Functional and Operatorial Statistics

Name: Functional and Operatorial Statistics
Availability: InStock
ISBN: 9783790820614

ISBN-10: 379082061X

ISBN-13: 9783790820614

Edition: 2008

Authors: Sophie Dabo-Niang, Frï¿½dï¿½ric Ferraty

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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,…

Book details

List price: $169.99
Copyright year: 2008
Publisher: Physica-Verlag
Publication date: 5/29/2008
Binding: Hardcover
Pages: 304
Size: 6.10" wide x 9.25" long x 0.30" tall
Weight: 3.058




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 ï¿½



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