Koul H.L., Fan J. (eds.) Frontiers in Statistics

London: Imperial College Press, 2006. — 552 p.During the last two decades, many areas of statistical inference have experienced phenomenal growth. This book presents a timely analysis and overview of some of these new developments and a contemporary outlook on the various frontiers of statistics. Eminent leaders in the field have contributed 16 review articles and 6 research articles covering areas including semi-parametric models, data analytical nonparametric methods, statistical learning, network tomography, longitudinal data analysis, financial econometrics, time series, bootstrap and other re-sampling methodologies, statistical computing, generalized nonlinear regression and mixed effects models, martingale transform tests for model diagnostics, robust multivariate analysis, single index models and wavelets. This volume is dedicated to Prof. Peter J Bickel in honor of his 65th birthday. The first article of this volume summarizes some of Prof. Bickel's distinguished contributions.Doing Well at a Point and Beyond
Distribution Free Tests Higher Order Expansions and Challenging Projects
From Adaptive Estimation to Semiparametric Models
Hidden Markov Models
Non- and Semi-parametric TestingBickel's PublicationSemiparametric ModelingTesting and Profile Likelihood Theory
Semiparametric Mixture Model Theory
Bayes Methods and Theory
Model Selection Methods
Transformation and Frailty Models
Semiparametric Regression Models
Extensions to Non-iid Data
Critiques and Possible Alternative TheoriesCharacterization of Efficient Estimators
Autoregression Parameter
Innovation Distribution
Innovation Density
Conditional Expectation
Stationary Distribution
Stationary Density
Transition DensityEstimation via Outer Product of Gradients
Global Minimization Estimation Methods
Sliced Inverse Regression Method
Asymptotic Distributions
Comparisons in Some Special Cases
Proofs of the TheoremsEstimating Function Based Cross-Validation
Some Examples
General Finite Sample Result
AppendixNonparametric MethodsPowerful Choices: Tuning Parameter Selection Based on Power
Introduction: Local Testing and Asymptotic Power
Maximizing Asymptotic Power
Examples
AppendixNonparametric Assessment of AtypicalityEstimating Atypicality
Theoretical Properties
Numerical Properties
Outline of Proof of TheoremWavelets
Nonparametric Regression
Inverse Problems
Change-points
Local Self-similarity and Non-stationary Stochastic ProcessLack-of-fit Tests
Censoring
Khamaladze Transform or BootstrapStatistical Learning and BootstrapBoosting and Functional Gradient Descent
L-Boosting for High-dimensional Multivariate Regression
L-Boosting for Multivariate Linear Time SeriesBootstrap for iid Data
Model Based Bootstrap
Block Bootstrap
Sieve Bootstrap
Transformation Based Bootstrap
Bootstrap for Markov Processes
Bootstrap under Long Range Dependence
Bootstrap for Spatial DataProof of Theorem
Evaluation of the Oscillatory TermLongitudinal Data AnalysisNonparametric Model with a Single Covariate
Partially Linear Models
Varying-Coefficient Models
An Illustration
Generalizations
Estimation of Covariance MatrixIntroduction and Review
The Functional Approach to Longitudinal Responses
Predicting Longitudinal Trajectories from a Covariate
IllustrationsStatistics in Science and Technology
Statistical Physics and Statistical Computing: A Critical Link
The Ising Model
The Swendsen-Wang Algorithm and Criticality
Instantaneous Hellinger Distance and Heat Capacity
A Brief Overview of Perfect Sampling
Huber's Bounding Chain Algorithm
Approximating Criticality via Coupling Time
A SpeculationNetwork Tomography: A Review and Recent DevelopmentsPassive Tomography
Active Tomography
An Application
Concluding RemarksFinancial EconometricsThe Univariate Case
Multivariate Likelihood Expansions
Connection to Saddlepoint Approximations
An Example with Nonlinear Drift and Diffusion Specifications
An Example with Stochastic Volatility
Inference When the State is Partially Observed
Application to Specification Testing
Derivative Pricing Applications
Likelihood Inference for Diffusions under NonstationarityThe Frontier Model
Envelope Estimators
Order-m Estimators
Conditional Frontier Models
OutlookParametric Techniques and InferencesNewton's Estimate of Mixing Distributions
Review of Newton's Result on Convergence
Convergence Results
Other Results
SimulationLinear Mixed Models
Generalized Linear Mixed Models
Nonlinear Mixed Effects ModelsRobustness Criteria
Robust Multivariate Location and Scatter Estimators
Applications
Conclusions and Future WorksKullback-Leibler Loss and Exponential Families
Mean Square Error Loss
Location Families
Approximate Solutions
Convergence of the Loss EstimateSubject Index
Author Index