Multivariate Analysis—III : Proceedings of the Third International Symposium on Multivariate Analysis Held at Wright State University, Dayton, Ohio, June 19-24, 1972

Multivariate Analysis — III contains the proceedings of the Third International Symposium on Multivariate Analysis held at Wright State University in Dayton, Ohio, on June 19-24, 1972. The papers explore the theory and applications of multivariate analysis and cover areas such as time series and stochastic processes; distribution theory and inference; characteristic functions and characterizations; and design and analysis of experiments. Classification, modeling, and reliability are also discussed. Comprised of 27 chapters, this volume begins with an introduction to two-dimensional random fields, giving results for a class of Gaussian processes with a multidimensional time parameter. The next chapter deals with concepts of consistency in spectral estimation for multivariate time series and considers the alternative of estimating the spectral distribution function or the spectral density function. Abstract martingales and ergodic theory are also examined, along with methods for assessing multivariate normality; inference and redundant parameters; characterization of the multivariate geometric distribution; and max-min designs in the analysis of variance. This monograph will be useful to statisticians and probabilists, as well as to scientists in other disciplines who are broadly interested in multivariate analysis. Content: Front Matter, Page iii Copyright, Page iv List of Contributors, Pages xiii-xiv Preface, Page xv Acknowledgments, Page xvii, P.R. Krishnaiah Two-Dimensional Random Fields, Pages 3-15, P. BICKEL, M. ROSENBLATT Concepts of Consistency in Spectral Estimation for Multivariate Time Series, Pages 17-30, F. EICKER Non-Anticipative Canonical Representations of Equivalent Gaussian Processes, Pages 31-44, G. KALLIANPUR Abstract Martingales and Ergodic Theory, Pages 45-60, M.M. RAO On the Modelling and Estimation of Communication Channels, Pages 61-78, W.L. ROOT Innovation and Nonanticipative Processes, Pages 79-92, YU.A. ROZANOV Methods for Assessing Multivariate Normality, Pages 95-116, D.F. ANDREWS, R. GNANADESIKAN, J.L. WARNER Asymptotic Expansions for the Distributions of Characteristic Roots When the Parameter Matrix Has Several Multiple Roots, Pages 117-127, A.K. CHATTOPADHYAY, K.C.S. PILLAI Aspects of the Multinomial Logit Model, Pages 129-142, A.P. DEMPSTER Inference and Redundant Parameters, Pages 143-156, D.A.S. FRASER The Variance Information Manifold and the Functions on It, Pages 157-169, A.T. JAMES Stopping Time in Sequential Samples from Multivariate Exponential Families, Pages 171-179, R.A. WIJSMAN An Isomorphism Method for the Study of I0n, Pages 183-197, ROGER CUPPENS A Characterization of the Multivariate Geometric Distribution, Pages 199-208, EUGENE LUKACS On Infinitely Decomposable Probability Distributions, and Helical Varieties in Hilbert Space, Pages 209-223, P. MASANI Limit Laws for Sequences of Normed Sums Satisfying Some Stability Conditions, Pages 225-237, K. URBANIK The Analysis of Time Series Collected in an Experimental Design, Pages 241-256, DAVID R. BRILLINGER Max-Min Designs in the Analysis of Variance, Pages 257-261, R.H. FARRELL Analysis of Covariance Structures, Pages 263-285, K.G. JÖRESKOG Optimum Designs for Fitting Biased Multiresponse Surfaces, Pages 287-297, J. KIEFER Asymptotic Properties of Some Sequential Nonparametric Estimators in Some Multivariate Linear Models, Pages 299-316, PRANAB KUMAR SEN, MALAY GHOSH Availability Theory for Multicomponent Systems, Pages 319-335, RICHARD E. BARLOW, FRANK PROSCHAN Some Measures for Discriminating between Normal Multivariate Distributions with Unequal Covariance Matrices, Pages 337-344, HERMAN CHERNOFF Correlation and Affinity in Gaussian Cases, Pages 345-349, KAMEO MATUSITA Identification of the Structure of Multivariable Stochastic Systems, Pages 351-368, M.B. PRIESTLEY, T. SUBBA RAO, H. TONG An Information Function Approach to Dimensionality Analysis and Curved Manifold Clustering, Pages 369-382, J.N. SRIVASTAVA Nonlinear Iterative Partial Least Squares (NIPALS) Modelling: Some Current Developments, Pages 383-407, HERMAN WOLD Titles of Contributed Papers, Pages 409-410 Two-dimensional Random Fields / P. Bickel And M. Rosenblatt -- Concepts Of Consistency In Spectral Estimation For Multivariate Time Series / F. Eicker -- Non-anticipative Canonical Representations Of Equivalent Gaussian Processes / G. Kallianpur -- Abstract Martingales And Ergodic Theory / M.m. Rao -- On The Modelling And Estimation Of Communication Channels / W.l. Root -- Innovation And Nonanticipative Processes / Yu. A. Rozanov -- Methods For Assessing Multivariate Normality / D.f. Andrews, R. Gnanadesikan And J.l. Warner -- Asymptomatic Expansions For The Distributions Of Characteristic Roots When The Parameter Matrix Has Several Multiple Roots / A.k. Chattopadhyay And K.c.s. Pillai -- Aspects Of The Multinomial Logit Model / A.p. Dempster -- Inference And Redundant Parameters / D.a.s. Fraser -- The Variance Information Manifold And The Functions On It / A.t. James -- Stopping Time In Sequential Samples From Multivariate Exponential Families / R.a. Wijsman --^ An Isomorphism Method For The Study Of I0[superscript N] / Roger Cuppens -- A Characterization Of The Multivariate Geometric Distribution / Eugene Lukacs -- On Infinitely Decomposable Probability Distributions, And Helical Varieties In Hilbert Space / P. Masani -- Limit Laws For Sequences Of Normed Sums Satisfying Some Stability Conditions / K. Urbanik -- The Analysis Of Time Series Collected In An Experimental Design / David R. Brillinger -- Max-min Designs In The Analysis Of Variance / R.h. Farrell -- Analysis Of Covariance Structures / K.g. Jöreskog -- Optimum Designs For Fitting Biased Multiresponse Surfaces / J. Kiefer -- Asymptotic Properties Of Some Sequential Nonparametric Estimators In Some Multivariate Linear Models / Pranab Kumar Sen And Malay Ghosh -- Availability Theory For Multicomponent Systems / Richard E. Barlow And Frank Proschan -- Some Measures For Discriminating Between Normal Multivariate Distributions With Unequal Covariance Matrices / Herman Chernoff --^ Correlation And Affinity In Gaussian Cases / Kameo Matusita -- Identification Of The Structure Of Multivariable Stochastic Systems / M.b. Priestley, T. Subba Rao And H. Tong -- An Information Function Approach To Dimensionality Analysis And Curved Manifold Clustering / J.n. Srivastava -- Nonlinear Iterative Partial Least Squares (nipals) Modeling : Some Current Developments / Herman Wold. Edited By Paruchuri R. Krishnaiah. Sponsored By The Aerospace Research Laboratories, Wright-patterson Air Force Base, Ohio. Includes Bibliographies.