bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Use of a Generalized Multinomial Distribution in the Estimation of Correlation in Discrete Data
Authors: Tallis G. M. 
Published: December 2018

SUMMARY
This paper presents a joint distribution for n identically distributed multinomial variates, Xq. The distribution is constructed so that C(Xq, Xr) = pV(X) for all q and r, q≠r, and applications of this model to the estimation of correlation in discrete data are discussed.
Tests of Goodness of Fit
Authors: Anscombe F. J. 
Published: December 2018

SUMMARY
An explicit account is given of a procedure for assessing goodness of fit of some observations with a hypothesis, generally known as a “test of significance”; the description is close in spirit to R. A. Fisher’s original conception. The relation of this test procedure with Bayesian procedures and with the Neyman–Pearson theory of tests is discussed. Some very tentative suggestions are made regarding the choice of a test criterion and the use to which the result of the test can be put. The role of conditional sampling distributions is studied. Various examples are discussed. In particular, a brief exploration is made in the apparently virgin territory of testing goodness of fit when the observations have been taken according to a sequential rule.
On the Normal Stationary Process—Areas Outside Given Levels
Authors: Leadbetter M. R. 
Published: December 2018

SUMMARY
Let x(t) be a normal stationary process, observed for 0 ≤ t ≤ T, and c a given positive constant. Formulae are derived for the mean and variance of the area above the level + c formed by the process x(t) in (0, T). Corresponding results are obtained for the sum and the difference of the areas above the level + c and below the level — c.
The Spectral Analysis of Point Processes
Authors: Bartlett M. S. 
Published: December 2018

SUMMARY
The spectral analysis of stationary point processes in one dimension is developed in some detail as a statistical method of analysis. The asymptotic sampling theory previously established by the author for a class of doubly stochastic Poisson processes is shown to apply also for a class of clustering processes, the spectra of which are contrasted with those of renewal processes. The analysis is given for two illustrative examples, one an artificial Poisson process, the other of some traffic data. In addition to testing the fit of a clustering model to the latter example, the analysis of these two examples is used where possible to check the validity of the sampling theory.
Local Conditional Sufficiency
Authors: Fraser D. A. S. 
Published: December 2018

Summary
The concept of sufficiency can be examined locally for a neighbourhood of a parameter point θ0 and it leads to an estimate that has minimum variance among locally-unbiased estimates (Fraser, 1964). This local estimate generates the natural global estimate for the case of the simple exponential model, but it does not do so for the important case of the general translation model. The global estimate, the Pitman estimate, for this translation model is rooted in ancillarity and conditional sufficiency. In this paper the concept of local conditional sufficiency is developed; the asymptotic distribution of the conditionally-sufficient statistic is investigated for large samples; and for the maximum-likelihood estimate a conditional large-sample variance is obtained which differs from that usually used.
Some Results for Fixed-Time Traffic Signals
Authors: Buckley D. J. , Wheeler R. C. 
Published: December 2018

Summary
An investigation is made of the queues and delays which occur when a Poisson traffic stream is subjected to a blockage. It has been assumed that the traffic is free-flowing when the blockage commences, that when the blockage is terminated delayed vehicles depart with constant time separations, and that no queueing occurs after the system has emptied for the first time. A blockage of duration ρ causes j vehicles to be delayed a total time w. Expressions are obtained for the Laplace transform of the joint distribution of j and w, the marginal distribution of j and the Laplace transform of the marginal distribution of w. The expected delay at a fixed-time traffic signal is then obtained for the case where there is a negligible probability that vehicles are still queueing at the end of the green phase.
On Local Inference and Information
Authors: Fraser D. A. S. 
Published: December 2018

Summary
Two techniques for local unbiased estimation have been developed in recent papers (Fraser, 1964a, b). In this paper these techniques are used to examine some aspects of inference and information. Both techniques show inadequacies for translation-invariant models, and this despite the development of the second technique on the basis of conditional sufficiency which is basic to translation-invariant models. Inference and information are then examined briefly for translation-invariant models and some modified definitions of information are proposed. The results are then extended to other models and lead to definitions of local structural probabilities on the parameter space and to a residual likelihood function.
On the Power of Two-Sample Rank Tests on the Equality of Two Distribution Functions
Authors: Gibbons Jean D. 
Published: December 2018

Summary
This paper is a comparative study of the power functions of two-sample rank tests of the hypothesis of equal distributions, H 0: H = G. Numerical results are given for the alternative of two extreme distributions, H1:H=1−(1−F)k,    G=Fk, with F an unspecified continuous cumulative distribution function, k = 2, 3, 4, sample sizes m = n ≤ 6, significance levels 0·01, 0·05, 0·10. Randomized decision rules are employed when necessary to attain the exact significance level. Some results are also given for unequal sample sizes. The tests considered are the most powerful rank test, Terry's test, one- and two-sided Wilcoxon tests, one- and two-sided median tests, the Wald-Wolfowitz runs test, and two new tests, called the Gamma and Psi tests. These are derived herein as the locally most powerful rank tests against slight variations of the alternative of two extreme distributions. Comparisons are made with the power of these same tests against normal alternatives differing only in location.
Spectral Analysis in the Presence of Variance Fluctuations
Authors: Herbst Laurence J. 
Published: December 2018

Summary
The present paper is concerned with the following questions: (1) If a random sequence Xt (t = 0, ± 1, ± 2, …) is not second-order stationary, can one meaningfully define a spectral density function ? (2) If so, can one hope to consistently estimate it ? For the special case of a random sequence of form Xt=∑0pajσt−jηt−j, where the ηt are independently, normally, distributed with zero means and unit variances and the aj and σt-j are non-random finite quantities, it is argued that the answers to both questions are affirmative provided σt2 (t = 0, α 1, α 2, …), while not, in general, constant, do satisfy the requirements σt2 ≤ Q &lt; ∞ (t = 0, α 1, + 2, …), where Q does not depend on t, and N−1∑1Nσt2→γ0&lt;∞ as N → ∞.
Note on a χ2-Approximation for the Multivariate Sign Test
Authors: Bennett B. M. 
Published: December 2018

Summary
Certain properties of the multivariate normal integral were employed by Bennett (1962) to propose a sign test for the equality of means in samples of n observations from two correlated p-variate populations for the cases p = 2, 3. Using the multinomial distributions for n = 10, 20, the exact distribution and significance points have been computed for the case p = 2, and compared with that of an approximate χ2-test and also that of the suggested modification by Wise (1963) of the χ2-test, when now maximum-likelihood estimates of the multinomial probabilities are used.
A Further Result on the Relevance of the Dispersion of a Radon–Nikodym Derivative to the Problem of Measuring Association
Authors: Ali S. M. , Silvey S. D. 
Published: December 2018

Summary
Let x and y be jointly distributed random variables (not necessarily real-valued) and let φ be the Radon–Nikodym derivative of their joint distribution with respect to the product of their marginal distributions. If x′ and y′ are functions of x and y respectively and φ′ is a corresponding derivative for x′ and y′, then the dispersion of φ, as determined by the product of the marginal distributions of x and y, is not less than that of φ′, this being true in the strongest possible sense.
Additional Results Concerning Estimable Functions and Generalized Inverse Matrices
Authors: Searle S. R. 
Published: December 2018

Summary
A method is derived for calculating the unbiased estimator of any estimable function of the parameters of a linear model. its variance and its covariance with the estimator of any other estimable function are also obtained. An expression is also given for the F-value required in testing a general linear hypothesis.
Certain Properties of Gaussian Processes and Their First-Passage Times
Authors: Mehr C. B. , McFadden J. A. 
Published: December 2018

Summary
The class of Gauss-Markov processes is characterized by their covariances. A functional equation is solved, giving the class of all Gauss–Markov processes with stationary transition probabilities. The notion of a conditionally Markov Gaussian process is introduced. A functional equation is solved which characterizes the class of stationary, conditionally Markov Gaussian processes. A class of non-stationary conditionally Markov Gaussian processes is constructed. Using a transformation of the Wiener process, an explicit expression is obtained for the first-passage-time density function, from level x 0 ≠ 0 at time t 0 to the level zero at time t &gt; t 0, for all Gauss–Markov (G.M.) processes. For two particular classes of G.M. processes an explicit expression is obtained for the density of the first-passage time, from any level x 0 at t 0 to any level x ≠ x 0 at time t &gt; t 0. Some of the results are extended to a class of Gaussian processes which are not Markovian.
An Experimental Study of Certain Screening Processes
Authors: Finney D. J. 
Published: December 2018

Summary
The paper discusses alternative procedures for successive selections from a population aimed at maximizing the mean value of the members finally selected. At each stage, errors of measurement obscure the attempt to select optimally, the magnitude of the errors being dependent both upon the proportion of the original population still surviving and the allocation of a part of the total available resources to measurement at the particular stage. Selection of a finite number of members at each stage is compared with selection of fractions from an infinite population, and the general trends are found to be similar. For all but the most trivial specifications of the selection, mathematical analysis is hopelessly intractable. A great amount of numerical study has been undertaken and is summarized in extensive tables. Some broad conclusions emerge, notably that little can be gained by going beyond three or four stages (with fixed total resources), and that both the selection fraction and the proportion of resources employed should be kept approximately constant from stage to stage.
An Extension of the Triangular Association Scheme to Three Associate Classes
Authors: John Peter W. M. 
Published: December 2018

Summary
The treatments in a triangular association scheme may be represented as ordered pairs of integers. This representation is extended to ordered triplets to give a scheme with three associate classes. The latent roots of the matrix NN', where N is the incidence matrix, are calculated and are used to establish the non-existence of some designs. Several series of designs are given together with their efficiencies.
On the Evaluation of Probabilities of Convex Polyhedra Under Multivariate Normal and t Distributions
Authors: John S. 
Published: December 2018

Summary
It is noted that probabilities of convex polyhedra in p-dimensional space can be expressed in terms of a function V(h1, h2, …, hp), if the distribution is normal, and in terms of a function Vn(h1, h2, …, hp), if the distribution is the t-distribution with n degrees of freedom. Formulae expressing V(h1, h2, …, hp) and Vn(h1, h2, …, hp) in terms of similar functions of lower order are obtained. An asymptotic expansion of Vn(h1,…, hp) in powers of n-1 is also included. The final section contains formulae connecting Vn(h1, h2, …, hp) with Vn±2(h1, K2, …, hp).
Some New Results on the Distribution of the Sample Correlation Coefficient
Authors: Ruben Harold 
Published: December 2018

Summary
A simple approximate normalization for the correlation coefficient in normal samples is obtained which is shown to compare favourably with previous normalization approximations (the usual large-sample normalization, Fisher's hyperbolic tangent transformation and Hotelling's improvement of that transformation). A second approximation, based on F and valid for large n | ρ | (n = sample size, ρ = population correlation), is also obtained. The results follow from a representation of the correlation in normal samples as the ratio of a linear combination of a standardized normal deviate and a Xn-1 to a Xn-2, where the three latter variates are independent.
The Use of the Concept of a Future Observation in Goodness-Of-Fit Problems
Authors: Guttman Irwin 
Published: December 2018

Summary
An attack on the problem of goodness of fit is made by combining a Bayesian and sampling argument; the Bayesian part is effected by using the distribution of a future observation, while the sampling argument concerns itself with the distribution of a “chi-squared like” statistic, which measures discrepancies of observed frequencies from those predicted by the distribution of the future observation. Examples are given for the case of sampling from the binomial, Poisson and normal distributions. An interesting application arising from the above approach is a procedure for estimating the degree of a polynomial response function.
On Fixed-Width Confidence Bounds for Regression Parameters and Mean Vector
Authors: Srivastava M. S. 
Published: December 2018

Summary
In this paper Chow and Robbins's (1965) sequential theory has been extended to construct a confidence region with prescribed maximum width and prescribed coverage probability for (i) the linear regression parameters, and (ii) the mean vector of a multivariate population. Except for the finiteness of the unknown variance and covariances in the respective two cases, no assumption regarding the form of their distribution functions is made. This result was announced in Srivastava (1966a). For some related results, refer to Gleser (1965), Srivastava (1966b) and Starr (1966).
Formal Expressions Which Can be Used for the Determination of the Operating Characteristic and Average Sample Number of a Simple Sequential Test
Authors: Kemp Kenneth W. 
Published: December 2018

Summary
In this paper expressions are developed which are useful for determining the characteristics of a sequential test designed to test a simple hypothesis against a simple alternative. Simple equations are derived which give upper and lower limits for the operating characteristic and average sample number of the test in situations where formal expressions for these are not available.
On a Special Subset Giving an Irregular Fractional Replicate of a 2N Factorial Experiment
Authors: Banerjee K. S. , Federer W. T. 
Published: December 2018

Summary
A special class of fractional replicates of 2n factorial experiments has been studied in this paper. Such fractional replicates are expected to be useful in practice where, for very large values of n, we may be interested only in the main effects. Analysis of such designs is simple in that the entire computational procedure is reducible to a simple routine.
A Bayesian Significance Test for Multinomial Distributions
Authors: Good I. J. 
Published: December 2018

Summary
A Bayesian significance test for multinomial distributions is discussed, together with the results of 18 numerical experiments in which the test is compared with non-Bayesian methods. Several different non-Bayesian criteria are considered because the circumstances under which their tail-area probabilities can be conveniently approximated differ from one to the other. A provisional empirical formula, connecting the Bayes factors with the tail-area probabilities, is found to be correct within a factor of 6 in the 18 experiments. As a by-product, a new non-Bayesian statistic is suggested by the theory, and its asymptotic distribution obtained. It seems to be useful sometimes when chi-squared is not, although chi-squared also has a Bayesian justification for large samples.
The work originated in, and is relevant to, the problem of the estimation of multinomial probabilities, but significance tests are a better proving ground for assumptions concerning the initial (prior) distribution of the physical probabilities.
On a Class of Gaussian Processes for Which the Mean Rate of Crossings is Infinite
Authors: McFadden J. A. 
Published: December 2018

Summary
A stationary Gaussian process X(t) is defined as locally Markov if the slope of its autocorrelation function has a finite jump at the origin. For such a process the mean rate of crossings at an arbitrary level a is infinite. For small (t2 − t1), the probability that X(t1) − a and X(t2) − a have opposite signs is calculated, both with and without the auxiliary condition, X(t3)∈ (x3, x3+dx3], …, X(tn+2)∈(xn+2, xn+2+dxn+2], where the times t3,…, tn+2 are all outside [t1,t2]. By inversion, it is shown that the conditional probability of this multiple event in X(t3), …, X(tn+2), given the sign change in (t1,t2), is asymptotically equal to the conditional probability of the same multiple event, given that X(t2) ϵ (a, a + da]. Again for small (t2 − t1). the probability that X(t) - a has one or more zeros is calculated, both marginally and conditionally. This event includes the case of a positive even number of crossings, which is not negligible. The above asymptotic equivalence between conditional probabilities can be extended also to this condition of one or more crossings. As an application, the probability of crossings in two small intervals (at different levels) is considered.
A Relatively Simple Form of the Distribution of the Multiple Correlation Coefficient
Authors: Gurland John 
Published: December 2018

Summary
A series is obtained for the cumulative distribution function of the multiple correlation coefficient in which the coefficients are interpretable as binomial probabilities. When N−p is even (N is the sample size and p is the number of components in the underlying multivariate normal distribution) the series is finite with 12(n−p)+1 terms. Other series are also considered. A comparatively simple approximation to the general distribution of the multiple correlation coefficient is presented which, in particular for p = 2, is more accurate than Fisher's z-transform over a large set of values of the parameters involved.
Rank-Order Tests of Linear Hypotheses
Authors: Bennett B. M. 
Published: December 2018

Summary
This paper considers tests for linear hypotheses using the ranks of independent observations from an unspecified distribution. By means of results on non-linear estimation of the regression vector (3 it is shown that the decomposition of, and tests for the sum of squares of ranks proceeds analogously to the usual analysis of variance model. These results are then applied to the Wilcoxon and Kruskal–Wallis tests and a multiple rank correlation coefficient.
Random Permutations
Authors: Plackett R. L. 
Published: December 2018

Summary
The problem of generating random permutations of the integers 1, 2, …, n arises, for example, when sampling a randomization distribution and when tables of permutations are required for application to experimental design. An algorithm is described which minimizes the amount of randomization necessary to generate a random permutation, although in practice longer but simpler procedures are likely to be preferable. We discuss the probability distributions for the number of digits required by standard methods of generation from a sequence of random digits. Particular attention is given to the asymptotically efficient multistage randomization procedure. We obtain approximate formulae for the mean and variance of the number of digits and compare them with the exact results. An argument of a partly conjectural nature is put forward for the asymptotic normality of this number. The possibility that the permutations have unequal probabilities is briefly considered.
A Central Tolerance Region for the Multivariate Normal Distribution
Authors: John S. 
Published: December 2018

Summary
In a multivariate normal distribution the probability density takes any particular value at all points on the surface of an ellipsoid whose centre is the mean of the distribution. Among such ellipsoids there is one, R, say, that contains 100α per cent of the individuals in the population. The paper deals with the problem of determining from a random sample a region which contains R with prescribed probability β. In the univariate case, R reduces to an interval with the mean as midpoint. Any linear function of variables whose joint distribution is normal has again a normal distribution. Let Ta denote the interval corresponding to R in the case of the linear combination with coefficients vector a. A method of determining from the sample intervals which simultaneously include Ta for all a with probability β is indicated.
Missing Data in Regression Analysis
Authors: Haitovsky Yoel 
Published: December 2018

Summary
Two alternative methods for dealing with the problem of missing observations in regression analysis are investigated. One is to discard all incomplete observations and to apply the ordinary least-squares technique only to the complete observations. The alternative is to compute the covariances between all pairs of variables, each time using only the observations having values of both variables, and to apply these covariances in constructing the system of normal equations. The former is shown to be equivalent to the Fisher–Yates method of assigning “neutral” values to missing entries in experimental design.
The investigation is carried out by means of simulation. Eight sets of regression data were generated, differing from each other with respect to important factors. Various deletion patterns are applied to these regression data. The estimates resulting from applying the two alternative methods to the data with missing entries are compared with the known regression equations. In almost all the cases which were investigated the former method (ordinary least squares applied only to the complete observations) is judged superior. However, when the proportion of incomplete observations is high or when the pattern of the missing entries is highly non-random, it seems plausible that one of the many methods of assigning values to the missing entries should be applied.
Experiments with Mixtures: A Generalization of the Simplex-Lattice Design
Authors: Lambrakis D. P. 
Published: December 2018

Summary
A theory is developed for experiments with mixtures of n “major” components with proportions ci (i = 1,2,..., n), where each component is itself a mixture of several other components with proportions xij(i=1,2,…,n;j=1,2,…,ni). The purpose of this theory is the empirical prediction of the response to any mixture of the n “major” components when the response depends only on the proportions ci and xij, but not on the total amount of the mixture.