Nonparametric Functional Estimation and Related Topics

About three years ago, an idea was discussed among some colleagues in the Division of Statistics at the University of California, Davis, as to the possibility of holding an international conference, focusing exclusively on nonparametric curve estimation. The fruition of this idea came about with the enthusiastic support of this project by Luc Devroye of McGill University, Canada, and Peter Robinson of the London School of Economics, UK. The response of colleagues, contacted to ascertain interest in participation in such a conference, was gratifying and made the effort involved worthwhile. Devroye and Robinson, together with this editor and George Metakides of the University of Patras, Greece and of the European Economic Communities, Brussels, formed the International Organizing Committee for a two week long Advanced Study Institute (ASI) sponsored by the Scientific Affairs Division of the North Atlantic Treaty Organization (NATO). The ASI was held on the Greek Island of Spetses between July 29 and August 10, 1990. Nonparametric functional estimation is a central topic in statistics, with applications in numerous substantive fields in mathematics, natural and social sciences, engineering and medicine. While there has been interest in nonparametric functional estimation for many years, this has grown of late, owing to increasing availability of large data sets and the ability to process them by means of improved computing facilities, along with the ability to display the results by means of sophisticated graphical procedures.

Inhalt

I. Curve and Functional Estimation.- Reproducing Kernels and Finite Order Kernels.- Laws of the Iterated Logaritm for Density Estimators.- Exponential Inequalities in Nonparametric Estimation.- Conservative Confidence Bands for Nonparametric Regression.- Data-Adaptive Kernel Estimation.- On the Nonparametric Estimation of the Entropy Functional.- II. Curve and Functional Estimation (Continued).- Analysis of Samples of Curves.- Bootstrap Methods in Nonparametric Regression.- On the Influence Function of Maximum Penalized Likelihood Density Estimators.- Nonparametric Curve Estimation and Simple Curve Characteristics.- Applications of Multiparameter Weak Convergence for Adaptive Nonparametric Curve Estimation.- On Asymptotic Efficiency of Average Derivative Estimates.- Nonparametric Estimation of Elliptically Contoured Densities.- Uniform Deconvolution: Nonparametric Maximum Likelihood and Inverse Estimation.- III. Parameter Selection, Smoothing.- Smoothing Parameter Selection in Image Restoration.- Estimating the Quantile-Density Function.- Data-Driven Smoothing Based on Convexity Properties.- Prospects for Automatic Bandwidth Selection in Extensions to Basic Kernel Density Estimation.- Root n Bandwidth Selection.- Estimating Smooth Distribution Functions.- Smoothing Techniques in Time Series Analysis.- IV. Regression Models.- Nonparametric Inference in Heteroskedastic Regression.- Bounded Influence Regression in the Presence of Heteroskedasticity of Unknown Form.- Linear Regression with Randomly Right-Censored Data Using Prior Nonparametric Estimation.- Universal Consistencies of a Regression Estimate for Unbounded Regression Functions.- Minimax Bayes Estimation, Penalized Likelihood Methods, and Restricted Minimax Estimation.- On Exponential Bounds on the Bayes Risk of the Nonparametric Classification Rules.- Nonparametric Regression Analysis of Some Economic Data.- V. Dependent Data.- Nonparametric Regression Methods for Repeated Measurements.- Nonparametric Prediction for Unbounded Almost Stationary Processes.- Monte Carlo and Turbulence.- Kernel Density Estimation Under a Locally Mixing Condition.- Nonparametric Estimation of Survival Functions Under Dependent Competing Risks.- Estimation of Transition Distribution Function and Its Quantiles in Markov Processes: Strong Consistency and Asymptotic Normality.- L1 Strong Consistency for Density Estimates in Dependent Samples.- VI. Time Series Analysis, Signal Detection.- Nonparametric Statistical Signal Detection Problems.- Functional Identification in Nonlinear Time Series.- Modelization, Nonparametric Estimation and Prediction for Continuous Time Processes.- Estimation of Chaotic Dynamic Systems with Control Variables.- Nonparametric Estimation of a Class of Nonlinear Time Series Models.- Semiparametric and Nonparametric Inference from Irregular Observations on Continuous Time Stochastic Processes.- VII. Various Topics.- Complexity Regularization with Application to Artificial Neural Networks.- Designing Prediction Bands.- Analysis of Observational Studies from the Point of View of Nonparametric Regression.- Some Issues in Cross-Validation.- Nonparametric Function Estimation Involving Errors-in-Variables.- VII. Various Topics (Continued).- A Consistent Goodness of Fit Test Based on the Total Variation Distance.- On a Problem in Semiparametric Estimation.- On the Integrable and Approximately Integrable Linear Statistical Models.- Nonparametric Techniques in Image Estimation.- Regularized Deconvolution on the Circle and the Sphere.- List of Attendants.- Contributed Papers.