bluuebunny/crossref_metadata_2025_split huggingface dataset:
Resolution Iv Designs of the 2M × 3 Series
Authors: Anderson D. A. , Srivastava J. N. 
Published: December 2018

Summary
It is shown that a resolution IV 2m × 3 factorial design without blocks permits the estimation of not only the main effects A1, …, Am, B and B2 (which are assumed estimable by definition) but also of (i) the interactions Ai B, and Ai B2 (i = 1, …, m), and (ii) at least one linear combination of the general mean μ and the interactions Ai Ai (i &lt; j; i, j = 1, …, m). Some methods of construction of 2m × 3 designs of resolution IV are discussed and “good” designs of this series with N = 4N* are presented for each m in the range 3 ⩽ m ⩽ 15, and N ⩽ 80. These designs may be conducted in blocks of size 4 or any multiple of 4.
Generalized Least Squares and Maximum Likelihood Estimation of Non-Linear Functional Relationships
Authors: Dolby G. R. 
Published: December 2018

Summary
A non-linear functional relationship between two mathematical variables is postulated. Departures of observed random variates from the mathematical variable values are assumed to have zero mean and general but known covariance matrix. Assuming normality we obtain by maximum likelihood an expression for the asymptotic covariance matrix of the structural parameter estimates. The expression involves a certain matrix Ψ. A generalized least squares method is proposed which involves minimizing a quadratic form with the same matrix Ψ. In the linear case, it is shown that the methods of generalized least squares, maximum likelihood and maximum relative likelihood are equivalent. The least squares procedure is identified with the intuitive approach of Sprent (1966).
Numerical Results on Approximate Confidence Limits for the Odds Ratio
Authors: Gart John J. , Thomas Donald G. 
Published: December 2018

Summary
Consider the comparison of two binomial variates with parameters p1 and p2. The parameter of non-centrality for the Fisher–Irwin exact test is the odds ratio, ψ = p1q2/p2q1, where qi = 1 – pi, i = 1, 2. Exact confidence limits for ψ may be calculated (Fisher, 1935, 1962; Cornfield, 1956) and several authors have suggested approximate methods. The various approximate methods are reviewed and, from both theoretical and numerical results, we find that Cornfield's approximate method and Method II of Gart (1962) yield the better approximations under various conditions. An F-test alternative to the exact test of 2 × 2 tables (Gart, 1962) is found to be accurate in small numbers.
Combining Possibly Related Estimation Problems
Authors: Efron B. , Morris C. 
Published: December 2018

Summary
We have two sets of parameters we wish to estimate, and wonder whether the James-Stein estimator should be applied separately to the two sets or once to the combined problem. We show that there is a class of compromise estimators, Bayesian in nature, which will usually be preferred to either alternative.
“The difficulty here is to know what problems are to be combined together— why should not all our estimation problems be lumped together into one grand melée?”
George Barnard commenting on the James–Stein estimator, 1962.
Assessing Uncertainty
Authors: Tversky Amos 
Published: December 2018

Summary
Intuitive judgments of probability are based on a limited number of heuristics that are usually effective but sometimes lead to severe and systematic errors. Research shows, for example, that people judge the probability of a hypothesis by the degree to which it represents the evidence, with little or no regard for its prior probability. Other heuristics lead to an overestimation of the probabilities of highly available or salient events, and to overconfidence in the assessment of subjective probability distributions. These biases are not readily corrected, and they are shared by both naive and statistically sophisticated subjects. The implications of the psychology of judgment to the analysis of rational behaviour are explored.
Pole-Seeking Brownian Motion and Bird Navigation
Authors: Kendall David G. 
Published: December 2018

Summary
This paper is not concerned with identifying the mechanism of bird navigation, but rather with assessing the degree of success possible using very bad navigational aids of whatever sort. Flight-paths are simulated using virtually no hypotheses, and all numerical parameters are determined ornithologically. The results are compared with the performance of actual birds, and also with a brownian model which is analytically convenient. It turns out that some formulae for the brownian theory can be used to graduate the results obtained from actual or simulated observations, and this is its sole ornithological relevance. The data imply a surprising numerical coincidence which allows of a Darwinian explanation.
It seems likely that under suitable asymptotic hypotheses, the ornithological model will converge weakly towards the brownian one, but that question is deliberately not investigated here. Indeed it is ornithologically of little interest because (i) we are certainly not at the limit and (ii) weak convergence theorems do not normally have anything useful to say about the rate of convergence. This suggests that there may be a general need for a shift of emphasis in our thinking, away from weak convergence theorems towards weak convergence approximations (validated by simulation).
A Generalized Dirichlet Distribution in Bayesian Life Testing
Authors: Lochner Robert H. 
Published: December 2018

Summary
Let F(x) be the c.d.f. for some population of life times. For real numbers t 1&lt;t 2&lt;…&lt;tk, where F(t l)&gt;0 and F(tk)&lt;l, let p 1 = F(t l) and pi = F(ti) – F(ti –1) for i = 2, 3,…, k. A generalized Dirichlet prior distribution for p = (pl …,pk) having density function f(p)∝Πi=1kpiαi−1(1−p1−…−pi)γi is considered. An intuitive justification for using this density is given and its properties are studied. Comparisons are made between this distribution and the Dirichlet distribution. The posterior distribution of F(ti) is also considered.
Model Building and the Analysis of Spatial Pattern in Human Geography
Authors: Cliff A. D. , Ord J. K. 
Published: December 2018

1. Introduction and SummaryIt is the purpose of this paper to determine how far various statistical models and methods of statistical inference have enabled the aims of geographical research to be met in the problem areas to which they have been applied. In so doing, we hope we can indicate to the statistician questions of geographical interest which cannot readily be answered by existing statistical methods; and to the geographer, some of the insights into geographical processes which may be gained from a statistical and model building approach. We would stress that we have not tried to be all inclusive in our coverage. Instead, we have tried to select some topics which best seem to convey the flavour of the kinds of things human geographers have been doing, and which will, at the same time, be of interest to statisticians on either theoretical or empirical grounds. In addition, our own interests mean that we have concentrated upon examples in human (economic and urban), rather than physical, geography, although similar approaches have been used there to a lesser degree. More general reviews are provided by Gould (1969), Berry (1971) and Wilson (1972).
Statistics of Directional Data
Authors: Mardia K. V. 
Published: December 2018

Summary
Directional data analysis is emerging as an important area of statistics. Within the past two decades, various new techniques have appeared, mostly to meet the needs of scientific workers dealing with directional data. The paper first introduces the two basic models for the multi-dimensional case known as the von Mises–Fisher distribution and the Bingham distribution. Their sampling distribution theory depends heavily on the isotropic case and some developments are discussed. An optimum property of an important test for the von Mises–Fisher case is established. A non-parametric test is proposed for the hypothesis of independence for observations on a torus. In addition to some numerical examples on the preceding topics, five case studies are given which illuminate the power of this new methodology. The case studies are concerned with cancer research, origins of comets, arrival times of patients, navigational problems and biological rhythms. Some unsolved problems are also indicated.
Matrix Weighted Averages and Posterior Bounds
Authors: Chamberlain Gary , Leamer Edward E. 
Published: December 2018

Summary
Bounds for matrix weighted averages of pairs of vectors are presented. The weight matrices are constrained to certain classes suggested by the Bayesian analysis of the linear regression model and the multivariate normal model. The bounds identify the region within which the posterior location vector must lie if the prior comes from a certain class of priors.
Measures and Models for Angular Correlation and Angular–Linear Correlation
Authors: Johnson Richard A. , Wehrly Thomas 
Published: December 2018

Summary
Population models for dependence between two angular measurements and for dependence between an angular and a linear observation are proposed. The method of canonical correlations first leads to new population and sample measures of dependence in this latter situation. An example relating wind direction to the level of a pollutant is given. Next, applied to pairs of angular measurements, the method yields previously proposed sample measures in some special cases and a new sample measure in general.
Block Designs for Fractional Factorial Experiments with Replication
Authors: Cotter Sarah C. 
Published: December 2018

Summary
This paper describes how incomplete block designs may be used to provide blocking plans for fractions of symmetrical factorial experiments. These designs introduce some replication, but provide a wide range of block sizes, from two units per block upwards. The blocking does not alter the aliasing of the design, and all estimable factorial effects are partially confounded, their estimates being mutually orthogonal. The analysis of these designs is described.
Super-Slowly Varying Functions in Extreme Value Theory
Authors: Anderson C. W. 
Published: December 2018

Summary
Large-deviation limit theorems for maxima of random samples in the domain of attraction of the extreme value distribution Φα are studied, motivated by examination of an approximation used in the statistical analysis of large observations. The large-deviation property is shown to be equivalent to a strengthened form of slow variation condition, called here super-slow variation, on the tail of the distribution of a single observation. Various conditions for super-slow variation are discussed and Karamata's representation for slowly varying functions is extended to a wide class of super-slowly varying functions.
Conditional Independence in Statistical Theory
Authors: Dawid A. P. 
Published: December 2018

Summary
Some simple heuristic properties of conditional independence are shown to form a conceptual framework for much of the theory of statistical inference. This framework is illustrated by an examination of the rôle of conditional independence in several diverse areas of the field of statistics. Topics covered include sufficiency and ancillarity, parameter identification, causal inference, prediction sufficiency, data selection mechanisms, invariant statistical models and a subjectivist approach to model-building.
The Use of Chi-Squared Statistics for Categorical Data Problems
Authors: Fienberg Stephen E. 
Published: December 2018

Summary
The use of χ2 statistics for categorical data problems was initiated by Karl Pearson, but it took several years before the asymptotic distribution of these statistics was well understood. The general structure of asymptotic results for χ2 statistics is reviewed and the applicability of the general structure to a variety of problems of practical interest is discussed. These problems include the use of χ2 statistics in small-sample situations and in large sparse tables, in cluster sampling, and in cases where they do not have asymptotic χ2 distributions.
Bandit Processes and Dynamic Allocation Indices
Authors: Gittins J. C. 
Published: December 2018

Summary
The paper aims to give a unified account of the central concepts in recent work on bandit processes and dynamic allocation indices; to show how these reduce some previously intractable problems to the problem of calculating such indices; and to describe how these calculations may be carried out. Applications to stochastic scheduling, sequential clinical trials and a class of search problems are discussed.
The Multiparameter Steady Model
Authors: Smith J. Q. 
Published: December 2018

SUMMARY
This paper generalizes and extends the idea of a steady evolution of a time series to multiparameter processes with any observational distribution. Particular examples of such processes are given. These include the multivariate steady process, univariate normal processes where the observational variance is unknown and series of multinomial observations with a steady model on the cell probabilities.
Equivalent Forms of the Multivariate Portmanteau Statistic
Authors: Hosking J. R. M. 
Published: December 2018

SUMMARY
The Box-Pierce portmanteau test for univariate autoregressive moving-average (arma) time-series models has been generalized to multivariate time-series models by several authors, and several different definitions of the test statistic have resulted. The purpose of this note is to point out that all these different forms of the portmanteau statistic are in fact identical.
On Linear Intensity Models for Mixed Doubly Stochastic Poisson and Self-Exciting Point Processes
Authors: Ogata Yosihiko , Akaike Hirotugu 
Published: December 2018

Summary
A flexible family of parametric models for intensity processes is introduced to represent a causal relationship between a point process and another stochastic process. Algorithms for the maximum likelihood computation and the procedure of model selection are discussed.
Approximate Posterior Distributions for Incomplete Data Problems
Authors: Laird Nan M. , Louis Thomas A. 
Published: December 2018

Summary
We consider the problem of developing a simple approximation to a posterior distribution arising from incomplete data sampling. We compare approximations based on the normal distribution and upon conjugate distributions, theoretically where feasible and in some numerical examples. Two general conclusions can be made on the basis of our numerical work. First, when there is missing data, approximations which fail to take loss of information into account give overly concentrated posterior distributions. Second, the Gaussian approximation matching mode and observed Fisher information is quite good with large sample sizes and true posteriors which are not highly skewed. Further work delimiting these conditions more precisely will be useful. Finally, the use of a conjugate posterior which matches both mode and information performs well in all of our examples, and is decidedly superior to the Gaussian approximation with small samples.
Definitions and Properties for M-Concurrence Designs
Authors: Jarrett R. G. 
Published: December 2018

Summary
Incomplete block designs can be regarded as being in some sense approximately partially balanced. In this paper, we show that parameters pjki corresponding to those used for partially balanced designs can be defined for certain designs with m distinct concurrences. These parameters have properties analogous to those for m associate-class partially balanced incomplete block (PBIB(m)) designs and have proved useful in searching for optimal designs. This leads to a new upper bound for the efficiency factor which, for given pjki values, is attained if a PBIB(2) design exists. Some results on complement and dual designs are also given.
Statistical Uses of the Spatial Median
Authors: Brown B. M. 
Published: December 2018

SUMMARY
The spatial median, called the mediancentre in an earlier paper by J. C. Gower, is defined as the bivariate location measure to minimize the sum of absolute distances to observations. its asymptotic efficiency relative to the sample mean vector with normal data is shown to exceed the usual univariate 2/π = 0.637. its estimating equations have an angular aspect and are used to develop “angle tests”, which are analogues of sign tests in one dimension.
On the Convergence of the EM Algorithm
Authors: Boyles Russell A. 
Published: December 2018

SUMMARY
An example is given showing that a sequence generated by a GEM algorthm need not converge under the conditions stated in Dempster et al., (1977). Two general convergence results are presented which suggest that in practice a GEM sequence will converge to a compact connected set of local maxima of the likelihood function; this limit set may or may not consist of a single point.
Nearest Neighbour (Nn) Analysis of Field Experiments
Authors: Wilkinson G. N. , Eckert S. R. , Hancock T. W. , Mayo O. 
Published: December 2018

SUMMARY
The paper is in two parts. Part I presents results of a Monte Carlo randomization study of Papadakis's covariance method of NN analysis which show that (i) a non-iterated Papadakis analysis tends to be conservatively biassed; (ii) iteration of the analysis as suggested by Bartlett (1978) leads to substantial positive bias in the treatment F ratio; (iii) the method is very inefficient when there are substantial trend effects in the data. A theoretical explanation of these results is given.
Part II describes a new method of NN analysis discovered by the first author and developed in collaboration with the co-authors. The method is essentially a “moving-block” analogue of classical forms of analysis for “fixed” blocks (or rows, columns). It avoids the defects of Papadakis's method and leads to approximately unbiassed analyses. It is nearly always and often substantially more efficient on average than classical analyses of complete or incomplete block experiments, and also more efficient than standard analyses of Latin or lattice square designs if there are appreciable row x column interactions in the data. New criteria of design for NN balance are described. Validity of the new method under randomization is demonstrated empirically with Monte Carlo studies.
Semi-Latin Squares and Related Designs
Authors: Preece D. A. , Freeman G. H. 
Published: December 2018

SUMMARY
A semi-Latin square for t = kn symbols is a rectangular arrangement with n rows and t columns, these latter being grouped into sets each containing k consecutive columns; each symbol occurs exactly once in each row and exactly once in each set of columns (Yates, 1935). Previous authors seem not to have considered the combinatorial possibilities of semi-Latin squares. For each pair of values k and t, the semi-Latin squares can be classified into “species” or “main classes”, akin to the species of Latin squares. The classification considered in this note disregards the ordering of the k symbols to be found where any row intersects any set of columns; for k = 2 and t = 4, 6 and 8, the numbers of species are 1, 2 and 10 respectively. The relationship between semi-Latin squares, Trojan squares and certain partially balanced incomplete block designs with two associate classes is discussed. The relevant semi-regular designs of Clatworthy (1973) are examined to see which can be obtained from semi-Latin (Trojan) squares, and some enumerations of squares obtainable from the semi-regular designs are reported.
Approximating Priors by Mixtures of Natural Conjugate Priors
Authors: Dalal S. R. , Hall W. J. 
Published: December 2018

SUMMARY
The purpose of this paper is twofold: First, to show that a natural enlargement of the class of natural conjugate priors–namely, mixtures of natural conjugate priors–also leads to mathematically tractable solutions. Secondly, to show that this enlargement is “adequate” in that any prior may be arbitrarily closely approximated by a suitable member of this class.
Specifically, a general method for approximating an arbitrary prior density is first given with approximation (convergence) defined pointwise or in the L 1 or total variation senses. Corresponding posterior densities are shown to provide approximations in corresponding senses, whether or not the approximating priors are those given herein. Then formulas are given for posterior densities when the prior is a mixture of natural conjugate priors, and it is shown that an arbitrary prior density and its posterior density may be approximated by such a mixture and its posterior. In these senses, Bayesians may find it satisfactory to confine attention to mixtures of natural conjugate priors. The results are illustrated by several exponential family examples.
Regression, Prediction and Shrinkage
Authors: Copas J. B. 
Published: December 2018

Summary
The fit of a regression predictor to new data is nearly always worse than its fit to the original data. Anticipating this shrinkage leads to Stein-type predictors which, under certain assumptions, give a uniformly lower prediction mean squared error than least squares. Shrinkage can be particularly marked when stepwise fitting is used: the shrinkage is then closer to that expected of the full regression rather than of the subset regression actually fitted. Preshrunk predictors for selected subsets are proposed and tested on a number of practical examples. Both multiple and binary (logistic) regression models are considered.
A Goodness-Of-Fit Test for the von Mises–Fisher Distribution
Authors: Mardia K. V. , Holmes D. , Kent J. T. 
Published: December 2018

SUMMARY
We derive a goodness-of-fit test for the von Mises-Fisher distribution which is an extension of a goodness-of-fit test for the von Mises distribution given by Cox (1975). A robust version of the test is also given. Computational aspects of the test statistic are discussed and a numerical example is given.
Canonical Parameterizations and Zero Parameter-Effects Curvature
Authors: Kass Robert E. 
Published: December 2018

SUMMARY
An equation derived by Hougaard (1982) characterizes certain canonical parameterizations of curved exponential families. The geometrical interpretation of Hougaard's equation is presented and, with this background, the relationship of work on Gaussian non-linear regression, by Bates and Watts (1980) and others, to that on general asymptotic inference, by Efron (1975) and Amari (1982a, b), is discussed. Hougaard's δ-parameterization is that in which there is zero “parameter-effects curvature” with respect to Amari's (1982b) α-connection geometry, when α= 1–2δ. For the generalized linear models of Nelder and Wedderburn (1972) there is a separate “parameter-effects” array for each α, and each is a convex combination of the exponential and mixture “parameter-effects” arrays. On the other hand, in non-linear regression, for any family of symmetric errors there is only one array and it is a constant multiple of that for the Gaussian family.
Upper Bounds for Factorial Efficiency Factors
Authors: Lewis S. M. , Dean A. M. 
Published: December 2018

SUMMARY
The use of the upper bound for the average efficiency factor of a 2-factor interaction derived by Dean and Lewis (1983) is extended to the case where neither main effect achieves full efficiency. It is shown how the resulting boundary surface can be used to assess a design and hence to aid the construction of efficient designs. The bound is also generalised to higher order interactions.