Kvam P.H., Vidakovic B. Nonparametric Statistics with Applications to Science and Engineering

Wiley Interscience, 2007. — 420 p. — (Lecture Notes–Monograph Series). — ISBN 0470081473.This book presents modern nonparametric statistics from a practical point of view. It is primarily intended for use with engineers and scientists. While the book covers the necessary theorems and methods of rank tests in an applied fashion, the novelty lies in its emphasis on modern nonparametric methods in regression and curve fitting, bootstrap confidence intervals, splines, wavelets, empirical and nonparametric likelihood, and goodness of fit testing. MatLAB is the computing and programming system of choice throughout the book because of its special applicability for research analysis and simulation.
Review:
"The authors' efforts to tailor the book to suit the needs of engineering students should pay off in the long run, as they have made the book more relevant and lively. The choice of topics covered is excellent. The rich content and information in this book should make this book a handy reference for many applied research workers." (Technometrics, May 2008)
"The authors' efforts to tailor the book to suit the needs of engineering students should pay off in the long run, as they have made the book more relevant and lively. The choice of topics covered is excellent. The rich content and information in this book should make this book a handy reference for many applied research workers." (Technometrics, May 2008)
"…an excellent introductory text to modern nonparametric methodology and also should make a useful reference for engineers and statisticians. The mixture of exemplary scholarship, good exposition, insightful examples, and occasional dashes of humor make this book an enjoyable read." (Journal of the American Statistical Association, September 2008)
"The book is an essential textbook for graduate courses in engineering and the physical sciences, and is also a valuable reference work for practitioners. It is accessible and thus useful to a wide audience." (Computing Reviews, Feb 2008)
"This book is clearly written and well organized. I liked very much the photos and historical details of statisticians." (International Statistical Review, 2008)Vector Spaces Theory
Vector Spaces
Linear Transformations
Inner Product Spaces
The Cauchy–Schwarz Inequality
The Space L(V,W)
Determinants and Eigenvalues
The Spectral TheoremRandom Vectors
Random Vectors
Independence of Random Vectors
Special Covariance StructuresThe Normal Distribution on a Vector Spaces
The Normal Distribution
Quadratic Forms
Independence of Quadratic Forms
Conditional Distributions
The Density of the Normal DistributionLinear Statistical Model
The Classical Linear Model
More About the Gauss–Markov Theorem
Generalized Linear ModelsMatrix Factorizations and Jacobians
JacobiansTopological Groups and Invariant Measures
Groups
Invariant Measures and Integrals
Invariant Measures on Quotient Spaces
Transformations and Factorizations of MeasuresFirst Applications of Invariance
Left On Invariant Distributions on n × p Matrices
Groups Acting on Sets
Invariant Probability Models
The Invariance of Likelihood Methods
Distribution Theory and Invariance
Independence and InvarianceThe Wishart Distribution
Basic Properties
Partitioning a Wishart Matrix
The Noncentral Wishart Distribution
Distributions Related to Likelihood Ratio TestsInference for Means in Multivariate Linear Models
The MANOVA Model
MANOVA Problems with Block Diagonal Covariance Structure
Intraclass Covariance Structure
Symmetry Models: An Example
Complex Covariance Structures
Additional Examples of Linear ModelsCanonical Correlation Coefficients
Population Canonical Correlation Coefficients
Sample Canonical Correlations
Some Distribution Theory
Testing for Independence
Multivariate RegressionAppendix
Comments on Selected Problems