bluuebunny/crossref_metadata_2025_split huggingface dataset:
Interactions in Multi-Factor Contingency Tables
Authors: Darroch J. N. 
Published: December 2018

SUMMARY
Interactions in contingency tables are compared with interactions in the analysis of variance. The comparison leads to a new formulation of the hypothesis of no second-order interaction in three-way contingency tables, to an explanation of the paradoxes associated with this hypothesis and to a comparatively simple method of constructing its likelihood-ratio test statistic. The extensions to higher-order interactions are merely outlined as they are not likely to be of practical interest.
A Simple Randomization Procedure
Authors: Sandelius Martin 
Published: December 2018

SUMMARY
The paper describes a randomization procedure consisting in distributing a deck of cards into 10 decks using random decimal digits and repeating this step with each deck consisting of three or more cards. One random digit is used for randomizing a deck of two cards. This procedure, which is essentially a particular case of a general procedure described by Rao (1961), is called the multistage randomization procedure, or MRP. Some applications are described. A recursive formula is given for the expected number of random digits required by MRP for the randomization of n symbols. A measure of the efficiency of a randomization procedure is presented. The efficiency of MRP is compared with the efficiencies of two other randomization procedures, and it is proved that MRP has an asymptotic efficiency of 100 per cent.
A Minimax-Regret Procedure for Choosing between Two Populations Using Sequential Sampling
Authors: Johnson N. L. , Maurice Rita J. 
Published: December 2018

SUMMARY
In this paper are considered sequential sampling procedures for two normal populations when it is required to select the one with the larger mean. The sequential probability ratio procedure is derived which minimizes the maximum regret (excess of expected loss over minimum possible expected loss) resulting from ignorance of the population means. The expected loss of the resulting sampling and selection procedure is compared with the expected loss when the procedure which minimizes the maximum expected loss is used.
Some Numerical Results for the Queueing System D/EK/1
Authors: Pike M. C. 
Published: December 2018

SUMMARY
Numerical, as opposed to Monte Carlo, methods have been used to study the appointment schemes recommended by Bailey (1955) to equalize the average waiting-times of successive customers in the finite queue. Results are presented to illustrate the exact nature of Bailey's proposed scheme and a simple method is given for obtaining approximate values of mean waiting-times and total mean idle-time (of the server). The roots of the integral equation describing the equilibrium distribution of D/Ek/1 are given for k = 1(1) 5 and the traffic intensity p = ***·1(***·05) ***·8(***·01) ***·99; and the mean waiting-times are given for the same range of k and ρ.
Estimation of the Spectral Density Function in the Presence of Harmonic Components
Authors: Priestley M. B. 
Published: December 2018

Summary
Consider a stationary process of the form Xt = Yt + Zt, where Yt is a linear process with a continuous spectrum, and Zt is a finite sum of harmonic components. We discuss two methods of estimating the spectral density function of Yt. In one method we first estimate the autocovariance function of Yt by “correcting” the sample autocovariance function of Xt, and then form the usual “smoothed” Fourier transform. In the other approach, we estimate the spectral density function directly from the autocovariance function of Xt by using the “double weight function” technique.
Mixture Designs for Four Factors
Authors: Draper N. R. , Lawrence W. E. 
Published: December 2018

Summary
Scheffé, in two recent papers (1958, 1963), has given designs for experimenting with mixtures. The basis of these designs is the choice of symmetrical arrangements of points in the factor space and the fitting of carefully chosen models which have exactly as many coefficients as there are data points. The designs are such that some of the experiments do not contain any of one or more ingredients of the mixture. This may or may not be a disadvantage depending on the problem involved. Here an alternative form of design selection is made for the case of mixtures of four factors. It extends the method used in the three-factor case in an earlier paper (Draper and Lawrence, 1965b). This involves the premise that, in the absence of specialist knowledge about the form of the true response function, it is desired to fit a response surface equation of first or second order over the factor space of possible mixtures, and experimental runs are needed which, in a certain sense, ensure the best surface fit possible. The principles used in the choice of appropriate designs will be those originally introduced by Box and Draper (1959).
On the Waiting-Time Distribution for Queues in Series
Authors: Loynes R. M. 
Published: December 2018

Summary
Suppose that customers leaving a queue M/E 2/1 immediately join another single-server queue in which the service-time is negative exponential: it will be shown that in equilibrium (if it is possible) the characteristic function of the waiting-time in the second queue is not meromorphic. This is somewhat surprising, and disagrees with a result of Ghosal (1962). If the first queue is of the type E 2/M/1 a similar though weaker result is obtained.
On Simple Rules for the Compound Decision Problem
Authors: Samuel Ester 
Published: December 2018

Summary
The general non-sequential and sequential compound decision problem is considered. A rule is simple if it uses the ith observation only, in order to make the ith decision. It is shown that simple rules, the components of which are Bayes rules for the component problem, are Bayes rules also for the compound problem, and hence, under certain regularity conditions, are admissible compound rules. Nevertheless, a property (A), usually aimed at in the compound situation, cannot be achieved by any simple rule, except in trivial cases.
Sequential Compound Rules for the Finite Decision Problem
Authors: Samuel Ester 
Published: December 2018

Summary
Asymptotically optimal rules are obtained for the sequential compound decision problem, where the component problem involves a finite parameter space and a finite action space. It is shown that under some regularity conditions the rule, which at each stage is a Bayes rule with respect to an estimate of the empirical distribution of the previous parameters, is asymptotically optimal. In the general situation, a randomized version of this rule is asymptotically optimal. Convergence of the compound risks and of the corresponding losses are considered.
A Generalized Least-Squares Approach to Linear Functional Relationships
Authors: Sprent P. 
Published: December 2018

Summary
A linear functional relationship between mathematical variables is postulated. The problem considered is the estimation of this relationship given observed random variate values, various assumptions being made about the distribution of the departures of these from the corresponding mathematical variable values. The least-squares principle is generalized to deal with cases in which these departures are correlated. The bivariate case is considered in detail. Extension to p variates involves no new principle if only a single linear relationship is postulated. A simple application in growth studies is discussed.
Locally Unbiased Type M Test
Authors: Krishnan Marakatha 
Published: December 2018

Summary
In certain tests of hypotheses concerning more than one parameter, it is found that the criterion of unbiasedness cannot be satisfied. In such situations, it is proposed to make the test locally unbiased in a modified sense, termed Type M. Here the power surface in the parametric space does not always lie above the level of significance of the test. However, the mean value of the power, in a small neighbourhood of the null point, exceeds the significance level. This paper demonstrates that the uniformly most powerful unbiased (UMPU) test (based on the sample sum of squares) for a normal variance (Neyman and Pearson, 1936; Rao, 1952; Ramachandran, 1958) is Type M unbiased against the wider class of alternatives permitting the means of the observations to differ, and similarly that the UMPU test (based on the sample variance ratio) for a population variance ratio is Type M unbiased against the same widened class of alternatives.
The Almost Full Dam with Poisson Input : Further Results
Authors: Hasofer A. M. 
Published: December 2018

Summary
The dam model investigated has infinite depth, unit release per unit time, and inputs which form a compound Poisson process.
The time-dependent content distribution for arbitrary initial content is obtained explicitly by a direct method and its asymptotic properties are investigated. The distribution of the time to first overflow as well as the probability of no overflow are also obtained explicitly by a similar method.
The Behaviour of the Variance Function of the Difference between Two Estimated Responses
Authors: Herzberg Agnes M. 
Published: December 2018

Summary
In this paper the variance function of the difference between the estimated responses at any two points in the factor space is developed. In particular, the variance function is considered when the design used is rotatable. The variance function in this situation is a function of the distances of the points from the origin of the design and the angle subtending the points at the origin. Variance functions for first-order and second-order rotatable designs are discussed in detail when the two points are equidistant from the origin of the design. Examples of the variance function for a rotatable and a non-rotatable design in two dimensions are given.
Estimating the Covariance and Spectral Density Functions from a Clipped Stationary Time Series
Authors: McNeil D. R. 
Published: December 2018

Summary
When estimating the covariance functions of a stationary time series from a digitalized record, adjustments to the estimates must be made to correct for the bias caused by digitalizing. In this paper we investigate a method which provides consistent estimates of the covariance and the spectral density functions, and discuss their asymptotic efficiencies.
A Non-Parametric Test for the Bivariate Two-Sample Location Problem
Authors: Mardia K. V. 
Published: December 2018

Summary
An unconditional non-parametric test for the bivariate two-sample problem is proposed. The test is shown to possess various desirable properties. We give critical values of the distribution, some approximations and its asymptotic distribution. For the shift type of alternative hypotheses, we show here that U is distributed asymptotically as a non-central chi-square. We have derived its Pitman's asymptotic efficiency relative to Hotelling's T 2 for these alternatives and shown that in the normal case the ARE is ¼π. Suitable examples are constructed to show that the ARE can approach zero and infinity. An extension to the multivariate multi-sample problem is also indicated.
Methods of Estimation Involving Discounting
Authors: Gilchrist W. G. 
Published: December 2018

Summary
In the estimation of the parameters in time series models arising in economic and business situations, it is often of value to introduce some method of discounting which produces updated estimators that give more weight to recent data than to that arising in the distant past. The simplest methods of introducing such discounting are to modify the traditional methods of estimation. Such modifications are discussed for the methods of moments, least squares and maximum likelihood. The final section discusses criteria upon which such techniques can be evaluated.
A Change-Over Design for Testing a Treatment Factor at Four Equally Spaced Levels
Authors: Berenblut I. I. 
Published: December 2018

Summary
A new design for testing a quantitative factor at four equally spaced levels is presented. This design is suitable for quick analysis when the presence of first residual effects can be adequately accounted for by a single (linear) degree of freedom. The calculation for testing this assumption and the analysis in the general case are given.
On the Economic Choice of Experiment Sizes for Decision Regarding Certain Linear Combinations
Authors: Ericson W. A. 
Published: December 2018

Summary
The author (1965) has presented an algorithm for choosing the sample sizes, ni (i = 1, …, k), to be selected from each of k independent normal data-generating processes having unknown means, μi, in order to minimize the posterior variance of an arbitrary given linear combination of these means subject to a budget constraint. The joint prior was taken to be a general k-dimensional normal distribution. In the present paper it is shown how, using this algorithm and for a wide class of loss functions, the optimal experimental design (choice of n1, …, nk) can be reduced to a univariate minimization problem. Several specific loss functions are considered as examples which provide generalization of decision models given by Raiffa and Schlaifer (1961), as well as a generalization of the earlier work of Grundy et al. (1956).
A Note on the Efficiency of Least-Squares Estimates
Authors: Cox D. R. , Hinkley D. V. 
Published: December 2018

Summary
A linear model is considered in which errors are independent and identically distributed with zero mean. If the error distribution is specified, except possibly for unknown parameters, the asymptotic efficiency of least-squares estimates relative to maximum-likelihood estimates can be found. For regression parameters orthogonal to the general mean the asymptotic efficiency, which is independent of the design matrix, is calculated explicitly for an Edgeworth series, for a Pearson Type VII distribution and for a log gamma distribution.
The Occurrence of Replications in Optimal Designs of Experiments to Estimate Parameters in Non-Linear Models
Authors: Box M. J. 
Published: December 2018

Summary
The occurrence of replications in optimal designs obtained by computer search is demonstrated for three non-linear estimation problems arising from the determination of chemical reaction rates. A theory is developed showing that some replicated designs are indeed optimal, whilst the rest, which have not been proved non-optimal, are certainly very good designs. Finally, recommendations are made as to the manner in which such experimental design problems might be attempted.
The Asymptotic Powers of Multivariate Tests with Grouped Data
Authors: McNeil D. R. 
Published: December 2018

Summary
In many situations (see, for example, Bennett, 1962), random variables which may be assumed to have a multivariate normal distribution cannot be measured exactly, but are each given one of a discrete number (usually two) of scores. One is therefore concerned with the problem of making inferences about the parameters of a multivariate normal distribution when the data are grouped. In this paper we consider the problem of testing the hypothesis that the mean vector is zero, and we will compare the asymptotic powers of certain tests.
Models for the Response of a Mixture
Authors: Becker N. G. 
Published: December 2018

Summary
Care needs to be exercised in the choice of model for a mixture system. The polynomial model, for example, cannot satisfactorily account for components which are inert or have additive effects and its coefficients lose their interpretative value when the variables are the proportions of components in the mixture. This paper proposes models constructed from functions homogeneous of degree one which overcome these difficulties, yet leave a wide choice of models.
A Unified Approach for Constructing a Useful Class of Non-Orthogonal Main Effect Plans in Kn Factorials
Authors: Raktoe B. L. , Federer W. T. 
Published: December 2018

Summary
This paper presents a unified approach for constructing main effect plans in any kn factorial, where the k levels are equally spaced. The method consists of forming kn/2 pairs (when k is even) or (kn − 1)/2 pairs (when k is odd) of treatment combinations with the property that differences within pairs are clear of “even” effects and sums are clear of “odd” effects. Selecting kn/2 pairs (when k is even) or (kn − n + 2)/2 pairs (when k is odd) of treatment combinations in a prescribed manner lead to main effect plans such that “even” main effects are clear of “odd” main effects. General formulae of information matrices are presented for the 2n and 3n series.
Estimation of Parameters of a Finite Mixture of Distributions
Authors: Kabir A. B. M. Lutful 
Published: December 2018

Summary
This paper is concerned with the estimation of the parameters of a finite mixture of distributions. The components of the mixture are assumed to belong to a subset of the exponential family of distributions. A procedure for estimation has been developed and the resulting estimators are shown to be consistent and asymptotically normally distributed. Finally, as applications, mixtures of two binomial and two exponential distributions have been considered.
Note on Discordant Observations
Authors: Hartigan J. A. 
Published: December 2018

Summary
Given a set of observations x1, …, x n, a Bayes measure of discordance of an observation x is defined to be the distance between the posterior distributions of a parameter, in the presence or absence of x. A measure of dissimilarity between two observations is also proposed. For large numbers of observations, these two measures may be approximated by simple functions of the log likelihood, thereby avoiding dependence on prior distributions. The theory is applied to data in which 13 judges ranked 20 mothers; each judge is supposed to give an independent observation on the mothers, with the analysis showing which judges are discordant from the rest and which judges are similar to each other.
On a Distribution Associated with Certain Stochastic Processes
Authors: Kemp Adrienne W. , Kemp C. D. 
Published: December 2018

Summary
The distribution discussed is (a) the total number of games lost by the ruined gambler starting with a monetary units against an infinitely rich adversary in the classical ruin problem; (b) the total size of an epidemic in an infinite population starting with a cases and with constant probabilities of infection and recovery; (c) the number of customers served in a busy period (starting with a customers) of the queue M/M/1. These derivations, the relationships between them and various properties of the distribution are discussed.
An Extension of Quenouille's Test for the Compatibility of Correlation Structures in Time Series
Authors: Rosenhead Jonathan 
Published: December 2018

Summary
Quenouille's test compares under stated assumptions the correlation structures of two lengths of time series to see if they are compatible. A test is here derived to compare any number of lengths of time series. As in Quenouille's test, the derivation depends on assumed or fitted values of autoregression coefficients; the test is shown to be insensitive to errors in these values.
Foundations for the Theory of Least Squares
Authors: Hill B. M. 
Published: December 2018

Summary
The Bayesian theory of least squares is founded upon a weaker and more tangible form of prior knowledge than the conventional assumption of normality. The underlying assumption is a form of conditional uniformity on spheres for the “actual errors” in the experiment. This provides a unified theory appropriate for randomization models in the analysis of variance as well as for classical least-squares analysis.
Experiments with Mixtures: Estimated Regression Function of the Multiple-Lattice Design
Authors: Lambrakis D. P. 
Published: December 2018

Summary
Lambrakis (1968) introduced the multiple-lattice design for experiments with mixtures as a generalization of the simplex-lattice design introduced by Scheffé (1958), and derived the estimating regression function of the double-lattice design. In this paper an expression due to Savage (see Kiefer, 1961, footnote 6), which generates orthogonal polynomials on the points of a simplex-lattice, is used to derive the estimated regression function of any multiple-lattice design.
Compound Decisions and Empirical Bayes
Authors: Copas J. B. 
Published: December 2018

Summary
The analysis of a sequence of decision problems of identical structure is considered, and the similarities and differences between the compound decision and empirical Bayes approaches explored. The paper includes a brief review of the literature and examines the criteria which have been used in comparing compound decision and empirical Bayes procedures with conventional methods. The performance of one of these procedures is examined in detail, and the previously accepted view that the compound decision approach is appropriate for situations outside those covered by empirical Bayes is questioned.
On Partitioning χ2 and Detecting Partial Association in Three-Way Contingency Tables
Authors: Goodman Leo A. 
Published: December 2018

Summary
This paper presents a method of partitioning a χ2 statistic for the I × J × K contingency table (viz. the χ2 statistic that is based upon the likelihood-ratio criterion for testing the null hypothesis that the three variables pertaining to the three-way table are mutually independent) into additive components that can be used to test (1) the null hypothesis of zero three-factor interaction, (2) the null hypothesis that the partial association between two of the variables in the three-way table is zero, and (3) some null hypotheses concerning the two-way marginal distributions. This paper also discusses the estimation of the degree of partial association between two of the variables in the I × J × K table both in the case where the observed row and column marginals in each of the K different I × J tables (which form the I × J × K table) are considered given, and also in the case where these marginals are not fixed. Both the conditional maximum-likelihood estimator (given the observed row and column marginals in the K different I × J tables) and the unconditional maximum-likelihood estimator are presented, and for the special case where I = J = 2 various approximations to these estimators are compared.
Multi-Stage Interval Estimations of the Largest Mean of k Normal Populations
Authors: Tong Yung Liang 
Published: December 2018

Summary
We have k normal populations (k ⩾ 1) with means θ1, θ2, …, θk and a common unknown variance σ2. A fixed-width confidence interval for θ*=max⁡1≤i≤k θi is desired so that the coverage probability is at least γ (preassigned) for every θ = (θ1, θ2, …, θk) and σ2 &gt; 0. A class of multistage procedures is considered for the solution of this problem. It is shown that at least for k ≤ 2, the efficiencies of those procedures are always less than one.
A Simple Problem with Strikingly Different Frequentist and Bayesian Solutions
Authors: Chambers M. L. 
Published: December 2018

Summary
Suppose that equal-sized samples are drawn from two normal populations which have unknown means but known and equal standard deviations. Then the paper considers the problem of making probabilistic statements about whether both population means exceed some lower bound. It seems natural to the author to expect procedures for computing this bound to have the property that the bound increases monotonically with the sample means observed. The paper, however, shows that whilst this is true of Bayesian procedures, it is, surprisingly, in general untrue of frequentist procedures.
Error Analysis by Replaced Samples
Authors: Hartigan J. A. 
Published: December 2018

Summary
For normal observations {Xi, j = 1, …, N}, certain weighted sums Yi, are used to draw inferences about the sum Y of a further N observations. The same family of weights {Wij} are applied in error analysis of general computations t on general samples x1, …, xN, with approximate validity in a wide range of situations.