Estimation of Parameters -- 3.1. Maximum Likelihood Estimation -- 3.2. Bootstrap Estimation of Standard Errors -- 4. Examples -- 4.1. Estimation of Monthly Mean Stream Flows -- 4.2. Signal Extraction for Monitoring Pesticide Concentrations in Water -- 5. Discussion and Extensions -- Dedication and Acknowledgments -- References -- Papers on Asymptotic Theory -- 20. Asymptotic Behavior of the Kernel Density Estimators for Nonstationary Dependent Random Variables with Binned Data J.-F. Lenain, M. Harel and M. L. Puri -- 1. Introduction -- 1.1. Kernel density estimators -- 1.2. Discretized kernel density estimators -- 1.3. Hypotheses of the convergence of the nonstationary process -- 2. Hypotheses and notations -- 3. Missing random variables form of the estimator -- 3.1. Bias.

3.2. Estimation of the Mean Square Error (MSE) between f and f.