Ebook: 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.

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Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Reproducing Kernels and Finite Order Kernels....Pages 3-18
Laws of the Iterated Logarithm for Density Estimators....Pages 19-29
Exponential Inequalities in Nonparametric Estimation....Pages 31-44
Conservative Confidence Bands for Nonparametric Regression....Pages 45-66
Data-Adaptive Kernel Estimation....Pages 67-79
On the Nonparametric Estimation of the Entropy Functional....Pages 81-95
Front Matter....Pages 97-97
Analysis of Samples of Curves....Pages 99-110
Bootstrap Methods in Nonparametric Regression....Pages 111-123
On the Influence Function of Maximum Penalized Likelihood Density Estimators.....Pages 125-131
Nonparametric Curve Estimation and Simple Curve Characteristics....Pages 133-139
Applications of Multiparameter Weak Convergence for Adaptive Nonparametric Curve Estimation....Pages 141-166
On Asymptotic Efficiency of Average Derivative Estimates....Pages 167-172
Nonparametric Estimation of Elliptically Contoured Densities....Pages 173-190
Uniform Deconvolution: Nonparametric Maximum Likelihood and Inverse Estimation....Pages 191-198
Front Matter....Pages 199-199
Smoothing Parameter Selection in Image Restoration....Pages 201-211
Estimating the Quantile-Density Function....Pages 213-223
Data-Driven Smoothing Based on Convexity Properties....Pages 225-240
Prospects for Automatic Bandwidth Selection in Extensions to Basic Kernel Density Estimation....Pages 241-249
Root N Bandwidth Selection....Pages 251-260
Estimating Smooth Distribution Functions....Pages 261-270
Front Matter....Pages 199-199
Smoothing Techniques in Time Series Analysis....Pages 271-283
Front Matter....Pages 285-285
Nonparametric Inference in Heteroskedastic Regression....Pages 287-296
Bounded Influence Regression in the Presence of Heteroskedasticity of Unknown Form....Pages 297-313
Linear Regression with Randomly Right-Censored Data Using Prior Nonparametric Estimation....Pages 315-328
Universal Consistencies of a Regression Estimate for Unbounded Regression Functions....Pages 329-338
Minimax Bayes Estimation, Penalized Likelihood Methods, and Restricted Minimax Estimation....Pages 339-346
On Exponential Bounds on the Bayes Risk of the Nonparametric Classification Rules....Pages 347-360
Nonparametric Regression Analysis of Some Economic Data....Pages 361-374
Front Matter....Pages 375-375
Nonparametric Regression Methods for Repeated Measurements....Pages 377-387
Nonparametric Prediction for Unbounded Almost Stationary Processes....Pages 389-403
Monte Carlo and Turbulence....Pages 405-418
Kernel Density Estimation under a Locally Mixing Condition....Pages 419-430
Nonparametric Estimation of Survival Functions under Dependent Competing Risks....Pages 431-441
Estimation of Transition Distribution Function and its Quantiles in Markov Processes: Strong Consistency and Asymptotic Normality....Pages 443-462
L1 Strong Consistency for Density Estimates in Dependent Samples....Pages 463-474
Front Matter....Pages 475-475
Nonparametric Statistical Signal Detection Problems....Pages 477-492
Functional Identification in Nonlinear Time Series....Pages 493-507
Modelization, Nonparametric Estimation and Prediction for Continuous Time Processes....Pages 509-529
Estimation of Chaotic Dynamic Systems with Control Variables....Pages 531-540
Nonparametric Estimation of a Class of Nonlinear Time Series Models....Pages 541-552
Front Matter....Pages 475-475
Semiparametric and Nonparametric Inference from Irregular Observations on Continuous Time Stochastic Processes....Pages 553-558
Front Matter....Pages 559-559
Complexity Regularization with Application to Artificial Neural Networks....Pages 561-576
Designing Prediction Bands....Pages 577-586
Analysis of Observational Studies from the Point of View of Nonparametric Regression....Pages 587-602
Some Issues in Cross-Validation....Pages 603-612
Nonparametric Function Estimation Involving Errors-in-Variables....Pages 613-627
Front Matter....Pages 629-629
A Consistent Goodness of Fit Test Based on the Total Variation Distance....Pages 631-645
On a Problem in Semiparametric Estimation....Pages 647-656
On the Integrable and Approximately Integrable Linear Statistical Models....Pages 657-667
Nonparametric Techniques in Image Estimation....Pages 669-677
Regularized Deconvolution on the Circle and the Sphere....Pages 679-690
Back Matter....Pages 691-708

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Content:
Front Matter....Pages i-xiii
Front Matter....Pages 1-1
Reproducing Kernels and Finite Order Kernels....Pages 3-18
Laws of the Iterated Logarithm for Density Estimators....Pages 19-29
Exponential Inequalities in Nonparametric Estimation....Pages 31-44
Conservative Confidence Bands for Nonparametric Regression....Pages 45-66
Data-Adaptive Kernel Estimation....Pages 67-79
On the Nonparametric Estimation of the Entropy Functional....Pages 81-95
Front Matter....Pages 97-97
Analysis of Samples of Curves....Pages 99-110
Bootstrap Methods in Nonparametric Regression....Pages 111-123
On the Influence Function of Maximum Penalized Likelihood Density Estimators.....Pages 125-131
Nonparametric Curve Estimation and Simple Curve Characteristics....Pages 133-139
Applications of Multiparameter Weak Convergence for Adaptive Nonparametric Curve Estimation....Pages 141-166
On Asymptotic Efficiency of Average Derivative Estimates....Pages 167-172
Nonparametric Estimation of Elliptically Contoured Densities....Pages 173-190
Uniform Deconvolution: Nonparametric Maximum Likelihood and Inverse Estimation....Pages 191-198
Front Matter....Pages 199-199
Smoothing Parameter Selection in Image Restoration....Pages 201-211
Estimating the Quantile-Density Function....Pages 213-223
Data-Driven Smoothing Based on Convexity Properties....Pages 225-240
Prospects for Automatic Bandwidth Selection in Extensions to Basic Kernel Density Estimation....Pages 241-249
Root N Bandwidth Selection....Pages 251-260
Estimating Smooth Distribution Functions....Pages 261-270
Front Matter....Pages 199-199
Smoothing Techniques in Time Series Analysis....Pages 271-283
Front Matter....Pages 285-285
Nonparametric Inference in Heteroskedastic Regression....Pages 287-296
Bounded Influence Regression in the Presence of Heteroskedasticity of Unknown Form....Pages 297-313
Linear Regression with Randomly Right-Censored Data Using Prior Nonparametric Estimation....Pages 315-328
Universal Consistencies of a Regression Estimate for Unbounded Regression Functions....Pages 329-338
Minimax Bayes Estimation, Penalized Likelihood Methods, and Restricted Minimax Estimation....Pages 339-346
On Exponential Bounds on the Bayes Risk of the Nonparametric Classification Rules....Pages 347-360
Nonparametric Regression Analysis of Some Economic Data....Pages 361-374
Front Matter....Pages 375-375
Nonparametric Regression Methods for Repeated Measurements....Pages 377-387
Nonparametric Prediction for Unbounded Almost Stationary Processes....Pages 389-403
Monte Carlo and Turbulence....Pages 405-418
Kernel Density Estimation under a Locally Mixing Condition....Pages 419-430
Nonparametric Estimation of Survival Functions under Dependent Competing Risks....Pages 431-441
Estimation of Transition Distribution Function and its Quantiles in Markov Processes: Strong Consistency and Asymptotic Normality....Pages 443-462
L1 Strong Consistency for Density Estimates in Dependent Samples....Pages 463-474
Front Matter....Pages 475-475
Nonparametric Statistical Signal Detection Problems....Pages 477-492
Functional Identification in Nonlinear Time Series....Pages 493-507
Modelization, Nonparametric Estimation and Prediction for Continuous Time Processes....Pages 509-529
Estimation of Chaotic Dynamic Systems with Control Variables....Pages 531-540
Nonparametric Estimation of a Class of Nonlinear Time Series Models....Pages 541-552
Front Matter....Pages 475-475
Semiparametric and Nonparametric Inference from Irregular Observations on Continuous Time Stochastic Processes....Pages 553-558
Front Matter....Pages 559-559
Complexity Regularization with Application to Artificial Neural Networks....Pages 561-576
Designing Prediction Bands....Pages 577-586
Analysis of Observational Studies from the Point of View of Nonparametric Regression....Pages 587-602
Some Issues in Cross-Validation....Pages 603-612
Nonparametric Function Estimation Involving Errors-in-Variables....Pages 613-627
Front Matter....Pages 629-629
A Consistent Goodness of Fit Test Based on the Total Variation Distance....Pages 631-645
On a Problem in Semiparametric Estimation....Pages 647-656
On the Integrable and Approximately Integrable Linear Statistical Models....Pages 657-667
Nonparametric Techniques in Image Estimation....Pages 669-677
Regularized Deconvolution on the Circle and the Sphere....Pages 679-690
Back Matter....Pages 691-708
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