Monte Carlo Tests -- Testing for Multivariate Distributions -- Asymptotics of Goodness-of-fit Tests for Symmetry -- A Test of Dimension-Reduction Type for Regressions -- Checking the Adequacy of a Partially Linear Model -- Model Checking for Multivariate Regression Models -- Heteroscedasticity Tests for Regressions -- Checking the Adequacy of a Varying-Coefficients Model -- On the Mean Residual…
Classification and Clustering -- Multi-Class Budget Exploratory Trees -- Methods to Compare Nonparametric Classifiers and to Select the Predictors -- Variable Selection in Cell Classification Problems: A Strategy Based on Independent Component Analysis -- Simplifying Classification Trees Through Consensus Methods -- Selecting the Training Set in Classification Problems with Rare Events -- A Cla…
Linear and Quadratic Programming -- General Optimization With Simple -- Advanced Issues in Mean-Variance Optimization -- Resampling and Portfolio Choice -- Scenario Optimization: Addressing Non-normality -- Robust Statistical Methods for Portfolio Construction -- Bayes Methods.In recent years portfolio optimization and construction methodologies have become an increasingly critical ingredient o…
Fundamentals of MDS -- The Four Purposes of Multidimensional Scaling -- Constructing MDS Representations -- MDS Models and Measures of Fit -- Three Applications of MDS -- MDS and Facet Theory -- How to Obtain Proximities -- MDS Models and Solving MDS Problems -- Matrix Algebra for MDS -- A Majorization Algorithm for Solving MDS -- Metric and Nonmetric MDS -- Confirmatory MDS -- MDS Fit Measures…
Why probability and statistics? -- Outcomes, events, and probability -- Conditional probability and independence -- Discrete random variables -- Continuous random variables -- Simulation -- Expectation and variance -- Computations with random variables -- Joint distributions and independence -- Covariance and correlation -- More computations with more random variables -- The Poisson process -- …
Motivating Studies -- Generalized Linear Models -- Linear Mixed Models for Gaussian Longitudinal Data -- Model Families -- The Strength of Marginal Models -- Likelihood-based Marginal Models -- Generalized Estimating Equations -- Pseudo-Likelihood -- Fitting Marginal Models with SAS -- Conditional Models -- Pseudo-Likehood -- From Subject-specific to Random-effects Models -- The Generalized Lin…
to Longitudinal Data -- Plots -- Simple Analyses -- Critiques of Simple Analyses -- The Multivariate Normal Linear Model -- Tools and Concepts -- Specifying Covariates -- Modeling the Covariance Matrix -- Random Effects Models -- Residuals and Case Diagnostics -- Discrete Longitudinal Data -- Missing Data -- Analyzing Two Longitudinal Variables -- Further Reading.Longitudinal data are ubiquitou…
Missing data -- Prologue -- Describing incompleteness -- Single imputation and related methods -- Multiple imputation -- Case studies -- Small-area estimation -- Models for small areas -- Using auxiliary information -- Using small-area estimators -- Case studies -- Combining estimators -- Model selection.This book develops methods for two key problems in the analysis of large-scale surveys: dea…
Pricing by Arbitrage -- Martingale Measures -- The First Fundamental Theorem -- Complete Markets -- Discrete-time American Options -- Continuous-Time Stochastic Calculus -- Continuous-Time European Options -- The American Put Option -- Bonds and Term Structure -- Consumption-Investment Strategies -- Measures of Risk.This book presents the mathematics that underpins pricing models for derivative…
Probability Theory -- Fundamentals of Statistics -- Unbiased Estimation -- Estimation in Parametric Models -- Estimation in Nonparametric Models -- Hypothesis Tests -- Confidence Sets.This book consists of four hundred exercises in mathematical statistics and their solutions, over 95% of which are in the author's Mathematical Statistics, Second Edition (Springer, 2003). For students preparing f…