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Functional and Operatorial Statistics

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ISBN-10: 379082061X

ISBN-13: 9783790820614

Edition: 2008

Authors: Sophie Dabo-Niang, Fr�d�ric Ferraty

List price: $219.99
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Description:

An increasing number of statistical problems and methods involve infinite-dimensional aspects. This is due to the progress of technologies which allow us to store more and more information while modern instruments are able to collect data much more effectively due to their increasingly sophisticated design. This evolution directly concerns statisticians, who have to propose new methodologies while taking into account such high-dimensional data (e.g. continuous processes, functional data, etc.). The numerous applications (micro-arrays, paleo- ecological data, radar waveforms, spectrometric curves, speech recognition, continuous time series, 3-D images, etc.) in various fields (biology,…    
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Book details

List price: $219.99
Copyright year: 2008
Publisher: Physica-Verlag
Publication date: 5/29/2008
Binding: Hardcover
Pages: 304
Size: 5.25" wide x 9.25" long x 1.00" tall
Weight: 1.320
Language: English

Introduction to IWFOS'2008
Historical and scientific setting
The STAPH group
The first IWFOS'2008
References
Solving Multicollinearity in Functional Multinomial Logit Models for Nominal and Ordinal Responses
Introduction
Functional multinomial response model
Nominal responses
Ordinal responses
Model estimation
Principal components approach
References
Estimation of Functional Regression Models for Functional Responses by Wavelet Approximation
Introduction
Functional linear model for a functional response
Model estimation
Wavelet approximation of sample curves
References
Functional Linear Regression with Functional Response:Application to Prediction of Electricity Consumption
Introduction
Estimation procedure
Computational aspects and simulations
Prediction of electricity consumption
References
Asymptotic Normality of Robust Nonparametric Estimator for Functional Dependent Data
Introduction
Model and estimation
Hypothesis and results
Conditional confidence curve
References
Measuring Dissimilarity Between Curves by Means of Their Granulometric Size Distributions
Introduction
Basic concepts
Methods and experimental results
References
Supervised Classification for Functional Data: A Theoretical Remark and Some Numerical Comparisons
Introduction
Consistency of the nearest neighbour rule
Comparison of several classification techniques
References
Local Linear Regression for Functional Predictor and Scalar Response
Introduction
Local linear smoothing for functional data
Performance of the estimator &mcirc;<sub>LL</sub>
References
Spatio-temporal Functional Regression on Paleoecological Data
Introduction
Data
Functional regression
References
Local Linear Functional Regression Based on Weighted Distance-based Regression
Introduction
Weighted distance-based regression (WDBR)
Local linear distance-based regression
A real data example: Spectrometric Data
References
Singular Value Decomposition of Large Random Matrices (for Two-Way Classification of Microarrays)
Introduction
Singular values of a noisy matrix
Classification via singular vector pairs
Perturbation results for correspondence matrices
Recognizing the structure
References
On Tensorial Products of Hilbertian Linear Processes
Introduction
The real case
The hilbertian case
References
Recent Results on Random and Spectral Measures with Some Applications in Statistics
Introduction and definitions
Convolution product of spectral measures
Tensor and convolution products of random measures
References
Introduction
Inner optimization: nuisance parameters
Middle optimization: structural parameters
Outer optimization: complexity parameters
Parameter cascading precedents
Parameter cascading advantages
References
Advances in Human Protein Interactome Inference
Introduction
Methods
Preliminary results
References
Functional Principal Components Analysis with Survey Data
Introduction
FPCA and sampling
FPCA in a finite population setting
The Horvitz-Thompson estimator
Linearization by influence function
Asymptotic properties
Variance approximation and estimation
A Simulation study
References
Functional Clustering of Longitudinal Data
Introduction
The methods
Discussion
References
Robust Nonparametric Estimation for Functional Data
Introduction
Model
Asymptotic results Ill
Convergence in probability and asymptotic normality
A uniform integrability result Ill
Moments convergence
Application to time series prediction
References
Estimation of the Functional Linear Regression with Smoothing Splines
Introduction
Construction of the estimator
Convergence results
References
A Random Functional Depth
Introduction
Functional depth
Randomness
Analysis of a real data set
References
Parametric Families of Probability Distributions for Functional Data Using Quasi-Arithmetic Means with Archimedean Generators
QAMML distributions
Gateaux density
GQAMML distributions
CQAMML distributions
Supervised classification
Conclusions
References
Point-wise Kriging for Spatial Prediction of Functional Data
Introduction
Point-wise kriging for functional Data
Example
References
Nonparametric Regression on Functional Variable and Structural Tests
Introduction
Nonparametric estimation
Structural tests
Bootstrap procedures and simulations
References
Vector Integration and Stochastic Integration in Banach Spaces
Introduction
Vector integration
The classical integral
The Bochner integral
Integration with respect to a vector-measure with finite variations
Integration with respect to a vector-measure with finite semivariation
The stochastic integral
References
Multivariate Functional Data Discrimination Using ICA: Analysis of Hippocampal Differences in Alzheimer's Disease
Introduction
Brain MR scans processing
Methodology: ICA and linear discriminant analysis
Results of the hippocampus study
References
Influence in the Functional Linear Model with Scalar Response
Introduction
The functional linear model with scalar response
Influence measures for the functional linear model
References
Is it Always Optimal to Impose Constraints on Nonparametric Functional Estimators? Some Evidence on the Smoothing Parameter Choice
Introduction
General constrained solutions
Regularized estimated solutions
Asymptotic behavior
References
Dynamic Semiparametric Factor Models in Pricing Kernels Estimation
Introduction
Pricing kernels
Pricing kernels estimation with DSFM
Empirical results
References
he Operator Trigonometry in Statistics
The origins of the operator trigonometry
The essentials of the operator trigonometry
The operator trigonometry in statistics
Operator trigonometry in general
Conclusions
References
Selecting and Ordering Components in Functional-Data Linear Prediction
Introduction
Linear prediction in a general setting
Arguments for and against the principal component basis
Theoretical argument in support of the ordering (3) of the principal component basis
Other approaches to basis choice
References
Bagplots, Boxplots and Outlier Detection for Functional Data
Introduction
Functional bagplot
Functional HDR boxplot
Comparison
References
Marketing Applications of Functional Data Analysis
Introduction
Methodology
Results
References
Nonparametric Estimation in Functional Linear Model
Introduction
Definition of the estimator of �
Risk bound when X is second order stationary
Risk bound when X is not second order stationary
References
Introduction
Back to the multivariate case
Presmoothing Y
Presmoothing X
Comments about efficiency
References
Probability Density Functions of the Empirical Wavelet Coefficients of Multidimensional Poisson Intensities
Introduction
Some basics and notations
Main results
Final remarks
References
A Cokriging Method for Spatial Functional Data with Applications in Oceanology
Introduction
Spatial linear model
Cokriging on coefficients
Dealing with real data
References
On the Effect of Curve Alignment and Functional PCA
Introduction
References
K-sample Subsampling
Introduction
Subsampling hypothesis tests in K samples
Subsampling confidence sets in K samples
Random subsamples and the K-sample bootstrap
References
Inference for Stationary Processes Using Banded Covariance Matrices
Introduction
The results
A class of nonlinear processes
Convergence of banded covariance estimators
Band selection
References
Automatic Local Spectral Envelope
Introduction
Basic approach
References
Recent Advances in the Use of SVM for Functional Data Classification
Introduction
SVM classifiers
Definition
Universal consistency of SVM
Using SVM to classify functional data
Kernels for functional data
Projection approach
Differentiation approach
References
Wavelet Thresholding Methods Applied to Testing Significance Differences Between Autoregressive Hilbertian Processes
Introduction
Preliminaries
Main results
Comparing two sequences of SFD in the ARH context
References
Explorative Functional Data Analysis for 3D-geometries of the Inner Carotid Artery
Introduction
Efficient estimation of 3D vessel centerlines and their curvature functions by free knot regression splines
Registration
Statistical analysis
References
Inference on Periodograms of Infinite Dimensional Discrete Time Periodically Correlated Processes
Introduction
Preliminaries and results
References