Contributions to Probability and Statistics: Applications and Challenges

Peter Brown, Shuangzhe Liu, Dharmendra Sharma9789812703910, 981-270-391-8

Contributed by world renowned researchers, the book features a wide range of important topics in modern statistical theory and methodology, economics and finance, ecology, education, health and sports studies, and computer and IT-data mining. It is accessible to students and of interest to experts. Many of the contributions are concerned with theoretical innovations, but all have applications in view, and some contain illustrations of the applied methods or photos of historic mathematicians.

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Table of contents :
CONTENTS……Page 8
Preface……Page 6
Part A Mathematics and Statistics in Society……Page 12
Estimating Internet Access for Welfare Recipients in Australia……Page 14
Two Classification Methods of Individuals for Educational Data and an Application……Page 22
Measurement of Skill and Skill Change……Page 28
Some Comments about Issai Schur (1875-1941) and the Early History of Schur Complements……Page 39
Part B Applications of Statistics……Page 78
Estimating the Number of SARS Cases in Mainland China in 2002-3……Page 80
Using Statistics to Determine the Effectiveness of Prescribed Burning……Page 84
A Fair Tennis Scoring System for Doubles in the Presence of Sun and Wind Effects – An Application of Probability……Page 100
Part C Theoretical Issues in Probability and Statistics……Page 108
Perturbed Markov Chains……Page 110
Matrix Tricks for Linear Statistical Models: A Short Review of our Personal Top Fourteen……Page 124
On Influence Diagnostics in Multivariate Regression Models under Elliptical Distributions……Page 140
A Necessary Condition for Admissibility of Nonnegative Quadratic Estimators of Variance Components when the Moments are not Necessarily as under Normality……Page 153
Small-Sample Performance of Robust Methods in Logistic Regression……Page 163
On the Asymptotic Distribution of the ‘Natural’ Estimator of Cronbach’s Alpha with Standardised Variates under Nonnormality, Ellipticity and Normality……Page 178
On the Approximate Variance of a Nonlinear Function of Random Variables……Page 183
On Oblique and Orthogonal Projectors……Page 189
Fiducial Inference of Means and Variances from Normal Populations under Order Restrictions……Page 203
Part D Probabilistic Models in Economics and Finance……Page 220
When Large Claims are Extremes……Page 222
Shrinkage Estimation of Gini Index……Page 245
On the Problem of Discriminating between the Tails of Distributions……Page 257
Part E Numerical Methods……Page 270
An Approximate Maximum a Posteriori Method with Gaussian Process Priors……Page 272
Data Extraction for Improved Prediction Outcomes in Organ Transplantation – A Hybrid Approach……Page 287
Mining Multiple Models……Page 300
Part F Abstracts without Papers……Page 308
Ranked Set Sampling: A Simple Idea of Great Use……Page 310
Properties of Nearest-neighbour Classifiers……Page 311
Large Covariance Matrices: Estimation and Inference in High Dimensions……Page 312
Bootstrapping in Clustered Populations……Page 313
On the Linear Aggregation Problem in the General Gauss-Markov Model……Page 314
Author Index……Page 316
Subject Index……Page 318