Nonparametric function estimation with stochastic data, otherwiseknown as smoothing, has been studied by several generations ofstatisticians. Assisted by the ample computing power in today'sservers, desktops, and laptops, smoothing methods have been findingtheir ways into everyday data analysis by practitioners. While scoresof methods have proved successful for univariate smoothing, onespractical in multivariate settings number far less. Smoothing splineANOVA models are a versatile family of smoothing methods derivedthrough roughness penalties, that are suitable for both univariate andmultivariate problems.In this book, the author presents a treatise on penalty smoothingunder a unified framework. Methods are developed for (i) regressionwith Gaussian and non-Gaussian responses as well as with censored lifetime data; (ii) density and conditional density estimation under avariety of sampling schemes; and (iii) hazard rate estimation withcensored life time data and covariates. The unifying themes are thegeneral penalized likelihood method and the construction ofmultivariate models with built-in ANOVA decompositions. Extensivediscussions are devoted to model construction, smoothing parameterselection, computation, and asymptotic convergence.Most of the computational and data analytical tools discussed in thebook are implemented in R, an open-source platform for statisticalcomputing and graphics. Suites of functions are embodied in the Rpackage gss, and are illustrated throughout the book using simulatedand real data examples.This monograph will be useful as a reference work for researchers intheoretical and applied statistics as well as for those in otherrelated disciplines. It can also be used as a text for graduate levelcourses on the subject. Most of the materials are accessible to asecond year graduate student with a good training in calculus andlinear algebra and working knowledge in basic statistical inferencessuch as linear models and maximum likelihood estimates.

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Product Description: Et mai . ..., si j'avait su comment en revenir. One service mathematics has rendered the human race. It has put common sense back je n'y serais point aIIe.' Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent: therefore we may be sense' ...read more

Product Description: Simulation of materials at the atomistic level is an important tool in studying microscopic structures and processes. The atomic interactions necessary for the simulations are correctly described by Quantum Mechanics, but the size of systems and the length of processes that can be modelled are still limited...read more

Product Description: This book contains the refereed papers which were presented at the international conference on multivariate approximation and splines held in Mannheim, Germany, on September 7-10, 1996. Fifty experts from Bulgaria, England, France, Israel, the Netherlands, Norway, Poland, Switzerland, Ukraine, the USA and Germany participated in the symposium...read more

This monograph describes advances in the theory of extremal problems in classes of functions defined by a majorizing modulus of continuity w. In particular, an extensive account is given of structural, limiting, and extremal properties of perfect w-splines generalizing standard polynomial perfect splines in the theory of Sobolev classes. In this context special attention is paid to the qualitative description of Chebyshev w-splines and w-polynomials associated with the Kolmogorov problem of n-widths and sharp additive inequalities between the norms of intermediate derivatives in functional classes with a bounding modulus of continuity. Since, as a rule, the techniques of the theory of Sobolev classes are inapplicable in such classes, novel geometrical methods are developed based on entirely new ideas. The book can be used profitably by pure or applied scientists looking for mathematical approaches to the solution of practical problems for which standard methods do not work. The scope of problems treated in the monograph, ranging from the maximization of integral functionals, characterization of the structure of equimeasurable functions, construction of Chebyshev splines through applications of fixed point theorems to the solution of integral equations related to the classical Euler equation, appeals to mathematicians specializing in approximation theory, functional and convex analysis, optimization, topology, and integral equations .

Product Description: We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book...read more