Contents -- Foreword -- Preface -- 1. High-Dimensional Discrete Statistical Models: UIP, MCP and CSI in Perspectives P. K. Sen -- 1.1. Introduction -- 1.2. Preliminary Notion -- 1.3. CATANOCOVA -- 1.4. UIP and CSI -- 1.5. Statistical Reasoning for HDDSM -- 1.6. UIP and MCP in HDDSM -- References -- 2. A Review of Multivariate Theory for High Dimensional Data with Fewer Observations M. S. Srivastava -- Contents -- 2.1. Introduction -- 2.2. Inference on the Mean Vector in One-Sample -- 2.2.1. Tests invariant under orthogonal and a non-zero scalar transformations -- 2.2.2. A Test invariant under scalar transformation of each component -- 2.2.3. Comparison of Power -- 2.3. Two-sample Tests -- 2.4. Multivariate Analysis of Variance (MANOVA) -- 2.5. Discriminant Analysis -- 2.6. Tests of Hypotheses on Covariance Matrices -- 2.6.1. One-sample case -- 2.6.1.1. Tests for the Sphericity Hypothesis -- 2.6.1.2. Testing that the covariance matrix is an identity matrix -- 2.6.1.3. Testing that the Covariance Matrix is a Diagonal Matrix -- 2.6.1.4. Testing that the covariance matrix is of intraclass correlation structure -- 2.6.1.5. Simulation results of power comparison and attained signifi- cance level -- 2.6.2. Two-Sample case -- 2.6.3. Testing the equality of covariances in MANOVA -- 2.7. Conclusion -- References -- 3. Model Based Penalized Clustering for Multivariate Data S. Ghosh and D. K. Dey -- 3.1. Introduction -- 3.2. Optimization Framework for Regularized K-means Clustering -- 3.3. Likelihood Formulation -- 3.4. Choices of Prior -- 3.5. Clustering Data Examples -- 3.5.1. Old faithful data: clustering analysis -- 3.5.2. Clustering result through correlation decomposition -- 3.5.3. Fisher's Iris Set: Clustering Analysis -- 3.6. Conclusion -- References -- 4. Jacobians Under Constraints and Statistical Bioinformatics K. V. Mardia -- Contents.

4.1. Introduction -- 4.2. Jacobians Under Constraints and the Haar Measure -- 4.3. The Euler-Angle Representation -- 4.4. The Jacobian -- 4.5. Discussion -- 4.6. Acknowledgements -- References -- 5. Cluster Validation for Microarray Data: An Appraisal V. Pihur, G. N. Brock and S. Datta -- Contents -- 5.1. Introduction -- 5.2. Validation Measures -- 5.2.1. Internal measures -- 5.2.1.1. Connectivity -- 5.2.1.2. Silhouette Width -- 5.2.1.3. Dunn Index -- 5.2.1.4. In-Group Proportion (IGP) -- 5.2.2. Stability measures -- 5.2.2.1. Average Proportion of Non-overlap (APN) -- 5.2.2.2. Average Distance (AD) -- 5.2.2.3. Average Distance between Means (ADM) -- 5.2.2.4. Figure of Merit (FOM) -- 5.2.3. Biological validation measures -- 5.2.3.1. Biological Homogeneity Index (BHI) -- 5.2.3.2. Biological Stability Index (BSI) -- 5.3. A Numerical Illustration -- 5.3.1. UPGMA -- 5.3.2. K-means -- 5.3.3. Diana -- 5.3.4. PAM -- 5.3.5. SOM -- 5.3.6. Model based clustering -- 5.3.7. Bayesian clustering -- 5.3.8. SOTA -- 5.3.9. Cluster validation results -- 5.4. Software for cluster validation -- 5.4.1. The clValid package -- 5.4.2. Other packages -- 5.5. Discussion -- References -- 6. Flexible Bivariate Circular Models B. C. Arnold and A. SenGupta -- Contents -- 6.1. Introduction -- 6.2. One Dimensional Circular Models -- 6.3. To Higher Dimensions Via Conditional Specification -- 6.4. Inference -- 6.5. Multivariate Extensions And Open Questions -- References -- 7. Optimal Text Space Representation of Student Essays Using Latent Semantic Analysis A. Villacorta and S. R. Jammalamadaka -- Contents -- 7.1. Introduction -- 7.2. Textual Decomposition and Circular Analysis -- 7.2.1. Vector space model and latent semantic analysis -- 7.2.2. Circular analysis -- 7.3. Optimal Vector Space Representation -- 7.3.1. Loss functions.

7.3.2. Testing hypotheses using circular analysis of variance -- 7.4. Results -- 7.4.1. Strict grade matching -- 7.4.2. Three level partition -- 7.4.3. Binary partitions -- 7.4.4. Comparison of orderings -- 7.4.5. Analysis of variance -- 7.5. Conclusions -- 7.6. Acknowledgements -- References -- 8. Linear Regression for Random Measures M. M. Rao -- Contents -- 8.1. Introduction -- 8.2. Conditioning Concepts and Regression -- 8.3. Regression for Random Measures -- 8.4. Regression for Random Integrals -- 8.5. Final Remarks -- References -- 9. Mixed Multivariate Models for Random Sums and Maxima T. J. Kozubowski, A. K. Panorska and F. Biondi -- Contents -- 9.1. Introduction -- 9.2. The BEG Model -- 9.2.1. Marginal distributions -- 9.2.2. Conditional distributions -- 9.2.2.1. The conditional distribution of (X -- N) given N > n -- 9.2.2.2. The conditional distribution of (X -- N) given X > u -- 9.2.3. Moments -- 9.2.4. Representations -- 9.2.5. Stability properties -- 9.2.6. Estimation -- 9.3. The BTLG Model -- 9.3.1. Marginal distributions -- 9.3.2. Conditional distributions -- 9.3.2.1. The conditional distribution of (Y -- N) given N > n -- 9.3.2.2. The conditional distribution of (Y -- N) given Y > u -- 9.3.3. Moments -- 9.3.4. Representations -- 9.3.5. Stability properties -- 9.3.6. Estimation -- 9.4. Extensions -- 9.4.1. The BGNB model -- 9.4.1.1. Conditional distributions -- 9.4.1.2. Moments and related parameters -- 9.4.1.3. Representations -- 9.4.2. The BGTLNB model -- 9.4.2.1. Conditional distributions -- 9.4.2.2. Moments and related parameters -- 9.4.2.3. Representations -- 9.5. Acknowledgements -- References -- 10. Estimation of the Multivariate Box-Cox Transformation Parameters M. Rahman and L. M. Pearson -- Contents -- 10.1. Introduction -- 10.2. Box-Cox Transformation -- 10.3. Maximum Likelihood Estimation Using The Newton-Raphson Method.

10.4. Maximization of the Multivariate Shapiro-WilkW Statistic -- 10.5. Simulation Study -- References -- 11. Generation of Multivariate Densities R. N. Rattihalli and A. N. Basugade -- Contents -- 11.1. Introduction -- 11.2. Generation of Densities by Contour Transformation -- 11.2.1. Bivariate densities obtained by two i.i.d. standard normal variates -- 11.2.2. General form of densities -- 11.2.3. Multivariate models obtained from circular contoured densities -- 11.3. Acknowledgement -- References -- 12. Smooth Estimation of Multivariate Distribution and Density Functions Y. P. Chaubey -- 12.1. Intoduction -- 12.2. Hille's Theorem: Univariate Case -- 12.2.1. Smooth estimation of Survival and Density Functions -- 12.3. Smooth Estimators of Other Functionals -- 12.3.1. Censored Data -- 12.3.2. Other Applications -- 12.3.3. Generalized Smoothing Lemma and Applications -- 12.4. Multivariate Generalization of Hille's Lemma -- 12.5. Further Developments -- 12.5.1. Quantile Estimation -- 12.5.2. Other Problems -- Acknowledgments -- References -- 13. Estimation Using Quantile Function Structure with Emphasis on Weibull Distribution G. D. Kollia, G. S. Mudholkar and D. K. Srivastava -- Contents -- 13.1. Introduction -- 13.2. The Approach in the General Setting -- 13.2.1. Construction of the pivotal statistics -- 13.2.2. The Jackknifed L-statistic and its variance estimate -- 13.2.3. The estimators -- 13.3. Estimation of Weibull Parameters -- 13.3.1. Closed form L-estimators -- 13.4. Comparisons -- 13.4.1. Competitors -- 13.4.2. A Monte Carlo experiment and results -- 13.5. Conclusions and Miscellaneous Remarks -- 13.6. Acknowledgments -- References -- 14. On Optimal Estimating Functions in the Presence of Nuisance Parameters P. Mukhopadhyay -- Contents -- 14.1. Introduction -- 14.2. An Optimal Estimating Function.

14.3. The Case of More Than One Nuisance Parameter -- 14.4. Examples -- References -- 15. Inference in Exponential Family Regression Models Under Certain Shape Constraints M. Banerjee -- Contents -- 15.1. Introduction and Background -- 15.1.1. Conditionally parametric response models: least squares and maximum likelihood estimates -- 15.2. Discrepancy Statistics for Testing The Null Hypothesis -- 15.2.1. Relevant stochastic processes and derived functionals -- 15.3. Limit Distributions for The Discrepancy Statistics and Methodological Implications -- 15.3.1. Incorporating further shape constraints -- 15.4. Concluding Discussion -- 15.5. Proof of Theorem 1 -- 15.6. Acknowledgements -- References -- 16. Study of Optimal Adaptive Rule in Testing Problem S. K. Bhandari, R. Dutta and R. G. Niyogi -- Contents -- 16.1. Introduction -- 16.2. Preliminaries and Main Results: Simple Hypothesis Case -- 16.2.1. Procedure I -- 16.2.2. Procedure II -- 16.2.3. Simulation studies (tables and results) -- 16.3. Appendix -- 16.4. Acknowledgement -- References -- 17. The G-IG Analogies and Robust Tests for Inverse Gaussian Scale Parameters G. S. Mudholkar, H. Wang and R. Natarajan -- Contents -- 17.1. Introduction -- 17.2. G-IG Analogies -- 17.3. Inferences Regarding Inverse Gaussian Scale Parameters -- 17.4. A Monte Carlo Study -- References -- 18. Clusterwise Regression Using Dirichlet Mixtures C. Kang and S. Ghosal -- Contents -- 18.1. Introduction -- 18.2. Method Description -- 18.3. Simulation Study -- 18.3.1. One dimension -- 18.3.2. Two dimension -- 18.3.3. Higher dimension -- 18.4. Conclusions -- 18.5. Acknowledgments -- References -- 19. Bayesian Analysis of Rank Data Using SIR A. K. Laha and S. Dongaonkar -- Contents -- 19.1. Introduction -- 19.2. One Transposition Error -- 19.3. Disjoint Transposition Errors -- 19.4. Cyclic Errors -- 19.5. The General Case.

19.6. Example.