bluuebunny/crossref_metadata_2025_split huggingface dataset:
Experiments with Mixtures: An Alternative to the Simplex-Lattice Design
Authors: Lambrakis D. P. 
Published: December 2018

Summary
Scheffé (1958) introduced the simplex-lattice design for experiments with mixtures of q components. The purpose of this design is the empirical prediction of the response to any mixture of the components when the response depends only on the proportions of the components but not on the total amount of the mixture. In this paper an alternative to the simplex-lattice design is developed in which all the features of the design are maintained except that the pure mixtures are replaced by the (q − 1)-nary mixtures.
A Fiducial Argument with Application to Survey Sampling
Authors: Godambe V. P. 
Published: December 2018

Summary
Sprott (1960) proposed certain restrictions on distributions a posteriori in terms of the likelihood function. Hacking (1965) put forward a criterion for irrelevance restricting the choice of the pivots in terms of the likelihoods. This paper presents an extended application of Hacking's criterion to accommodate ancillary statistics. This extension is utilized to obtain the fiducial distribution of the mean of a survey (finite) population based on the given random sample. The fiducial distribution so obtained is inseparably tied to the method of randomization and as such it provides an interpretation of “randomization”. In contrast, as shown by the author (1966a, b, c), the Bayes posterior of the population mean does not depend on “randomization”. This is further discussed in Section 8. An alternative method of obtaining the fiducial distribution via Bayes's theorem is explored in Section 9.
Two Queues in Parallel
Authors: Hunter Jeffrey J. 
Published: December 2018

Summary
A queueing system consisting of two queues, each with single servers (independent negative exponential service time distributions) and correlated bivariate Poisson input, is discussed. The joint stationary probabilities for the respective numbers of customers in the two queues in equilibrium are found in the case where we have finite waiting rooms of different sizes for each individual queue. For the model where the waiting-room capacities are unlimited, we derive a functional relationship for the joint probability generating function of the equilibrium probabilities. A survey of published research on queues in parallel is also presented.
A Bivariate Non-Parametric c-Sample Test
Authors: Mardia K. V. 
Published: December 2018

Summary
A non-parametric test for the bivariate c-sample problem is proposed. The test is an extension of a bivariate two-sample test given by Mardia (1967) and possesses various desirable properties. We derive the asymptotic distribution of this test and obtain the Pitman efficiency of the test relative to Wilks's criterion A for the translation types of alternatives. We give the critical values of the distribution and some approximations. The test is applied to a numerical example.
Durbin's New Multistage Variance Estimator
Authors: Brewer K. R. W. , Hanif M. 
Published: December 2018

Summary
A new variance estimator was suggested implicitly by Durbin (1967), for use in a particular multistage sampling procedure. The suggestion can easily be extended to cover the general case in which selection at the first stage is without replacement (the probabilities of inclusion in sample being arbitrary) and in which unbiased estimators are used at all stages of sampling. As compared with the earlier Durbin multistage variance estimator, the new estimator has this advantage; that the conditional expectation (given any particular first-stage sample selection) of the contribution to the estimate of total variance from the second and lower stages is equal to the conditional contribution from these stages to the total variance itself. As a result of this advantage, the new estimator will nearly always be more efficient than the old. The results of a numerical example, however, suggest that the gains in efficiency are unlikely to assume large proportions, at least where the Horvitz–Thompson estimator of total is used. Formulae are also given for use with des Raj, Murthy, and Rao, Hartley and Cochran estimators.
Goodness of Fit of a Discriminant Function from the Vector Space of Dummy Variables
Authors: Kshirsagar A. M. 
Published: December 2018

Summary
The problem of discrimination among several groups can be looked upon as the problem of “association” between the vector of variables under consideration and a vector of “dummy” variables representing the contrasts among the groups. In certain situations, observations on one or more of these dummy variables are explicitly available and tests have been derived by Bartlett and Williams, for the adequacy of a set of assigned discriminant functions from among these dummy variables. In this paper, the statistical distributions of these test criteria are derived analytically, assuming the null hypothesis to be true.
On a Statistic for Rank Analysis of Variance
Authors: Peritz E. 
Published: December 2018

Summary
Gabriel and Sen (1968) have presented a family of statistics for univariate and multivariate one-way rank analysis of variance. The present note considers the univariate Gabriel–Sen statistic of the Mann–Whitney family. An elementary derivation of its asymptotic null distribution is pointed out. It is shown that simultaneous testing procedures (s.t.p.) based on the above statistic are asymptotically coherent.
Nearest-Neighbour Systems and the Auto-Logistic Model for Binary Data
Authors: Besag J. E. 
Published: December 2018

Summary
Bartlett (1966) and Whittle (1963), respectively, have proposed alternative, non-equivalent definitions of nearest-neighbour systems. The former, conditional probability definition, whilst the more intuitively attractive, presents several basic problems, not least in the identification of available models. In this paper, conditional probability nearest-neighbour systems for interacting random variables on a two-dimensional rectangular lattice are examined. It is shown that, in the case of 0, 1 variables and a homogeneous system, the only possibility is a logistic-type model but in which the explanatory variables at a point are the surrounding array variables themselves. A spatial–temporal approach leading to the same model is also suggested. The final section deals with linear nearest-neighbour systems, especially for continuous variables. The results of the paper may easily be extended to three or more dimensions.
Results in the Theory and Construction of D-Optimum Experimental Designs
Authors: Wynn Henry P. 
Published: December 2018

Summary
A method of generating D-optimum design measures as defined by Kiefer and Wolfowitz is briefly described. The relevant theorem is generalized to yield a method of generating D8-optimum design measures for a specific subset of s of the parameters in the regression model. The one parameter case is described in further detail. An analogous theorem for discrete designs with a fixed number of points is proved giving a lower bound to the optimality achievable with such designs.
A final section is devoted to the loss in efficiency entailed by almost equal replication of a given discrete design. The discussion is extended to the one-dimensional polynomial model and the optimality of the replication is conjectured for the general case and proved for the quadratic case.
A Combinatorial Proof of the Distribution of the Time to First Emptiness of an Infinite Dam with Markovian Inputs
Authors: Matthews Jane P. 
Published: December 2018

Summary
In this note the combinatorial lemma of Mott (1963) for an infinite dam with independent inputs is extended to obtain the distribution of the time to first emptiness of an infinite dam with Markov dependent integral inputs subject to steady unit demand. A new expression for this distribution is obtained in terms of the trace of the matrix probability generating function of the inputs. The result is shown to agree with the expressions given by Gani (1969) and Brockwell and Gani (1970), in terms of the principal eigenvalue of this matrix.
A Model for Studying Robustness of Estimators and Informativeness of Labels in Sampling with Varying Probabilities
Authors: Cassel Claes-Magnus , Särndal Carl-Erik 
Published: December 2018

Summary
This paper presents a model for investigating how information contained in the labels of a finite population may be utilized in order to reduce variance when sampling from a finite population with varying probabilities. The model assumes a population of N values of a characteristic X given as Xi = Yi + Zi (i = 1, …, N), where the mean of X is to be estimated. Here Yi is a systematic component in the sense that its relation to the label i is a priori known, or intelligently guessed at, while Zi is an error component. In the with-replacement case, a sample of labels is selected with possibly unequal probabilities pi,(i = 1, …, N) attached to the various labels in each of the n draws. Assuming that N is reasonably large, the variance of the usual estimator is studied under various assumptions about the shape of the continuous distribution approximating the Y-distribution (e.g. gamma, Pareto, Weibull shapes), various assumptions about the influence of the error component Z, and different designs for distributing the probabilities Pi among the N labels.
An Asymptotically Efficient, Sequential Equivalent of the t-Test
Authors: Weiss L. , Wolfowitz J. 
Published: December 2018

Summary
Let X1, X2, …, be independent, normally distributed chance variables, each with mean μ and variance σ2, both unknown to the statistician. Let it be required to test sequentially the hypothesis that (make a decision between) μ = μ1 against the alternative μ = μ2, μ1 &lt; μ2. When the sample size is fixed the Student t-test is usually used for this purpose. In the present paper we give a sequential procedure for performing this test which is consistent and asymptotically efficient as (μ2 – μ1) approaches zero.
Central Limit Analogues for Markov Population Processes
Authors: McNeil Donald R. , Schach Siegfried 
Published: December 2018

Summary
It is shown in this paper that several birth-death-type models (univariate as well as multivariate) can be approximated by Ornstein–Uhlenbeck processes as certain parameters become large. Such approximations are valuable whenever the Kolmogorov differential equation cannot be solved in closed form.
Lagged Regression with Unknown Lags
Authors: Hannan E. J. , Robinson P. M. 
Published: December 2018

Summary
The problem considered is that of determining the parameters in a lagged regression of one stationary time series on another when the lag is unknown and is not an integral multiple of the time interval between observations. The residual in the regression is also taken to be a stationary time series. The method of estimation is based on the maximization with respect to the lag of a form of autocorrelation between the two series. However, the autocorrelation is defined via the Fourier transformed data which enables non-integral lags to be considered and an optimal weighting of frequencies to be introduced. The estimation procedure's validity depends upon the satisfaction of an identification (aliasing) condition. Limit theorems are proved for the estimates and the method is extended to multivariate regressions. The method is applied to some economic and to some oceanographic data.
Bayesian Spline Regression when the Number of Knots is Unknown
Authors: Halpern Elkan F. 
Published: December 2018

Summary
The problem of selecting the model and coefficients for a spline regression curve with normal errors is considered. The locations of all possible knots are assumed to be known; which subset of these is the set of actual knots is unknown. Each subset forms a model.
Priors of the form of a marginal distribution on the index of the model and a conditional distribution for each model on the coefficients and variance are allowed. The posterior distribution is explicitly derived for natural conjugate and vague priors.
The optimal predictor is derived for a loss function which is a generalization of that appearing in Lindley (1968). All that is required of the opinion is the marginal distribution for the model and the mean vector for the coefficients.
Some Monotonicity Theorems for χ2, F and T Distributions with Applications
Authors: Ghosh B. K. 
Published: December 2018

Summary
The probability that a non-central χ2, F or t variable exceeds c is a function of c, the degrees of freedom and the non-centrality parameter. The behaviour of these probabilities as functions of the degrees of freedom is investigated when c and the non-centrality parameters are fixed. It is also shown that, when c refers to the 100α% point of the corresponding central distribution, the probabilities are monotone in the degrees of freedom. Some allied results and possible applications are discussed.
Asymptotic Properties of the Wiener–Kolmogorov Predictor. I
Authors: Bhansali R. J. 
Published: December 2018

Summary
“Windowed” estimates of the spectral density function are used to carry out the factorization of the sample spectral density function and hence estimate the Wiener-Kolmogorov prediction coefficients. Expressions are derived for the asymptotic mean and variance of all the statistics necessary to estimate the predictor. The covariances and asymptotic normality of these estimates are also investigated. In particular, an expression for the asymptotic mean-square error or predicting one step, and more than one step, ahead is given.
Ridge-Type Estimators for Regression Analysis
Authors: Goldstein M. , Smith A. F. M. 
Published: December 2018

Summary
An examination of the mean-square error properties of a class of shrinkage estimators for the normal regression model leads to a new derivation of the Hoerl–Kennard (1970) Ridge estimator and its generalization. Comparison is made with the James–Stein estimator, and with the generalized-inverse estimator proposed by Marquardt (1970). A Bayesian approach is noted.
Generalized Linear Models Specified in Terms of Constraints
Authors: Wedderburn R. W. M. 
Published: December 2018

Summary
A modification of the method of Nelder and Wedderburn (1972) is given for fitting models with the same error distributions as discussed there but with the systematic part of the models specified in terms of constraints. It is possible to fit these by the method described by Nelder and Wedderburn using iterative weighted regression, but it turns out to be simpler to replace each regression calculation of that method by another one with the property that the fitted values of one regression calculation are the residuals of the other and vice versa. The method is applied to testing for marginal homogeneity in contingency tables.
Minimum Full Sequences of 2N–MResolution Iii Plans
Authors: Pajak Thomas F. , Addelman Sidney 
Published: December 2018

Summary
A criterion is developed for determining the minimum number of stages required in order to obtain a sequence of 2n–m Resolution III plans which permits the estimation of all main and two-factor interaction effects. In order to achieve this minimum, equivalent families of defining contrasts are utilized to generate the treatment combinations which constitute each stage of the sequence.
The Influence of Reference Values and Estimated Variance on the Arl of Cusum Tests
Authors: Bagshaw Michael , Johnson Richard A. 
Published: December 2018

Summary
An approximation, based on the Wiener process, is applied to Page's cusum statistic. Based on the average run length, the optimal reference value is determined analytically and shown to agree with results from studies using numerically determined run lengths. Next, we study the effect of using an estimate for variance and how this interacts with the choice of a reference value.
Comments and Queries on Patterns of Efficiency-Balanced Designs
Authors: Puri P. D. , Nigam A. K. 
Published: December 2018

Summary
By an efficiency-balanced design is meant one in which all contrasts are estimated with equal efficiency. A sufficient condition is found in the off-diagonal elements of the matrix, nk−ş n', where n is the incidence matrix and k the vector of block sizes.
On Multi-Server Stochastic Scheduling
Authors: Glazebrook K. D. , Nash P. 
Published: December 2018

Summary
Several identical components are available for use in a piece of machinery. The number of components needed to operate the machine is a function of time, probably constant, and the lifetime of each component is described by a probability distribution. After a certain number of component failures, there will not be enough components remaining to operate the machine. The problem is considered of how to use the available components to postpone this occurrence for as long as possible. The Lady's Nylon Stocking Problem of Cox is solved for certain classes of lifetime distribution.
A Bayesian Interpretation of Pretesting
Authors: Leamer Edward E. , Chamberlain Gary 
Published: December 2018

Summary
The usual posterior mean or mode of a k-dimensional regression coefficient is shown to be (1) a weighted average of 2k constrained least-squares points, (2) a weighted average of k + 1 “ideal” points and (3) a weighted average of k + 1 principal component points. These results are used to interpret pretesting procedures which select a constrained least-squares estimate. For special classes of priors a somewhat distorted Bayesian analysis leads to a posterior measure of location that is an F-weighted average of restricted and unrestricted least squares. A spherical prior can be associated with methods that drop principal components. Multilevel testing is shown to imply a non-traditional prior.
The Subset Problem in Multivariate Analysis of Variance
Authors: Hawkins Douglas M. 
Published: December 2018

Summary
As with most other multivariate techniques, methods such as discriminant analysis which depend on multivariate analysis of variance are affected adversely by the inclusion of irrelevant variables. This paper discusses the problem of finding a parsimonious subset of variables that is essentially as good as the full set. As a result of the close computational similarity to multiple regression, a stepwise procedure, and a best subset method are derived from their regression counterparts. The inferential aspects of the stepwise procedure are also investigated.
Non-Parametric Estimation of a Smooth Regression Function
Authors: Clark R. M. 
Published: December 2018

Summary
This paper presents a new family of non-parametric estimators of a smooth regression function, which are shown to have theoretical advantages in small samples over some alternative estimators. The new estimator has practical computational advantages over spline functions, while its smoothing properties are very close to the optimal smoothing properties of cubic splines. A simulation experiment demonstrates the remarkable success of the cross-validation technique as a means of determining the appropriate degree of smoothing.
Spearman's Footrule as a Measure of Disarray
Authors: Diaconis Persi , Graham R. L. 
Published: December 2018

Summary
Spearman's measure of disarray D is the sum of the absolute values of the difference between the ranks. We treat D as a metric on the set of permutations. The limiting mean, variance and normality are established. D is shown to be related to the metric I arising from Kendall's τ through the combinatorial inequality I ≤ D ≤ 2I.
A Note on Infinitely Divisible Point Processes
Authors: Shanbhag D. N. , Westcott M. 
Published: December 2018

Summary
In the discussion of Cliff and Ord (1975), Westcott mentioned the problem of determining those point processes which are both doubly stochastic Poisson processes and Poisson cluster processes—the dual nature is of interest in model interpretation since the underlying mechanisms are radically different. This was related to the question of which doubly stochastic Poisson processes are infinitely divisible, and it was conjectured that this occurs if and only if the random rate process is infinitely divisible. The object of this note is to mention three relevant results.
Distributional Expansions for Canonical Correlations from Contingency Tables
Authors: O'Neill M. E. 
Published: December 2018

Summary
The asymptotic distribution of the canonical correlations from contingency tables was investigated by the author (1978) for a general theoretical correlation structure. In this paper, the structure examined is one in which all theoretical, non-zero correlations are different. For the observed canonical correlations corresponding to non-zeros, an analytic expansion is obtained enabling not only the asymptotic distributions to be obtained, but also a correction for “bias”. A condition is found for determining when the sum of the canonical components corresponding to zero correlations is distributed as χ2.
An Optimal Strategy in Multi-Server Stochastic Scheduling
Authors: Weber Richard R. , Nash Peter 
Published: December 2018

Summary
Identical components are available for use in a piece of machinery. The number of components needed to operate the machine is a function of time and the lifetime of each component is described by a known probability distribution. Once a certain number of components have failed there will not be enough left to operate the machine. We find a strategy which for certain lifetime distributions delays this occurrence for as long as possible.
A Unified Derivation of the Asymptotic Distributions of Goodness-Of-Fit Statistics for Autoregressive Time-Series Models
Authors: Hosking J. R. M. 
Published: December 2018

Summary
The portmanteau and Quenouille goodness-of-fit tests for an ar(p) model are derived as likelihood-ratio tests against particular alternative hypotheses, and their asymptotic distributions are thereby obtained.
On a Model for Concordance between Judges
Authors: Feigin Paul D. , Cohen Ayala 
Published: December 2018

Summary
When a group of judges rank a collection of objects one might be interested in two questions : (i) What is the “true” or underlying order of the objects? and (ii) How homogeneously do the judges act? In this paper we investigate the ramifications, with respect to these questions, of a model originally proposed by Mallows (1957). It is shown that the model fits well to an empirical data set.
The Estimation of an Autocorrelation Parameter of a Gaussian Vector Process
Authors: McDunnough Philip 
Published: December 2018

Summary
A procedure based on differences is used to yield an estimator of an unknown parameter occurring in the autocorrelation structure of a stationary Gaussian vector process. Various properties of the estimator including its existence, consistency and asymptotic normality are shown. Necessary and sufficient conditions are given for the estimator to be efficient.
Maximum Likelihood Estimation of a Linear Structural Relationship with Replication
Authors: Chan Lai K. , Mak Tak K. 
Published: December 2018

Summary
Maximum likelihood estimation of the parameters of a linear structural relationship when repeated observations are available is considered. The maximum likelihood estimate of the slope parameter is found to be a root of a fourth-degree polynomial and to be consistent as the number of replicates increases. The asymptotic variances and covariances of the estimates of the parameters are obtained through simplified formulae.
Edgeworth and Saddle-Point Approximations with Statistical Applications
Authors: Barndorff-Nielsen O. , Cox D. R. 
Published: December 2018

Summary
A simple exposition is given of Edgeworth and saddle-point approximations for some univariate, multivariate and conditional distributions. The application of these approximations to some problems of conditional statistical inference within the exponential family is illustrated. Examples connected with the time-dependent Poisson process, the von Mises distribution and with bioassay are among those studied in a little detail. Some general results are derived about conditional likelihoods and about the distribution of the maximum likelihood ratio test statistic. An appendix discusses regularity conditions.