Advances in statistics, combinatorics and related areas : selected papers from the SCRA2001-FIM VIII, Wollo[n]gong conference, University of Woolongong, Australia, 19-21 December 2001

The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This work looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric. To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, and more Efficient Estimators of Different Types for Domains (M C Agrawal & C K Midha); Chisquared Components as Tests of Fit for Discrete Distributions (D J Best & J C W Rayner); Simulating Transects Through Two-Phase Particles (B M Bray); Long Memory Processes -- An Economist's Viewpoint (C W J Granger); An Indifference Zone Approach to Testing for a Two-Component Normal Mixture (M Haynes & K Mengersen); Semiparametric Density Estimation with Additive Adjustment (K Naito); Bioinformatics: Statistical Perspectives and Controversies (P K Sen); Monitoring Pavement Construction Processes (R Sparks & J Ollis); Hypothesis Testing of Multivariate Abundance Data (D Warton & M Hudson); Statistical Process Monitoring for Autocorrelated Date (N F Zhang); and other papers This book is a collection of selected refereed papers presented at the International Conference on Statistics, Combinatorics and Related Areas, and the Eighth International Conference of the Forum for Interdisciplinary Mathematics. It includes contributions from eminent statisticians such as Joe Gani, Clive Granger, Chris Heyde, R. Nishii, C.R. Rao, P.K. Sen and Sue Wilson. By exploring and investigating deeper, these papers enlarge the reservoir in the represented areas of research, such as bioinformatics, estimating functions, financial statistics, generalized linear models, goodness of fit, image analysis, industrial data analysis, multivariate statistics, neural networks, quasi-likelihood, sample surveys, statistical inference, stochastic models, and time series This book is a collection of selected refereed papers presented at the International Conference on Statistics, Combinatorics and Related Areas, and the Eighth International Conference of the Forum for Interdisciplinary Mathematics. It includes contributions from eminent statisticians such as Joe Gani, Clive Granger, Chris Heyde, R Nishii, C R Rao, P K Sen and Sue Wilson. By exploring and investigating deeper, these papers enlarge the reservoir in the represented areas of research, such as bioinformatics, estimating functions, financial statistics, generalized linear models, goodness of fit, image analysis, industrial data analysis, multivariate statistics, neural networks, quasi-likelihood, sample surveys, statistical inference, stochastic models, and time series. Some Comparisons of Clustering and Classification Techniques Applied to Transcriptional Profiling Data1 Introduction; 2 Microarrays; 3 Sporulation data; 4 Comparison of clustering methods; 5 Classification; 6 Validation; 7 Concluding remarks; Acknowledgments; REFERENCES; Mean-Variance Edge Plots for Ensemble Voting Schemes; 1 Introduction; 2 Edge behaviour of a fixed observation; 3 Mean-variance state space; 4 Conclusion; REFERENCES; Approximating the Cauchy Principal Value Integral via Hermite-Hadamard Type Inequalities; 1 Introduction; 2 The main results; 3 Numerical experiments; REFERENCES Nonhomogeneous Susceptibles and Infectives Among Needle Sharing Ivdus1 Introduction; 2 The effect of vaccination; 3 Two types of infectives and two types of susceptibles; 4 Two waves of infectives; REFERENCES; Long Memory Processes - An Economist's Viewpoint; 1 Introduction and some definitions; 2 Fractionally integrated processes; 3 Generalizations; 4 Transformation of random walks; 5 Transformations of fractionally integrated processes; 6 The economists' viewpoint - empty boxes; REFERENCES; An Indifference Zone Approach to Testing for a Two-Component Normal Mixture; 1 Introduction 2 Testing for a mixture3 Testing predictive distributions; 4 Example; REFERENCES; Risk Models for Individual Decision Making; 1 Introduction; 2 Management decisions in early breast cancer; 3 Statistical Methods; 4 Conclusion; Acknowledgments; REFERENCES; Adaptive M-Estimation Procedure: Adequacy and Alternative Approach; 1 Introduction; 2 Bimodal distributions; 3 Alternative regression procedure; 4 Simulation example; 5 Conclusion; REFERENCES; Bayesian Inference for Categorical Data with Misclassification Errors; 1 Introduction; 2 Misclassified observed data and Bayesian computation On the Determination of an Appropriate Hedging Strategy1 Introduction; 2 Notation; 3 Comparison of hedging methods; 4 Forecasting hedge ratios; 5 Example; 6 Conclusion; REFERENCES; Simulating Transects Through Two-Phase Particles; 1 Introduction; 2 Random secants; 3 Mean random lengths; 4 Theoretical liberation indices; 5 Simulations of the liberation index; 6 Conclusion; REFERENCES; New Bounds for the Three-Point Rule Involving the Riemann-Stieltjes Integral; 1 Introduction; 2 Results for trapezoidal type rules; 3 Results for three point rules; REFERENCES Preface; Contents; Efficient Estimators of Different Types for Domains; 1 Introduction; 2 Two efficient estimators of the domain mean; 3 Numerical illustration; REFERENCES; Neural Network Nonlinear Regression Modeling and Information Criteria; 1 Introduction; 2 Neural Network Nonlinear Regression Modeling; 3 Information criteria; 4 Numerical results; Acknowledgments; REFERENCES; Chisquared Components as Tests of Fit for Discrete Distributions; 1 Introduction; 2 Definitions; 3 Three examples; 4 Conclusion; Appendix 1; Appendix 2; REFERENCES