Developments in Statistics Series

Development in Statistics, Volume 1 is a collection of papers that deals with theory and application of parameter estimation in stochastic differential systems, the comparative aspects of the study of ordinary time series, and real multivariate distributions. Some papers discuss covariance analysis of nonstationary time series, nonparametric repeated significance tests, as well as discrete optimal factorial designs for statisticians and investigators of experiments. One paper cites an application of parameter estimation in stochastic differential systems in approximates of stability and control derivatives from flight test data. Another paper cites cases where procedures of ordinary time series (or point processes) have direct analogs in the study of point processes (or ordinary time series). One paper explains the applications of multivariate distributions in simultaneous tests on the equality of eigenvalues toward the covariance matrix, canonical correlation matrix, and a matrix associated with the multivariate analysis of variance. Another paper reviews two types of repeated significance tests, namely, the genuinely distribution-free tests based on a broad class of nonparametric statistics; and the asymptotically distribution-free tests based on a broad class of parametric statistics but having asymptotically nonparametric behavior. Both types can provide a unified solution to a broad class of problems. The collection can be valuable for mathematicians, students, and professors of calculus, statistics, or advanced mathematics.

Development in Statistics, Volume 2 is a collection of papers that deals with one- and two- dimensional structures, the statistical theory of linear systems, bispectra, and energy transfer in grid-generated turbulence. Several papers discuss simultaneous test procedures, stochastic Markovian fields, as well as the stopping of invariant sequential probability ratio tests. One paper examines the relationships between excitation and response statistics for one-dimensional structures, and then as extended to two-dimensional structures. The special features issuing from these extensions are related to simple supported rectangular and square plates excited by a stationary random force applied at a single point. Another paper discuses the relationship between the measurable bispectra and the one-dimensional energy transfer terms, and which bispectra will vanish in an isotropic turbulent flow field. One paper reviews simultaneous test procedures, including the evaluation of the probability integrals of multivariates, multivariate gamma distributions, distributions of correlated quadratic forms. Another paper analyzes two concerns regarding the random sample size N, also known as stopping time. These are if N is finite with a probability of one, or the rate that the tail probabilities in the distribution of N go to zero. Mathematicians, statisticians, students, and professors of calculus or advanced mathematics will surely appreciate the collection.

Development in Statistics, Volume 3 is a collection of papers that deals with asymptotic expansions in parametric statistical theory, orthogonal models for contingency tables, statistical concepts in economic analysis, and an exposition of path analysis. One paper presents an inference model based on a sample of independent identically distributed observations to arrive at a general statistical theory founded on asymptotic methods. Another paper discusses the applicability of statistical concepts to economics and related areas, with emphasis on not-so-obvious applications (known as utility and expected loss). The paper explains information theory concepts for the measurement of income inequality, intergenerational occupational mobility, as well as to first- and second-order moments of univariate and bivariate distributions (such as measurements applied to the cost of living and of real income). One paper notes that the starting point in path analysis is a linear predictor (in the least-squares sense) for one random variable in terms of a number of others. The paper adds that the work of Koopmans and Hood (1953) on econometrics is part of the starting point. Statisticians, economists, mathematicians, students, and professors of calculus or advanced mathematics will surely appreciate the collection.

Developments in Statistics, Volume 4 reviews developments in the theory and applications of statistics, covering topics such as time series, identifiability and model selection, and missing data. The application of structured exploratory data analysis to human genetics, specifically, the mode of inheritance, is also considered. Comprised of four chapters, this volume begins with an introduction to spectrum parameter estimation in time series analysis, restricting the discussion to the simplest univariate (that is, scalar) real-valued time series X(t). An accurate formulation of the general problem is presented. The accuracy of different consistent estimates obtained for large but fixed values of T (maximum likelihood estimates, Whittle's estimates, and simplified asymptotically efficient estimates) is also compared. The next chapter deals with identifiability and modeling in econometrics, focusing on the theoretical framework relating realization theory, identification, and parametrization. The realization theory is illustrated on various levels of generality by means of examples related to econometrics, along with some advanced applications of system theory. The book also examines inference on parameters of multivariate normal populations when some data are missing before concluding with an evaluation of structured exploratory data as applied to the study of the mode of inheritance. This monograph will be of interest to students and practitioners of statistics.