bluuebunny/crossref_metadata_2025_split huggingface dataset:
Evolutionary Spectra and Non-Stationary Processes
Authors: Priestley M. B. 
Published: December 2018

Summary
We develop an approach to the spectral analysis of non-stationary processes which is based on the concept of “evolutionary spectra”; that is, spectral functions which are time dependent, and have a physical interpretation as local energy distributions over frequency. It is shown that the notion of evolutionary spectra generalizes the usual definition of spectra for stationary processes, and that, under certain conditions, the evolutionary spectrum at each instant of time may be estimated from a single realization of a process. By such means it is possible to study processes with continuously changing “spectral patterns”.
Alternative Analyses of Contingency Tables
Authors: Gart John J. 
Published: December 2018

Summary
Modifications of the logit and likelihood-ratio methods of analysing two-and three-dimensional contingency tables are developed from a semi-empirical approximation to the multinomial distribution. The modified likelihood-ratio test is shown to have an approximate relationship to the Freeman and Halton (1951) criterion for choosing a critical region for the exact test. A Bayesian argument leading to the same results is discussed.
Delay at Traffic Intersections
Authors: Hawkes A. G. 
Published: December 2018

Summary
The distribution of delay to vehicles is found for two models of behaviour at traffic intersections. In the first part we consider vehicles turning both left and right from a minor road onto a major road which has two-way traffic. In Section 5 we study the delay on a major road caused by vehicles wishing to turn right and which must wait for a gap in the oncoming traffic in order to do so. Some numerical evaluation of mean delays shows the benefit which may be expected from certain road improvements.
A New Approach to Sampling from Finite Populations. I Sufficiency and Linear Estimation
Authors: Godambe V. P. 
Published: December 2018

Summary
Barnard (1963) introduced the concept of linear sufficiency in connection with the Gauss-Markov set-up of estimation. In the present article the concept of linear sufficiency is redefined to suit the problem of estimation in survey sampling where, as demonstrated by the present author (Godambe, 1955, 1965), the Gauss-Markov set-up is fundamentally inapplicable. According to this redefined concept, a certain estimator is shown to be uniquely (up to a constant multiplier), linearly sufficient for the population total in the entire class (defined by the author (1955)) of linear estimators. The significance of this result will be clear on the background of the author's previous result (Godambe, 1955) demonstrating the non-existence of a uniformly minimum variance estimator in the entire class of unbiased linear estimators for the population total. Practically, the results are summarized in Theorems 5.1 and 6.3.
A New Approach to Sampling from Finite Populations. II Distribution-Free Sufficiency
Authors: Godambe V. P. 
Published: December 2018

Summary
The idea that in some situations the prior knowledge about the unknown parameters could be formulated as a class of prior distributions, which could be used, not necessarily through Bayes posterior probability, for subsequent inference, is already present in Godambe (1955). In the present paper, the concept of distribution-free linear sufficiency or in short linear sufficiency, originally due to Barnard (1963b) but redefined by the present author (Part I), is extended by defining distribution-free sufficiency, removing the restriction of linearity. This extension again is based on the assumption that in some situations prior knowledge could be formulated as a class of prior distributions. A certain linear estimator of the population total, which in Part I was shown to satisfy the redefined criteria of linear sufficiency uniquely in the class of all linear estimators, is now shown to satisfy this extended criteria of distribution-free sufficiency in the entire class of estimators. Further the general relationship between the linear sufficiency of Part I and the distribution-free sufficiency introduced here is investigated. Broadly the result is that, if we restrict to linear estimators only, distribution-free sufficiency is identical with linear sufficiency. Finally, some remarks are offered by way of comparison between the result obtained by the author previously (Godambe, 1955) and the result here, about the utilization of the prior information. The approach of this paper clearly implies a generalization of Fisherian sufficiency suitable for the situations when prior knowledge consists of a class of prior distributions. An alternative generalization when the prior knowledge consists of a group structure is due to Barnard (1963a).
The Almost Full Dam with Poisson Input
Authors: Hasofer A. M. 
Published: December 2018

Summary
In this paper, the content of a dam with infinite depth, unit release per unit time and inputs which form a compound Poisson process is investigated by means of an integral equation technique. The Laplace transform of the content distribution for an initially full dam is calculated and inverted. The asymptotic behaviour of the content is described and its mean and variance obtained. Duality relationships with the almost empty dam with Poisson input are pointed out and used to obtain various explicit expressions.
Some Asymptotically Efficient Sequential Procedures for Ranking and Slippage Problems
Authors: Srivastava M. S. 
Published: December 2018

Summary
In this paper Chow and Robbins's (1965) sequential theory has been applied to ranking and slippage problems (including a multivariate slippage problem) and a class of asymptotically efficient sequential procedures is given for each problem. Except for the finiteness of the variance, no assumption regarding the form of the distribution function is made.
A Technique for Discussing the Passage Time Distribution for Stable Systems
Authors: Keilson Julian 
Published: December 2018

Summary
For many processes arising in reliability and congestion studies, passage time distributions required are difficult to exhibit. An asymptotic discussion is often available centring about a limit theorem given previously, and asymptotic equality of the mean passage time and an associated mean sojourn time, the latter obtainable directly from the ergodic distribution for the process. Theorems are presented exhibiting this equality for a variety of Markov chains.
Topics in the Investigation of Linear Relations Fitted by the Method of Least Squares
Authors: Anscombe F. J. 
Published: December 2018

Summary
Various topics are reviewed: the effect of modern computers on statistical calculation; analysis by vector components rather than analysis merely of variance; “stepwise regression”; testing goodness of fit by examining residuals. Possible alternatives to the method of least squares appropriate when the distribution of errors has long tails, and computation of the likelihood function resulting from a Pearson Type VII distribution of errors, are considered. Some of the methods discussed are illustrated by study of several sets of observations already well known in the literature.
Ex Post Determination of Significance in Multivariate Regression When the Independent Variables are Orthogonal
Authors: Geary R. C. 
Published: December 2018

Summary
In multivariate regression, when the regressors are orthogonal, the estimates of the coefficients may be regarded, in the normal case, as an independent normal random sample with estimable variance. Significance is determined by the absolute magnitude of the highest member of the sample, after consideration of order statistics more generally in this context.
The method is applied to time series data analysed by Fisher and Yates (1957): while these authors identified, by their essentially ex ante approach, the first and second orthopolynomials as significant, ex post only the second is identifiable.
The Analysis of Association Among Many Variates
Authors: Williams E. J. 
Published: December 2018

Summary
The methods used to estimate the nature and form of linear relations among sets of variates are developed in a simple manner based on a multivariate extension of the analysis of covariance. The link between these methods of analysis and the canonical analysis is discussed; it is shown how the two analyses can complement each other. Since it is of practical importance to represent the association among the variates in terms of a minimal set of derived variates, various tests of significance for the adequacy of such sets are presented. The methods make no use of non-central distributions, the only distribution theory involved being that of determinantal ratios whose three parameters are effectively the numbers of variates in the two associated sets and the number of observations of each. The methods have been set out in enough detail to show that they are not only relevant to many practical situations but also readily computable.
The Theory of Risk
Authors: Borch Karl 
Published: December 2018

Summary
The classical theory of risk is reviewed. It is shown to be a static theory and this is adduced to be its main disadvantage. A dynamic theory was introduced by Lundberg in 1909. This is discussed and Lundberg's achievement is reaffirmed. However, it is pointed out that this theory, in spite of extensive mathematical development, has found virtually no application in practice. The major difficulty lies in the formulation of insurance problems in a convincing way. In the last section a new approach is called for. A model incorporating dynamic features of Lunberg's collective risk theory with more realistic constraints is investigated. Possible directions for future research are suggested.
An Analysis of Departures from the Exponential Distribution
Authors: Jackson O. A. Y. 
Published: December 2018

Summary
A test for a Poisson process based on ordered sample values is proposed and its distribution and other properties derived. The test statistic is shown to be asymptotically normal and some further approximations to its distribution are investigated. The asymptotic relative efficiency of the test with respect to the asymptotically most powerful test against the alternative of gamma-distributed intervals is derived. Finally, a test for an incomplete sample is outlined.
An Estimation Procedure for Mixtures of Distributions
Authors: Choi Keewhan , Bulgren W. G. 
Published: December 2018

Notation
The symbols for estimators in this paper have been printed in light italic type. This is an exception from our usual typographic convention of showing matrices and vector quantities in bold black type, since in this case the large number of such symbols would seriously interfere with readability.

Summary
A general method is proposed for estimating the mixing measures of combinations of known distributions. The method is applicable to continuous and discrete mixtures. The small sample behaviour of the method is investigated by Monte Carlo methods. In large samples it is shown that the estimator converges to the true mixing measure with probability 1 at the rate of almost O(n-½) and has an asymptotic normal distribution.
Multivariate Beta Distribution and a Test for Multivariate Normality
Authors: Wagle B. 
Published: December 2018

Summary
This paper presents an application of the multivariate beta distribution to the problem of testing whether a given sample of multivariate observations could have come from a multivariate normal population with an unknown mean vector and dispersion matrix. By using a series of transformations and the principle of randomization it is shown that the above problem can be reduced to that of testing for univariate normality. No attempt is made to investigate the power of this test; but some brief thoughts are expressed in the concluding section.
On the Concept of the Spectrum for Non-Stationary Processes
Authors: Loynes R. M. 
Published: December 2018

Summary
Following a brief general description of the attitude adopted here to statistical models and definitions, a study of the problem of defining a spectrum for non-stationary processes is made. The approach is to determine first what one would wish to use such a spectrum for, and then attempt to discover whether this is possible. By the nature of the case no conclusive answer is possible, but the tentative conclusion drawn is that it is not.
Estimation of the Cross-Spectrum of a Stationary Bivariate Gaussian Process from its Zeros
Authors: Brillinger David R. 
Published: December 2018

Summary
Under regularity conditions the cross-spectrum of a stationary, bivariate, Gaussian process, continuous in mean and with unit variance, may be estimated consistently as T → ∞ from the zeros in the interval [0, T] of its two components and the knowledge that the components have the same or opposite sign at time 0. The power spectra of the components may be estimated from the respective components' zeros alone. The estimates are asymptotically normal and unbiased. During the course of the paper a bound, that may be of independent interest, is given for the joint cumulants of certain functions of multivariate normal random variables. A general theorem on the joint asymptotic normality of spectral and cross-spectral estimates is presented. There is also a worked example.
The Stationary Distribution of a Branching Process Allowing Immigration: A Remark on the Critical Case
Authors: Seneta E. 
Published: December 2018

Summary
For a branching process in which the individuals reproduce from generation to generation as in a Galton-Watson process, and are also subject to an immigration component at each generation, it is known that a stationary-limiting distribution sometimes exists. In particular, this is so if the mean number of offspring per individual is less than unity and the immigration distribution is reasonably behaved. We show that such a distribution may exist even when the mean number of offspring is unity, under special circumstances for which we give sufficient conditions.
On the Null Distribution of a Non-Parametric Test for the Bivariate Two-Sample Problem
Authors: Mardia K. V. 
Published: December 2018

Summary
A non-parametric test criterion U for the bivariate two-sample problem has been proposed by Mardia (1967). It is shown in Mardia (1968) that a two-sample test on a circle proposed by Wheeler and Watson (1964) has the same null distribution as that of U. In view of this additional application, we extend the table of critical values of U given in Mardia (1967), give a new approximation to the null distribution and compare it with the approximations given in Mardia (1967). We also apply the U-test to a geological problem.
Estimating the Parameters of a Convolution
Authors: Sclove S. L. , van Ryzin J. 
Published: December 2018

Summary
Parametric estimation problems are considered when one observes a random variable which is the sum of two independent non-identically distributed random variables. Some basic identifiability theorems are given which suggest the method of moments as a general method for attacking such problems, particularly when one of the summand variables is discrete. Moment estimators and their asymptotic distributions are examined for various specific examples. Some applications are suggested.
Inference Concerning Probabilities and Quantiles
Authors: Green J. R. 
Published: December 2018

Summary
It is intended to make inferences on the basis of a set of observations resulting from n replicates of an experiment, where each observation X has distribution F(x; θ), in order to provide information about a future performance of the same experiment, or a small number of such future performances. In such a situation the inference should concern the probability of an event occurring in the future experiment, rather than directly concern the parameter θ (a vector in general). Appropriate kinds of inference are considered, using the correspondence between tolerance limits and tests and confidence intervals for quantiles. The interpretation of tolerance intervals, etc. is considered.
Tests for Specification Errors in Classical Linear Least-Squares Regression Analysis
Authors: Ramsey J. B. 
Published: December 2018

Summary
The effects on the distribution of least-squares residuals of a series of model mis-specifications are considered. It is shown that for a variety of specification errors the distributions of the least-squares residuals are normal, but with non-zero means. An alternative predictor of the disturbance vector is used in developing four procedures for testing for the presence of specification error. The specification errors considered are omitted variables, incorrect functional form, simultaneous equation problems and heteroskedasticity.
Distinguishing Among Multinomial Populations: A Decision Theoretic Approach
Authors: Stromberg John L. 
Published: December 2018

Summary
This paper presents a method for determining, on the basis of sample data, which of several multinomial populations are the same and which are distinct. The method is compared with alternative approaches and is shown to have certain advantages. its limitations are also discussed. It is then applied to the specific anthropological problem of distinguishing among six burial sites of Northern California Indians.
Resolution Iv Fractional Factorial Designs
Authors: Margolin Barry H. 
Published: December 2018

Summary
Fractional factorial designs of resolution IV permit estimation of all the main effects with no aliasing by two-factor interactions. This paper produces a lower bound for the number of observations required for a general fractional factorial design to be of resolution IV. This lower bound agrees with a lower bound obtained by Rao for orthogonal arrays of strength 3. In addition, it is proved that this lower bound is attainable for the t. 2n factorial design series for t even and n ≡ 3 (mod 4) in plans which permit orthogonal estimation of the main effects. Finally, Webb's conjecture that there exist no resolution IV 2n factorial designs with 2n runs except for those constructed by the fold-over technique is proved to be valid.
Multicollinearity and Imprecise Estimation
Authors: Silvey S. D. 
Published: December 2018

Summary
For the standard linear model containing several explanatory variables, the precision of estimation of linear parametric functions is analysed in terms of latent roots and vectors of X'X, where X is the matrix of values of explanatory variables. This analysis provides a practical method for detecting multicollinearity, and it is demonstrated that it is also useful in solving problems of optimum choice of new values of explanatory variables.
On Priority Queues in Heavy Traffic
Authors: Mazumdar Sati 
Published: December 2018

Summary
For single-server, first-come-first-served queues, specified completely by the sequences of interarrival times and service times, if these sequences are stationary and if (in some sense) there is not too much dependence within or between them, it has been shown by Kingman (1962) that the waiting-time distribution is, in heavy traffic, approximately negative exponential. This result has been extended in the present paper when there are two types of customer, one type of customer having priority of service over that of the other.
On the Asymptotic Relative Efficiencies of Certain Location Parameter Estimates
Authors: Loynes R. M. 
Published: December 2018

Summary
If, by analogy with means and medians, one computes that value such that the sum of the absolute pth powers of the sample deviations about that point takes on its minimum, one obtains an estimate of the central value of a symmetric distribution. Such estimates, for p ≥ 1 and under reasonable conditions, are known to be asymptotically normal as the sample size becomes large, and here the asymptotic relative efficiency of any pair is obtained, both for the general case and when the distribution sampled is also supposed unimodal.
On a Sequential Analogue of the Behrens–Fisher Problem
Authors: Srivastava M. S. 
Published: December 2018

Summary
Srivastava (1966) proposed a class of asymptotically efficient sequential procedures for an analogue of the Behrens–Fisher problem. Recently, Robbins et al. (1967) also proposed the same class of sequential procedures. The object of this note is to give the details of our proof for the asymptotic efficiency, assuming only the finiteness of the variances.
The multivariate analogue of this problem has also been considered.
Estimation of the Branch Points of a Branching Diffusion Process
Authors: Edwards A. W. F. 
Published: December 2018

Summary
A solution to the problem of estimating the positions and times of the branch points of a Brownian-motion/Yule process, given the positions of all the particles at a particular time, is outlined. A likelihood approach is used, and it is shown that the solution involves maintaining a clear distinction between likelihood and conditional probability if difficulties over mathematical singularities are to be avoided. Several unsolved mathematical problems are encountered, and it is concluded that some simulation studies may be required for a complete solution. Questions of scientific inference which the problem raises are discussed briefly.
A Short Cut in the Fitting of Autoregressive Series
Authors: Ray W. D. 
Published: December 2018

Summary
The set of k equations arising from the asymptotic least-squares estimation procedure for fitting the unknown parameters in kth-order autoregressive models is shown to degenerate into two subsets, each of m equations for the even case (k = 2m), or two subsets, one of m equations and one of (m + 1) equations for the odd case (k = 2m + 1).
Simultaneous Confidence Bands in Regression Analysis
Authors: Wynn Henry P. , Bloomfield P. 
Published: December 2018

Summary
Simultaneous confidence intervals for linear combinations of parameters in a regression analysis are discussed, and a desirable property is described. Confidence intervals having this property are characterized and the Working–Hotelling band is discussed with reference to it. It is shown how this band may be sharpened to give exact confidence levels in linear and quadratic regression. Tables are given from which the confidence bands may be constructed.
The Effect of the Demand Distribution in Inventory Models Combining Holding, Stockout and Re-Order Costs
Authors: Foster F. G. , Rosenhead J. V. , Siskind V. 
Published: December 2018

Summary
The well-known square-root formula of inventory theory is based on the assumption of known, constant demand. When demand is probabilistic, the values of inventory control variables which minimize the expected total costs will depend on the shape of the distribution. In this paper we consider the effect of several demand distributions on a re-order cycle inventory system; however, the method of analysis is standard and could be applied to a number of other models. Formulae for the iterative calculation of optimal values of control variables are derived, and illustrated by worked examples. In the process, some results in distribution theory are developed.
Bayes, Fiducial and Frequency Aspects of Statistical Inference in Regression Analysis in Survey-Sampling
Authors: Godambe V. P. , Thompson Mary E. 
Published: December 2018

Summary
In this paper an attempt is made to show how the regression analysis generally used for hypothetical populations can also be validated for the actual populations commonly dealt with in statistical surveys. This validation is based on a frequency distribution generated by randomization. In this context some comments are made on the relationships between Bayes, fiducial and frequency theories of statistical inference.