bluuebunny/crossref_metadata_2025_split huggingface dataset:
Single Replicate Factorial Experiments in Generalized Cyclic Designs: I. Symmetrical Arrangements
Authors: John J. A. , Dean A. M. 
Published: December 2018

Summary
Single replicate generalized cyclic designs are constructed from a set of generating treatments. This flexible class of designs is used to provide a general method of confounding in symmetrical factorial experiments. It is shown how the confounding scheme can be determined from an examination of the generating treatments.
Equivalence Theorems for Polynomial-Projecting Predictors
Authors: Godolphin E. J. , Harrison P. J. 
Published: December 2018

Summary
Under certain conditions, the predictors of Integrated Moving Average processes, Markov Polynomial processes, Multiple Exponential Smoothing models and Exponentially Weighted Regression models are identical. In this paper, these conditions are determined and some implications and generalizations are examined.
Independent Inter-Departure Times in M/G/1/N Queues
Authors: Daley D. J. , Shanbhag D. N. 
Published: December 2018

Summary
This paper extends the results of Finch (1959) and King (1971) on the stationary departure process of the queueing system M/G/1/N by establishing, among others, the existence of the systems other than M/D/1/1 and M/M/1/∞ with two successive inter-departure times independent.
Errors of Prediction for Markov Chain Models
Authors: Bartholomew D. J. 
Published: December 2018

Summary
When Markov chain models are used for predicting the state distribution the forecasts are liable to error for a variety of reasons. The sources of such error are identified and methods are given for finding the contribution which each source makes to the total error of prediction. In particular it is shown that the error arising from the estimation of the parameters is likely to be of the same order of magnitude as the inherent variation arising from the stochastic assumptions of the model. The theory is first derived for a closed system and then generalized to two kinds of open system.
Estimation of Linear Functional Relationships: Approximate Distributions and Connections with Simultaneous Equations in Econometrics
Authors: Anderson T. W. 
Published: December 2018

Summary
When both variables are subject to error, a straight line may be fitted by minimizing the sum of squared distances of the observed points to the line. Approximate distributions of the slope of this line and of the angle it makes to one axis are given when the errors are normal, uncorrelated, and with equal variances. These distributions and corresponding ones for the line fitted by ordinary least squares are found by making the model equivalent to a model of simultaneous equations in econometrics.
Plausibility Inference
Authors: Barndorff-Nielsen O. 
Published: December 2018

Summary
A scheme for inference—plausibility theory—is proposed. It parallels likelihood theory, the analogue of the likelihood function L(ω) = p(t; ω) being the plausibility function π(ω) = p(t; ω)/supt p(t; ω), but likelihood and plausibility throw light on different aspects of the evidence in the data t. The ordinate test for significance (which rejects for small values of the probability (density) function, of a simple hypothesis), the maximum ordinate estimate (which equals the set of ω's such that p(·; ω) has mode at t), and M-ancillarity are, to some extent in modified form, integrated in plausibility theory. Among the subthemes, particular attention is given to relevant properties of universality (in its origin a preconcept for M-ancillarity), to exponential models, and, naturally, to similarities and contrasts between plausibility inference and likelihood inference. The logic connected with the ordinate test is also attended to.
Approximating the Lower Tail-Areas of the Kolmogorov–Smirnov One-Sample Statistic
Authors: Pelz Wolfgang , Good I. J. 
Published: December 2018

Summary
Various methods for calculating the Kolmogorov–Smirnov one-sample statistic have been developed in the literature. A transformation of an approximation method is here derived and some of its properties discussed. The main value of the new formulae is to obtain more convenient approximations in the lower tail than have been possible using other methods. The relationships between various methods are given, as well as recommendations for each method of a usable range of the independent variable.
Eliminating Singularities of Stein-Type Estimators of Location Vectors
Authors: Berger James O. , Bock M. E. 
Published: December 2018

Summary
In estimating a multivariate location vector in three or more dimensions, it is well known that Stein-type estimators can offer considerable improvement in risk over the best invariant estimator. A common problem arising in the use of such estimators is that simple versions often have a singularity at zero. Methods of eliminating such singularities are discussed in this paper. The resulting estimators are usually considerably better than the uncorrected versions, and yet are still quite simple.
The Aliasing Problem in Differential Equation Estimation
Authors: Robinson P. M. 
Published: December 2018

Summary
This paper is concerned with the estimation of the parameters in a simple open-loop differential equation model. We suggest first some frequency-domain “narrow-band” and “broad-band” estimators that are based on the assumption that the observable input variable has no spectral mass beyond Nyquist frequency. We study the asymptotic biases of these estimators under the contradictory hypothesis that the spectral density of the input is a rational function of frequency. On considering the limiting situation of the sampling interval converging to zero, we derive relatively simple multiplicative correction factors that can be applied to the original estimates, with the objective of reducing the bias.
Bayesian Forecasting
Authors: Harrison P. J. , Stevens C. F. 
Published: December 2018

Summary
This paper describes a Bayesian approach to forecasting. The principles of Bayesian forecasting are discussed and the formal inclusion of “the forecaster” in the forecasting system is emphasized as a major feature. The basic model, the dynamic linear model, is defined together with the Kalman filter recurrence relations and a number of model formulations are given. Multi-process models introduce uncertainty as to the underlying model itself, and this approach is described in a more general fashion than in our 1971 paper. Applications to four series are described in a sister paper. Although the results are far from exhaustive, the authors are convinced of the great benefits which the Bayesian approach offers to forecasters.
On a Test for Normality Based on Sample Entropy
Authors: Prescott P. 
Published: December 2018

Summary
Sensitivity contours are used to examine the effect of outliers on a test of normality based on sample entropy. The contours are compared with those of the Shapiro–Wilk W-test and it is shown that the entropy test is considerably less sensitive to outliers than the W-test. This is illustrated using the results of a confounded 25 factorial experiment.
Parameter Estimation for the Carrier-Borne Epidemic Model
Authors: Saunders Roy , Kryscio Richard J. 
Published: December 2018

Summary
We derive the maximum likelihood estimates (m.l.e.) of the infection and removal rates of the carrier-borne epidemic model when the process has been observed continuously for a fixed or random period of time. For both sampling schemes we derive the distribution of the m.l.e. of the inverse of the removal rate. We also consider the problem of estimating the relative removal rate of the model when the process has been observed continuously for a period of time, but the exact times between events is unknown. In this case, we propose an estimator which is appropriate for populations having a large initial number of susceptibles.
Oscillations in the Finite Random Sequence
Authors: Imhof J. P. 
Published: December 2018

Summary
Oscillations are defined for a random sequence of finite length. The oscillation of maximal amplitude is preceded by oscillations of increasing amplitudes and followed by oscillations of decreasing amplitudes. The joint law of their numbers is determined. There is analogy with known results for upper and lower records. A sampling experiment gives some idea of the behaviour of oscillations in the presence of a trend in mean or in standard deviation.
Bayesian Life Table Analysis
Authors: Cornfield Jerome , Detre Katherine 
Published: December 2018

Summary
The moments of the posterior p.d.f. of the probability of surviving to time t, P(t), are obtained, assuming a time-dependent Poisson process for failures and i.i.d. gamma prior densities for the hazard function. For improper densities the results reduce to the Kaplan–Meier estimate of p(t) and to the Cox result for the comparison of two survival curves, which, because of the use of improper priors, may be inadmissible with respect to mean square error loss. A way of estimating the priors from the data, and hence of obtaining estimates that may be uniformly superior to those of Kaplan–Meier and Cox, is given. The use of a class of more realistic, but still non-parametric, priors is discussed.
Exact and Approximate Maximum Likelihood Estimators for Vector Moving Average Processes
Authors: Osborn Denise R. 
Published: December 2018

Summary
This paper derives the exact likelihood function for the vector moving average process; the method used is a generalization of that adopted by Box and Jenkins (1970, Appendix A7.4) for the univariate process. Tunnicliffe Wilson (1973) has previously considered the estimation of parameters in multivariate time series models, and his procedure for moving averages is shown to be an approximation to maximum likelihood. A procedure for the computation of the exact likelihood function is also suggested.
On Resolving the Controversy in Statistical Inference
Authors: Wilkinson G. N. 
Published: December 2018

Summary
The controversy concerning the fundamental principles of statistics still remains unresolved. It is suggested that one key to resolving the conflict lies in recognizing that inferential probability derived from observational data is inherently noncoherent, in the sense that their inferential implications cannot be represented by a single probability distribution on the parameter space (except in the Objective Bayesian case). More precisely, for a parameter space R 1, the class of all functions of the parameter comprise equivalence classes of invertibly related functions, and to each such class a logically distinct inferential probability distribution pertains. (There is an additional cross-coherence requirement for simultaneous inference.) The non-coherence of these distributions flows from the nonequivalence of the relevant components of the data for each.
Noncoherence is mathematically inherent in confidence and fiducial theory, and provides a basis for reconciling the Fisherian and Neyman–Pearsonian viewpoints. A unified theory of confidence-based inferential probability is presented, and the fundamental incompatibility of this with Subjective Bayesian theory is discussed.
The Distribution of Quadratic Forms in Non-Normal Variables and an Application to the Variance Ratio
Authors: Knuri A. I. , Good I. J. 
Published: December 2018

Summary
Good (1968a, b) using non-rigorous arguments, gave an expression for the characteristic function C.F. (x‘A x, t) of a quadratic form in a non-normal random column vector x whose characteristic function is known, where A is positive semi-definite. A general formula for C.F. (x‘A x, t) is proved here, which coincides with Good's expression when x has a real stable characteristic function. In the general formula, A need not be positive semi-definite and this greater generality is of value for finding the distribution of the ratio of two quadratic forms in non-normal variables. The theory is used for finding approximately the distribution of a ratio of quadratic forms in a three-dimensional random vector x having an even stable distribution with exponent 3/2. The procedure of regarding x as normal, combined with the Cornish–Fisher expansion, would have been far from robust in this example.
Spectral Analysis of Intervals between Events in Stationary Bivariate Point Processes
Authors: Charnock D. M. 
Published: December 2018

Summary
A method is developed for analysing stationary bivariate point processes through their interval properties. The technique is based on representing the intervals as processes in continuous time. Expressions for a cross-covariance function and the corresponding cross-spectrum are given and some examples are considered. We note that use of this technique together with the device of smoothing makes computation of spectral estimates for point processes more efficient.
A Procedure for Estimating Seasonal Moving Average Models Based on Large-Sample Estimation of the Correlogram
Authors: Godolphin E. J. 
Published: December 2018

Summary
In recent years considerable interest has centred on a family of moving average models proposed by Box and Jenkins (1970) for the description of time series which contain a seasonal component. A method is given in the paper for estimating the parameters of the seasonal models based on a principle due to Walker (1961) for the estimation of non-zero members of the autocorrelation function. An illustration of the method is given.
A General Family of Discrete Distributions with Hypergeometric Probabilities
Authors: Tripathi Ram C. , Gurland John 
Published: December 2018

Summary
A three-parameter family of distributions which belongs to Kemp's wide class, and which extends a two-parameter family of Katz, is investigated. Relations involving moments and probabilities are utilized in obtaining minimum χ2 estimators of the parameters. The asymptotic relative efficiency of various estimators is compared and a numerical example given.
Variable Selection in Multivariate Regression : An Application of Simultaneous Test Procedures
Authors: McKay R. J. 
Published: December 2018

Summary
Simultaneous procedures for variable selection in multiple linear regression have recently been given by Aitkin. One of these procedures, proposed for the case when the regression equation is to be used for descriptive purposes, is an application of each of a number of simultaneous procedures concerned with the multivariate general linear model and given by Gabriel with applications in the manova context. The applications of Gabriel's procedures to multivariate linear regression are presented here and illustrated as generalizations of Aitkin's technique.
The Inverse Gaussian Distribution and its Statistical Application—A Review
Authors: Folks J. L. , Chhikara R. S. 
Published: December 2018

Summary
This paper reviews the development of the inverse Gaussian distribution and of statistical methods based upon it from the paper of Schrödinger (1915) to the present (1978). After summarizing the properties of the distribution, the paper presents tests of hypotheses, estimation, confidence intervals, regression and “analysis of variance” based upon the inverse Gaussian. its potential role in reliability work is discussed and work on Bayesian statistics is reviewed briefly. An extensive set of references to the distribution is given.
On the Distribution of Residual Autocorrelations in Box–Jenkins Models
Authors: McLeod A. I. 
Published: December 2018

Summary
The large sample distribution of the residual autocorrelations in the arma model is derived. The main advantage of this derivation over that of Box and Pierce (1970) is that it extends directly to more general situations. Generalizations of the derived distribution are presented for the residual autocorrelations in the multiplicative seasonal arma model and for the autocorrelations of a subseries of the residuals.
Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression
Authors: Wahba Grace 
Published: December 2018

Summary
Spline and generalized spline smoothing is shown to be equivalent to Bayesian estimation with a partially improper prior. This result supports the idea that spline smoothing is a natural solution to the regression problem when one is given a set of regression functions but one also wants to hedge against the possibility that the true model is not exactly in the span of the given regression functions. A natural measure of the deviation of the true model from the span of the regression functions comes out of the spline theory in a natural way. An appropriate value of this measure can be estimated from the data and used to constrain the estimated model to have the estimated deviation. Some convergence results and computational tricks are also discussed.
A Class of Shrinkage Estimators
Authors: Farebrother R. W. 
Published: December 2018

Summary
In this paper we define a class of shrinkage estimators, all of whose members have a mean square error matrix which is less than that of the ordinary least squares estimator by a positive semidefinite matrix if (β-b *)T X T X (β-b *) ≤ σ2. The ridge regression, principal component and minimum conditional mean square error estimators are members of this class.
Two-Way Elimination of Heterogeneity
Authors: Singh M. , Dey A. 
Published: December 2018

Summary
A general method of analysis of non-orthogonal three-way designs (designs eliminating heterogeneity in two directions) is proposed. Analogous to the efficiency-balanced block designs, efficiency-balanced three-way designs are defined. The utility of the proposed method of analysis is demonstrated by giving simplified analyses of known three-way designs.
A Quasi-Bayes Sequential Procedure for Mixtures
Authors: Smith A. F. M. , Makov U. E. 
Published: December 2018

Summary
Coherent Bayes sequential learning and classification procedures are often useless in practice because of ever-increasing computational requirements. On the other hand, computationally feasible procedures may not resemble the coherent solution, nor guarantee consistent learning and classification. In this paper, a particular form of classification problem is considered and a “quasi-Bayes” approximate solution requiring minimal computation is motivated and defined. Convergence properties are established and a numerical illustration provided.
Nearest Neighbour Models in the Analysis of Field Experiments
Authors: Bartlett M. S. 
Published: December 2018

Summary
The method of adjusting plot values by covariance on neighbouring plots in randomized field experiments, suggested by Papadakis in 1937, is re-examined theoretically for both one-dimensional and two-dimensional layouts, making use of Markovian and autonormal models.
The gain in efficiency over orthodox randomized block analysis can be appreciable when the number of treatments is fairly large, and can be increased by iterating the analysis; this also reduces the discrepancy between the apparent accuracy from the residual sum of squares, and the true accuracy of the treatment comparisons after adjustment. Some illustrative examples are included.
Least Squares Approximation of Matrices by Additive and Multiplicative Models
Authors: Gabriel K. R. 
Published: December 2018

Summary
Reduced rank approximation of matrices by Householder–Young methods is shown to be equivalent to fitting of a bilinear (multiplicative) model and to projection onto an optimally chosen subspace. The relation to linear approximation is made evident. Least squares fitting of a mixed linear (additive) and bilinear (multiplicative) model is proved to be a two-stage process: (1) fit the linear part of the model, then take residuals, and (2) fit the bilinear part to the residuals. Extensions of this result are given as well as some results on distributions of residuals and tests against alternatives of given rank. Statistical applications are shown in principal component analysis, in biplot graphical display and in fitting additive or Mandel-type models to two-way tables.
Discrete Time Series Generated by Mixtures Ii: Asymptotic Properties
Authors: Jacobs Patricia A. , Lewis Peter A. W. 
Published: December 2018

Summary
The darma (discrete mixed autoregressive-moving average) processes are a broad but parametrically simple class of models for a stationary sequence of dependent discrete random variables. A darma process is formed as a random linear combination of independent identically distributed discrete random variables. The process is specified by the distribution of the independent variables, which is also the marginal distribution of the random process, and several other chosen parameters which independently determine the covariance structure of the process. In this paper the asymptotic properties of the darma process are studied. Limiting results for estimates of moments, percentiles and quantiles are obtained. Asymptotic properties of the χ2 test for goodness-of-fit for the marginal distribution of the process are also studied.
A Non-Parametric Test for Comparing Two Non-Independent Distributions
Authors: Raviv Alona 
Published: December 2018

Summary
Using a sample from an unknown bivariate distribution, we propose a test for the hypothesis that one marginal distribution is stochastically larger than the other. We show that the test statistic has an asymptotic normal distribution, and that the proposed test is asymptotically non-parametric. This test is compared to the paired t-test for large samples in terms of asymptotic relative efficiency and for samples of size 20 by simulation estimates of size and power. There are important cases in which the power of the proposed test exceeds that of the paired t-test; whereas even under normality its power is near that of the paired t-test.
Some Two-Dimensional Designs Balanced for Nearest Neighbours
Authors: Freeman G. H. 
Published: December 2018

Summary
The construction of row and column designs balanced for nearest neighbours is given, the commonest practical application being to polycross designs for seed production. In some designs all plants may be used either as seed parents or as pollinators, but for others only the interior plants can be seed parents, the outside plants being pollinators only. Some small designs are given, but the construction of others could well require long computer searches. Latin squares of a special type known as complete Latin squares are particularly suitable.
Algorithms to Search for Optimal Row-And-Column Designs
Authors: Jones Byron 
Published: December 2018

Summary
An algorithm is described that searches for the row and column components to form an optimal row-and-column design. It is based on one given previously (Jones, 1976) for block designs. A second algorithm is described for combining the components to form a row-and-column design. Both algorithms are suitable for use on a computer. The optimality criterion used allows treatment contrasts to be weighted. Examples of the use of the algorithms are given and their performance is discussed.
Inference on Symmetric Functions of Exchangeable Populations
Authors: Sugden R. A. 
Published: December 2018

Summary
A model is proposed for inference on symmetric functions of a finite population where the only prior information available is exchangeability of the unknown unit values. It is shown through sufficiency that the labels convey no information.
When the sample size is fixed, the order statistic is complete as well as sufficient so that optimal estimators are symmetric. In particular, the sample mean is the minimum variance unbiased estimator of the population mean, averaging under the model being equivalent to averaging firstly over the sample design and then over all permutations of the units.
A new subjective justification is therefore found for the use in practice of classical formulae based on simple random sampling, but now for any sample design.