bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Mean and Variance of Watson's Distribution
Authors: Dent Warren T. , Broffitt James D. 
Published: December 2018

Summary
Watson's distribution is the distribution of the ratio of two linear combinations of independent x22 variables (the denominator being positive). Such ratios arise, for example, in the consideration of, or in approximations to, certain serial correlation coefficients. The moments of these ratios are known only in specialized cases. We derive the first two moments for the more general Watson distribution.
Planning Experiments for Discriminating between Models
Authors: Atkinson A. C. , Cox D. R. 
Published: December 2018

Summary
Results in the theory of optimum regression designs are used to develop experimental designs for discriminating between several regression models. An extension of the Kiefer–Wolfowitz general equivalence theorem is used to establish properties of the procedures. A sequential data-dependent strategy is described and its properties investigated for specific examples. In conclusion, some difficulties in the Bayesian analysis of discrimination experiments are considered.
On Bird Navigation, with Some Statistical Undertones
Authors: Matthews G. V. T. 
Published: December 2018

Summary
Young migratory birds appear innately programmed to fly for given distances in given directions. The orientations of the circular distributions of their escape attempts from cages, or of vanishing points in free flight, have been subjected to refined statistical analysis recently.
Time-compensated sun- and moon-orientations have been demonstrated. Compass directions are also obtained from the alignment of the constellations. Non-astronomical methods of orientation are of secondary importance.
Adult birds have the ability to correct for geographical displacement, sometimes over thousands of kilometres. A form of bi-coordinate navigation is probably involved, but the bases of the navigational grid remain uncertain. Pigeons can detect and react to small changes in sun altitude in terms of latitudinal displacement. The sun's position along its arc in relation to time may give longitudinal information.
Homeward orientation is not of phenomenal accuracy, leaving open the possibility that random search for the known area plays a part.
Environmental Impacts of Highway Traffic as Two-Sided Filtered Markov Renewal Processes
Authors: Marcus Allan H. 
Published: December 2018

Summary
Traffic noise, microscale air pollution and other adverse environmental impacts of highways can often be represented as the superposition of the impacts of the individual vehicles. A Markov renewal process is often a useful representation of vehicle positions in multi-type “follow-the-leader” traffic flow. The impact of the vehicles is thus a filtered Markov renewal process whose moments can be calculated recursively using the method of L. Takacs and W. K. Smith.
Random Discrete Distributions
Authors: Kingman J. F. C. 
Published: December 2018

Summary
It is impossible to choose at random a probability distribution on a countably infinite set in a manner invariant under permutations of that set. However, approximations to such a choice can be made by considering exchangeable probability measures on the class of probability distributions over a finite set, and letting the size of that set increase without limit. Under suitable conditions the resulting probabilities, when arranged in descending order, have non-degenerate limiting distributions. These apparently arcane considerations lead to rather concrete conclusions in certain problems in applied probability.
Asymptotic Approximations for Distributions of Ratios of Linear Functions of Random Variables
Authors: Broffitt J. D. , Dent W. T. 
Published: December 2018

Summary
Normal asymptotic approximations for the distribution of the ratio of linear functions of independent and identically distributed random variables are derived. These approximations are checked for accuracy by comparisons with exact known distributions in specific examples. In particular, the examples considered are the distribution of the circular serial correlation coefficient and Watson's distribution. The comparisons suggest that for sample sizes as small as 10 or 20 the asymptotic results are most satisfactory.
Row-And-Column Designs with Two Groups of Treatments Having Different Replications
Authors: Freeman G. H. 
Published: December 2018

Summary
Row-and-column designs are described for two groups of treatments with different replications. One group of treatments may have only one member, but generally both groups contain several treatments. For most of the designs both groups of treatments are either orthogonal or balanced with respect to each of rows and columns separately, and such designs are classified into 23 types. There are also some designs requiring both rows and columns for balance. Methods are given for constructing the designs, for each type and for general classes within the types, where these exist. Some small designs are illustrated and the choice of designs for use in practice is discussed.
Techniques for Testing the Constancy of Regression Relationships Over Time
Authors: Brown R. L. , Durbin J. , Evans J. M. 
Published: December 2018

Summary
Methods for studying the stability over time of regression relationships are considered. Recursive residuals, defined to be uncorrelated with zero means and constant variance, are introduced and tests based on the cusum and cusum of squares of recursive residuals are developed. Further techniques based on moving regressions, in which the regression model is fitted from a segment of data which is moved along the series, and on regression models whose coefficients are polynomials in time are studied. The Quandt log-likelihood ratio statistic is considered. Emphasis is placed on the use of graphical methods. The techniques proposed have been embodied in a comprehensive computer program, timvar. Use of the techniques is illustrated by applying them to three sets of data.
On the Concepts of Sufficiency and Ancillarity in the Presence of Nuisance Parameters
Authors: Dawid A. P. 
Published: December 2018

Summary
Examples are presented to show how ambiguities may arise from attempts to define and apply analogues of sufficiency and ancillarity in the presence of nuisance parameters. It is necessary to tread with caution if one wishes to avoid inconsistencies or unexpected consequences inherent in principles which, on first acquaintance, appear unexceptionable.
Addition to the Nearest Whole Unit
Authors: Richardson J. W. 
Published: December 2018

Summary
It is well known that, where a unit consists of a finite number of subunits, the distribution of the error committed by adding a sufficiently large number, n, of items rounded to the nearest whole unit, is approximately normal. This is true of both the probability function and the distribution function.
In this note, the differences from normality are obtained in the form of inequalities, of order n −1; and, with certain minimal restrictions on the parameters, the upper bounds of departure from normality are shown to be strikingly small.
An Extension of the T-Method to General Unbalanced Models of Fixed Effects
Authors: Hochberg Yosef 
Published: December 2018

1.
Introduction and Summary
Among the various procedures for simultaneous interval estimation, Tukey's T-method gives the shortest confidence intervals for pairwise contrasts when it is applicable. (Cf. Scheffé, 1959, Ch. 3; Miller, 1966, Ch. 2.) However, the T-method in its exact formulation (excluding one way anova, see Spjøtvoll and Stoline, 1973) is restricted to well-balanced designs.
In this paper we discuss a generalized T-type procedure for simultaneous interval estimation of all estimable parametric functions in general fixed effects, univariate linear models. The new method, which we subsequently abbreviate as the GT method, is an extension of a generalized T-procedure for the unbalanced one-way anova model given in Spjøtvoll and Stoline (1973).
In Section 2 we derive the new procedure in full-rank and in less than full-rank models. Some important features of the procedure are discussed in Section 3. In order to gain insight into the types of models where the new procedure is expected to produce satisfactory confidence intervals for pairwise contrasts, we illustrate, in Section 4, the application of the GT method in some unbalanced designs. In Section 5 we discuss a modified GT procedure which constitutes a combination of the GT1 in Hochberg (1974) and the GT methods. The proofs of some of the theorems are given in an Appendix for purposes of a convenient reading.
Factorization of Likelihood Functions for Full Exponential Families
Authors: Barndorff-Nielsen O. 
Published: December 2018

Summary
Examples are presented of full exponential families for which the likelihood function factorizes into a product of functions in such a way that each of the factor functions depends on a subparameter only and these subparameters vary independently of each other. A number of results are then discussed, concerning the key case of just two factors, one being the marginal likelihood for a statistic u, the other the conditional likelihood given u. Any statistic u which effects such a factorization is called a cut. Various conditions are given for a statistic to be a cut, and a method for constructing regular exponential families with cuts is indicated.
Histosplines with Knots Which are Order Statistics
Authors: Wahba Grace 
Published: December 2018

Summary
The histospline considered here is a quadratic spline density estimate analogous to the Boneva–Kendall–Stefanov (BKS) histospline, with their equally spaced knots replaced by knots at every knth-order statistic. This estimate can be expected to be relatively more “flexible” where the density is greatest. We obtain “mean square error at a point” convergence rates. The rates obtained are uniform over classes of densities which have first (alternatively second or third) derivatives in a bounded set in ℒp. If kn is chosen optimally, then this estimate shares the same “near optimal” convergence rates of certain BKS estimates when the knot spacing is chosen optimally, kernel estimates when the scale factor is chosen optimally, and orthogonal series estimates when the length of the series is chosen optimally.
Resolvable Paired-Comparison Designs
Authors: Williams E. R. 
Published: December 2018

Summary
A general method is given for the construction of resolvable paired-comparison designs for v treatments using the initial block of a cyclic incomplete block design for 12v treatments. The efficiency factor of the resulting design is shown to be a function of the efficiency factor of the cyclic design. Comparisons are made between the new designs and existing cyclic paired-comparison designs.
Noniterative Least Squares Estimates, Standard Errors and F-Tests for Analyses of Variance with Missing Data
Authors: Rubin Donald B. 
Published: December 2018

Summary
This article generalizes Rubin's method of least squares estimation of missing values in an analysis of variance. The general method produces not only least squares estimates of all parameters and the residual mean square, but also the correct least squares standard error and t-test for each contrast as well as the least squares sum of squares and F-test for each collection of contrasts. The method is non-iterative and requires only those subroutines designed to handle complete data plus a subroutine to find the inverse of an m x m symmetric matrix, where m is the number of missing values.
The Empirical Distribution Function with Arbitrarily Grouped, Censored and Truncated Data
Authors: Turnbull Bruce W. 
Published: December 2018

Summary
This paper is concerned with the non-parametric estimation of a distribution function F, when the data are incomplete due to grouping, censoring and/or truncation. Using the idea of self-consistency, a simple algorithm is constructed and shown to converge monotonically to yield a maximum likelihood estimate of F. An application to hypothesis testing is indicated.
Maximum Likelihood from Incomplete Data Via the EM Algorithm
Authors: Dempster A. P. , Laird N. M. , Rubin D. B. 
Published: December 2018

Summary
A broadly applicable algorithm for computing maximum likelihood estimates from incomplete data is presented at various levels of generality. Theory showing the monotone behaviour of the likelihood and convergence of the algorithm is derived. Many examples are sketched, including missing value situations, applications to grouped, censored or truncated data, finite mixture models, variance component estimation, hyperparameter estimation, iteratively reweighted least squares and factor analysis.
Continuous Time Spectral Analysis of Intervals between Events in Stationary Point Processes
Authors: Charnock D. M. 
Published: December 2018

Summary
The sequence of intervals between events in a stationary point process is considered as a process in continuous time. Expressions are given for a covariance function and the corresponding spectrum. Some examples are given to illustrate that the properties of the intervals as a process in continuous time are not the same as those of the intervals as a sequence. The methods developed are used to analyse a process consisting of times of R peaks in an electrocardiogram record. A remarkable similarity between this analysis and one based on the counting process is noted.
The von Mises–Fisher Matrix Distribution in Orientation Statistics
Authors: Khatri C. G. , Mardia K. V. 
Published: December 2018

Summary
When n distinguishable directions in p dimensions are required to describe each orientation, Downs (1972) has extended the von Mises–Fisher distribution. We obtain the normalizing constant which leads to the investigation of various basic properties of the distribution. In particular, an explicit expression for the first population moment as well as the asymptotic distribution of the basic statistics are provided. The estimation problem, important testing problems, and exact sampling distributions are dealt with, and some techniques are applied to a set of vectorcardiogram data. An extension of the distribution is also proposed.
On the Moments of a Beta Function Transformation of a Poisson Variate
Authors: Veevers A. , Tweedie M. C. K. 
Published: December 2018

Summary
A certain beta function of a Poisson variate has been shown to exhibit desirable variance-stabilizing properties comparing favourably with those of the more usual square-root transformations. This note reports an interesting relationship existing between the moments of these special forms of beta function of a Poisson variate and the standard normal ordinate and integral functions.
Spherical Matrix Distributions and a Multivariate Model
Authors: Dawid A. P. 
Published: December 2018

Summary
We consider inference about the parameters of a multivariate linear model, in which the usual assumption of normality for the errors is replaced by a weaker assumption of spherical symmetry. Structural distributions and confidence regions are derived, and it is shown that inference about means is identical with that appropriate under normality, being based on a matrix generalization of “Studentization”. Some relevant distribution theory is developed, the approach throughout being “density-free”.
Time Savings in Censored Life Testing
Authors: Muenz Larry R. , Green Sylvan B. 
Published: December 2018

Summary
It is often possible to achieve a saving of time in a life testing experiment by allowing right-censoring. This concept is important in clinical trials in which an early decision procedure is used. We describe the use of the ratio of order statistics as a measure of time savings, and give results on the distribution of such ratios. Numerical results are tabled and discussed for several underlying distributions of failure time (uniform, exponential, Pareto). We outline the application of this approach to the evaluation of early stopping procedures, with particular emphasis on analysing the time savings achieved by two-sample rank tests.
A Queueing Model for Traffic Flow
Authors: Gipps P. G. 
Published: December 2018

Summary
A model for queue formation and disintegration is proposed for traffic on a road where flow is unimpeded. The model assumes that vehicles are travelling in random queues and a distribution for queue length is derived having as a single parameter the ratio of the rate of mergings between pairs of queues and the rate of overtaking from queues of more than one vehicle. The first moment and maximum likelihood estimator associated with the distribution are derived and compared in a simulation study. The distribution is then fitted to data collected in different sites, with varying results.
On Goodness of Fit Tests Based on the Empirical Distribution Function for Uniform Spacings
Authors: Koziol James A. 
Published: December 2018

Summary
In a review of tests based on spacings, Pyke (1965) constructs an empirical distribution function of uniform spacings, and suggests that goodness of fit problems could be investigated with Kolmogorov–Smirnov and Cramér–von Mises type statistics when applied to this empirical distribution function, were the appropriate exact or asymptotic critical values available. It is shown in this note that the limiting distributions of these statistics are indeed available, but that the powers of tests based on these statistics generally compare unfavourably with the powers of the corresponding tests applied to the usual empirical distribution function of order statistics. Components of a Cramér–von Mises statistic based on spacings are also briefly investigated.
Invariance Properties of Uncorrelated Residual Transformations
Authors: Godolphin E. J. , Tullio M. 
Published: December 2018

Summary
The problem of obtaining an uncorrelated residual in the general linear model of full rank which is orthogonal to the design matrix has been discussed by Theil (1965), Brown et al. (1975) and others. In this paper it is shown that the problem is equivalent to stipulating an invariance requirement for the corresponding residual sum of squares, thus implying that alternative uncorrelated residuals are necessarily related by an orthogonal transformation. The set of uncorrelated residuals satisfying a given partitioning of the design matrix is derived. It is also shown that each member of this set enjoys an additional invariance property which enables it to be expressed as the same transformation of the vectors of observations, disturbances or least-squares residuals. Several implications of the results are discussed.
Curve Fitting and Optimal Design for Prediction
Authors: O'Hagan A. 
Published: December 2018

Summary
The optimal design problem is tackled in the framework of a new model and new objectives. A regression model is proposed in which the regression function is permitted to take any form over the space X of independent variables. The design objective is based on fitting a simplified function for prediction. The approach is Bayesian throughout.
The new designs are more robust than conventional ones. They also avoid the need to limit artificially design points to a predetermined subset of X. New solutions are also offered for the problems of smoothing, curve fitting and the selection of regressor variables.
On the Half-Sample Method for Goodness-Of-Fit
Authors: Stephens M. A. 
Published: December 2018

Summary
Two interesting processes, related to the empirical distribution function, have been pointed out by Rao (1972) and by Durbin (1973). The second, in particular, leads to the half-sample method, an elegant and simple technique for dealing with unknown parameters in goodness-of-fit testing, without the necessity of new tables of percentage points for each distribution tested. to those who have spent some effort in producing such tables, it is natural to wonder whether this effort has been in vain. In this paper we show that the answer is no.
Discrete Time Series Generated by Mixtures. I: Correlational and Runs Properties
Authors: Jacobs P. A. , Lewis P. A. W. 
Published: December 2018

Summary
A broad but parametrically simple model for a stationary sequence of dependent discrete random variables is given and several submodels are discussed. The structure of the model is specified by the marginal distribution of the random variables and several other parameters. The sequence of random variables is formed by a probabilistic linear combination of i.i.d. discrete random variables and is in general not Markovian. Second-order joint moments and spectra are obtained for the model, as well as some properties for the lengths of runs. The special case of a process in which the variables take on only two values is considered; this binary process is useful as a model for the counting process in a discrete-time point process.
A Note on a Matrix Inversion in Multiple Exponential Smoothing
Authors: McKenzie E. , Peterson M. M. 
Published: December 2018

Summary
In discussing the equivalence of certain polynomial predictors, Godolphin and Harrison (1975) note a matrix U employed in Multiple Exponential Smoothing whose inverse has not been obtained explicitly. The inverse of a related matrix p is obtained here and the relationship between the two matrices U and p reveals why no inverse has been obtained in general for U.
Confidence Intervals for the Quantiles of a Finite Population: Simple Random and Stratified Simple Random Sampling
Authors: Sedransk J. , Meyer J. 
Published: December 2018

Summary
Given a finite population consisting of N units, it is desired to have a confidence interval for the (t/N)th quantile, Y (t), of the population. Assuming simple random sampling, a confidence interval procedure is suggested and several expressions for the associated confidence coefficient are given. With stratified simple random sampling, for L = 2 strata, three confidence interval procedures are suggested. The associated confidence coefficients are derived under each of two (illustrative) assumptions about the nature of the stratification. (These assumptions refer to a probabilistic knowledge about the stratification.) The procedures are then compared using data from several finite populations.
Studies in the Robustness of Multidimensional Scaling: Perturbational Analysis of Classical Scaling
Authors: Sibson Robin 
Published: December 2018

Summary
This series of papers is devoted to the investigation of the extent to which the accuracy of operation of multidimensional scaling methods can be put onto a quantitative footing. This second paper investigates the response of the classical scaling method to small errors by making expansions in powers of the error term, and retaining the lowest non-cancelling power. Effects on individual eigenvalues and eigenvectors are considered, and shown to lead to useful auxiliary techniques for choice of dimensionality or for correction of bias. Procrustes statistics, as developed in the first paper of this series, are used to provide an overall picture of the error response; a perturbation theory for these is worked out, and is shown to lead to an approximate distribution theory. The details are worked out illustratively for a simple type of error structure.