Time Series, Fuzzy Analysis & Miscellaneous

Madan Lal Puri, Selected Collected Works, Vol. 3

By P.G. Hall, M. Hallin, & G.G. Roussas

December 2003

VSP

ISBN: 90-6764-386-6

784 pages, Illustrated

$344.00 Hardcover

Professor Puri is one of the most versatile and prolific researchers in the world in mathematical statistics. His research areas include nonparametric statistics, order statistics, limit theory under mixing, time series, splines, tests of normality, generalized inverses of matrices and related topics, stochastic processes, statistics of directional data, random sets, and fuzzy sets and fuzzy measures. His fundamental contributions in developing new rank-based methods and precise evaluation of the standard procedures, asymptotic expansions of distributions of rank statistics, as well as large deviation results concerning them, span such areas as analysis of variance, analysis of covariance, multivariate analysis, and time series, to mention a few. His in-depth analysis has resulted in pioneering research contributions to prominent journals that have substantial impact on current research.

CONTENTS: PART I. TIME SERIES AND RELATED TOPICS Linear serial rank tests for randomness against ARMA alternatives Linear and quadratic serial rank tests for randomness against serial dependence Locally asymptotically optimal tests for randomness Optimal rank-based procedures for time series analysis: testing an ARMA model against other ARMA models On locally asymptotically maximin tests for ARMA processes Asymptotically most powerful rank tests for multivariate randomness against serial dependence Weak convergence of the U-statistic and weak invariance of the one-sample rank order statistic for Markov processes and ARMA models Weak convergence of serial rank statistics under dependence with applications in time series and Markov processes Asymptotic normality of L-statistics based on m(n)-decomposable time series Time series analysis via rank order theory: signed-rank tests for ARMA models Rank tests for time series analysis. A survey Nonparametric prediction for random fields Asymptotic behavior of L-statistics for a large class of time series Aligned rank tests for linear models with autocorrelated error terms Change curves in the presence of dependent noise A multivariate Wald-Wolfowitz rank test against serial dependence Nonparametric approach for non-Gaussian vector stationary processes The limiting density of unit root test statistics: A unifying technique PART II. FUZZY SET THEORY AND RELATED TOPICS Integration on fuzzy sets A possibility measure is not a fuzzy measure Strong law of large numbers for Banach space valued random sets Strong law of large numbers with respect to a set-valued probability measure Differentials of fuzzy functions The concept of normality for fuzzy random variables Limit theorems for random compact sets in Banach space Fuzzy random variables Gaussian random sets in Banach space Limit theorems for fuzzy random variables Convergence theorem for fuzzy martingales Limit theorems for fuzzy random variables Central limit theorem for Banach space valued fuzzy random variables Strong law of large numbers for Banach space valued fuzzy random variables PART III. MISCELLANEOUS TOPICS Local maxima of the sample functions of the N-parameter Bessel process Realization of lp by spaces of random variables Shorted operators and generalized inverses of matrices Complex planar splines Shorted matrices --- an extended concept and some applications The fundamental bordered matrix of linear estimation and the Duffin--Morley general linear electromechanical systems Complex Chebyshev polynomials and generalizations with an application to the optimal choice of interpolating knots in complex planar splines Strong solutions of stochastic differential equations for multiparameter processes A new semigroup technique in Poisson approximation Information A local algorithm for constructing non-negative cubic splines The time spent by the Wiener process in a narrow tube before leaving a wide tube Maximum likelihood estimation for stationary point processes On time-reversibility and the uniqueness of moving average representations for non-Gaussian stationary time series Locally asymptotically rank-based procedures for testing autoregressive moving average dependence On some limit laws for perturbed empirical distribution functions

Mathematics

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