Hardle W., Simar L. Maths & Stats Applied Multivariate Statistical Analysis

Version: 29th April 2003. — 488 pages.Most of the observable phenomena in the empirical sciences are of a multivariate nature.
In financial studies, assets in stock markets are observed simultaneously and their joint
development is analyzed to better understand general tendencies and to track indices. In
medicine recorded observations of subjects in different locations are the basis of reliable
diagnoses and medication. In quantitative marketing consumer preferences are collected in
order to construct models of consumer behavior. The underlying theoretical structure of
these and many other quantitative studies of applied sciences is multivariate. This book
on Applied Multivariate Statistical Analysis presents the tools and concepts of multivariate
data analysis with a strong focus on applications.Descriptive TechniquesComparison of Batches
Boxplots
Histograms
Kernel Densities
Scatterplots
Cherno -Flury Faces
Andrews' Curves
Parallel Coordinates Plots
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ExercisesMultivariate Random Variables
A Short Excursion into Matrix Algebra
Elementary Operations
Spectral Decompositions
Quadratic Forms
Derivatives
Partitioned Matrices
Geometrical Aspects
ExercisesMoving to Higher Dimensions
Covariance
Correlation
Summary Statistics
Linear Model for Two Variables
Simple Analysis of Variance
Multiple Linear Model
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ExercisesMultivariate Distributions
Distribution and Density Function
Moments and Characteristic Functions
Transformations
The Multinormal Distribution
Sampling Distributions and Limit Theorems
Bootstrap
ExercisesTheory of the Multinormal
Elementary Properties of the Multinormal
The Wishart Distribution
Hotelling Distribution
Spherical and Elliptical Distributions
ExercisesTheory of Estimation
The Likelihood Function
The Cramer-Rao Lower Bound
Exercises
Hypothesis Testing
Likelihood Ratio Test
Linear Hypothesis
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ExercisesMultivariate Techniques
Decomposition of Data Matrices by Factors
The Geometric Point of View
Fitting the p-dimensional Point Cloud
Fitting the n-dimensional Point Cloud
Relations between Subspaces
Practical Computation
ExercisesPrincipal Components Analysis
Standardized Linear Combinations
Principal Components in Practice
Interpretation of the PCs
Asymptotic Properties of the PCs
Normalized Principal Components Analysis
Principal Components as a Factorial Method
Common Principal Components
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More Examples
ExercisesFactor Analysis
The Orthogonal Factor Model
Estimation of the Factor Model
Factor Scores and Strategies
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ExercisesCluster Analysis
The Problem
The Proximity between Objects
Cluster Algorithms
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ExercisesDiscriminant Analysis
Allocation Rules for Known Distributions
Discrimination Rules in Practice
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ExercisesCorrespondence Analysis
Motivation
Chi-square Decomposition
Correspondence Analysis in Practice
ExercisesCanonical Correlation Analysis
Most Interesting Linear Combination
Canonical Correlation in Practice
ExercisesMultidimensional Scaling
The Problem
Metric Multidimensional Scaling
The Classical Solution
Nonmetric Multidimensional Scaling
Shepard-Kruskal algorithm
ExercisesConjoint Measurement AnalysisDesign of Data Generation
Estimation of Preference Orderings
ExercisesApplications in Finance
Portfolio Choice
E cient Portfolio
E cient Portfolios in Practice
The Capital Asset Pricing Model (CAPM)
ExercisesHighly Interactive, Computationally Intensive Techniques
Simplicial Depth
Projection Pursuit
Sliced Inverse Regression
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ExercisesSymbols and NotationData
Boston Housing Data
Swiss Bank Notes
Car Data
Classic Blue Pullovers Data
US Companies Data
French Food Data
Car Marks
French Baccalaur eat Frequencies
Journaux Data
US Crime Data
Plasma Data
WAIS Data
ANOVA Data
Timebudget Data
Geopol Data
US Health Data
Vocabulary Data
Athletic Records Data
Unemployment Data
Annual Population DataBibliography
Index