bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Test of Equality of Block-Diagonal Covariance Matrices and its Role of Unification
Authors: John S. 
Published: December 2018

Summary
Let Cb, b = 0, 1, …, B, be the class of all d-dimensional matrices (i.e. having d rows and d columns) with a block-diagonal structure, the blocks along the diagonal being the identity matrix of order d1b, and mjb repetitions of a symmetric dsb-dimensional positive-definite matrix σsb, s = 2, 3, …, Sb. One or more of the dsb's may be zero. The model specifies initially that observations Wb, b ⩾ 1, are independent Wishart matrices of nb degrees of freedom and expected value nb σb, σb ∈ Cb. The hypothesis H0 to be tested is that σb, b ⩾ 1, are all equal to a matrix σ0 in C0. It is assumed that C0⊂C1∩C2∩…∩CB. The likelihood-ratio test criterion is obtained. Several current multivariate test criteria are shown to be special cases, but they do not exhaust the cases that are useful. From the Mellin transform of the test criterion, a χ2 series, a χ2 approximation, a non-central χ2 series and a non-central χ2 approximation are derived for the null distribtion of the test criterion. The error in the non-central χ2 approximation is of the order of n−3b, while the error in the χ2 approximation is of the order of n−2b.
Some Specific Results in Sequential Design
Authors: Bohrer Robert 
Published: December 2018

Summary
Chernoff–Whittle and Paulson type decision rules are defined for a selection problem of some practical interest. Non-asymptotic risks of these rules are derived where possible. These are compared with asymptotic approximations, derived more generally. Examples motivate general conjectures about relative gain with good sequential designs and about convergence to the asymptotic case as functions of experimental informativeness and experimental flexibility.
The Relative Position of the Two Regression Curves
Authors: Finucan H. M. 
Published: December 2018

Summary
In a non-singular bivariate Gaussian distribution the regression curve of y on x has smaller slope (measured by dy/dx) than the regression curve of x on y. Calling this the standard position and defining in a fairly obvious way a “clear-cut reversal” of it, we show that, for a distribution whose mean exists, such a reversal is impossible overall if the curves cross only once, and impossible at the extremities if the curves interlace in a more complicated way. Examples are given of distributions in which a ‘reversed’ configuration is found in a central portion of the range, and of pathological distributions (having no mean) with a reversed configuration everywhere.
Some extensions to the trivariate case are indicated.
Symmetric-Simplex Block Designs for Mixtures
Authors: Saxena S. K. , Nigam A. K. 
Published: December 2018

Summary
In the present paper generalized block designs for experiments with mixtures of n components, where some or all the n components have non-zero proportions, have been obtained. These designs allow for the exploration of the simplex in any region which may be of interest. The block designs of Nigam (1970) turn out to be particular cases of the designs suggested here. The procedure outlined in this paper also permits the experimenter to have any number of blocks.
F-Independence and Null Correlation of Continuous, Bounded-Sum, Positive Variables
Authors: Darroch J. N. , James I. R. 
Published: December 2018

Summary
The concept of F-independence, previously discussed (Darroch, 1971) for integer-valued variables, is here developed for r continuous, positive variables whose sum is bounded. Part of the theory parallels the theory for integer-valued variables and differs only in some additional mathematical questions which are encountered. Several topics discussed in this paper are special to continuous variables. These include the relationship of neutrality, of the Dirichlet distribution and of the beta distribution to F-independence. These relationships are effected through the concept of proportion-invariance. The paper concludes with an account of some correlation theory for bounded-sum variables.
A Total Entropy Criterion for the Dual Problem of Model Discrimination and Parameter Estimation
Authors: Borth David M. 
Published: December 2018

Summary
A total entropy criterion is developed for the sequential design of experiments. The criterion is applicable to the dual problem of model discrimination and parameter estimation. The total entropy measures both the uncertainty about which mathematical model is correct and the uncertainty about the parameter vector for each model. The criterion is shown to lead to the choice of experiment for which the outcome is most uncertain, relative to the uncertainty due to experimental error.
A Sequential Test for Certain Composite Hypotheses
Authors: Whitehead John 
Published: December 2018

Summary
A sequential procedure is developed to distinguish between null and alternative hypotheses of the type H 0: θ ≤ θ0 and H 1: θ ≥ θ1 (θ0 ≤ θ1) for one-parameter exponential families in such a way that the risks of type I and type II errors are smaller than some predetermined bounds. This is accomplished using observations of a sequence of random variables whose distribution is known up to the parameter θ, and involves the theory of certain tests with power one. The average sample number for this procedure is compared with that for Wald's sequential probability ratio test applied to the same problem.
Coefficients in D-Optimal Experimental Design
Authors: Sibson Robin , Kenny Alan 
Published: December 2018

Summary
We give a new proof of an inequality on design measures due to Attwood; the proof given here allows the investigation of when equality is attained. The result obtained is that, in a D-optimal design for a problem satisfying mild regularity conditions, either the number of distinct levels equals the number k of parameters and each level receives weight 1/k, or the number of levels is greater and each receives weight strictly less than 1/k. A complementary result proved as a lemma explores the structure of the set of designs defined by such conditions. The consequences of these results for the construction of design algorithms are discussed briefly.
On Alias Matrices and Generalized Defining Relationships of Equi-Information Factorial Arrangements
Authors: Raktoe B. L. 
Published: December 2018

Summary
In many practical situations a fraction of the full replicate of a k 1 x k 2 x ... x kt factorial is used by an experimenter to estimate a subset of effects under the assumption that the rest of the effects are negligible. to get a deeper insight in what precisely is being estimated if the assumption of negligibility of the suppressed effects is not valid it is imperative that the experimenter has a complete knowledge of the aliasing structure. This paper shows how to compute the aliasing structure and hence the generalized defining relationship of any design in a particular class of equi-information designs, the class being generated by the action of the group of level permutations on a given design. It is shown that the calculations in the case of the 2' factorial are extremely simple and a practical example is given to illustrate the results.
Asymptotic Properties of the Wiener–Kolmogorov Predictor. Ii
Authors: Bhansali R. J. 
Published: December 2018

Summary
The asymptotic properties of the autoregressive estimates a (T)(u) obtained using the fles method (Bhansali, 1974) suggest that, in practice, a decision on truncating the a (T)(u) at u = p, say, will need to be taken. This truncated sequence of the auto-regressive estimates is used to form alternative estimates of the linear predictor, the autoregressive spectral density function and the innovation variance. Some of the asymptotic properties of these estimates are derived for the case when the observed time series is a sample of an infinite, as well as a finite, order autoregressive process. A comparison of these estimates with the corresponding estimates obtained using the time domain autoregressive coefficients is carried out.
Recursive Estimation of the General Linear Model with Dependent Errors
Authors: McGilchrist C. A. , Sandland R. L. 
Published: December 2018

Summary
The techniques for recursive estimation of the general linear model are extended to the case of dependent errors with known second-order properties. Recurrence relations for computation and a sequence of independent recursive residuals, useful for testing the constancy of the regression relation over time, are derived and studied. Computational savings are available when the error process is stationary.
Robust Estimation of Power Spectra
Authors: Kleiner B. , Martin R. D. , Thomson D. J. 
Published: December 2018

Summary
Outliers in time series can play havoc with conventional power spectrum density estimation techniques when the spectrum features of interest consist of one or more peaks of relatively low amplitude. Furthermore, the outliers need not be large relative to the scale of the process in order to have considerable impact on the estimate; they only need to be large relative to the scale of the innovations process. Following a tutorial review of the central notions of robustness and the principles guiding conventional spectrum estimation, methods are presented for computing robust spectral densities. These are quite insensitive to such outliers and produce reliable estimates reflecting the structure of the core portion of the data. Two distinct methods are described. Both are based on robust prewhitening and on weighting the resulting residuals. They differ only in the way prewhitening is done: the first method computes the prewhitened values iteratively through a filtering operation; the second fits a robust autoregressive representation to the data by iterated weighted least squares. Each approach can be regarded as the solution to an intuitively appealing minimization problem, where the solution is exact in one case, approximate in the other. Both procedures have proved to be successful over a wide variety of data sets as will be demonstrated with real and simulated data.
An Influence Curve for Two-Sample Rank Tests
Authors: Eplett W. J. R. 
Published: December 2018

Summary
An influence curve for two-sample linear rank tests is introduced. This influence curve can be viewed as a derivative of the limiting power and reflects the stability of the power to deviations from the assumed hypothesis testing model. It can also be interpreted in terms of the limit in probability of the test statistic and then it indicates the effect that small changes in the observations have upon the test statistic. The stability properties of several tests are examined using the influence curve. In view of the findings, two alternatives to the Normal scores test are studied. The influence curve appears to be useful both for detecting instability and for suggesting new, more robust, tests.
Exchange and Interchange Procedures to Search for Optimal Designs
Authors: Jones Byron , Eccleston John A. 
Published: December 2018

Summary
An algorithm to search for optimal block designs is described. This algorithm consists of an exchange procedure and an interchange procedure. During the exchange procedure the “correct” treatment replications are determined and during the interchange procedure an optimal set of treatment concurrences is searched for. The optimality criterion is the sum of the weighted variances of a set of treatment contrasts of interest. Examples which illustrate how the algorithm can be used to obtain designs which have a variance structure that reflects the interest expressed in a set of treatment contrasts are given and the performance of the algorithm is discussed.
An Approximation to Certain Multivariate Normal Probabilities
Authors: Henery R. J. 
Published: December 2018

Summary
In models of disease transmission, in which liability to disease is assumed to be normally distributed, the problem arises of calculating the probability that a given member of a group of individuals will contract the disease conditional on the other members exceeding some threshold. The special case in which the truncated variables are uncorrelated with each other occurs frequently and we consider here an approximation, based on a Gram-Charlier expansion, for the probabilities which arise in this case. In two dimensions the method is a serious rival to the tetrachoric series expansion only for large positive truncation levels. In higher dimensions other methods are either approximate or difficult to use.
The Estimability Structure of Linear Models and Submodels
Authors: Stewart I. , Wynn H. P. 
Published: December 2018

SUMMARY
When a group of parameters in a linear model is estimable it remains estimable under a smaller model “containing” those parameters. However, there are more subtle relationships between the estimability of models and submodels. Writing A ~ B if model A is estimable under B, the full properties of “ ~ ” are discussed. It is shown that they can all be derived by identifying a special sublattice of submodels namely those models which are fully inestimable in that every factor has at least one inestimable contrast. The use of the ideas in writing efficient programmes to discover the estimability structure is discussed and a complete list of all possible structures for three factor models given with examples.
Non-Parametric Estimation for Non-Decreasing Lévy Processes
Authors: Basawa I. V. , Brockwell P. J. 
Published: December 2018

Summary
Three non-parametric estimates of the measure corresponding to a non-decreasing Lévy process are discussed. Consistency and the limit distributions of the estimates are studied. The empirical process corresponding to one of the estimates is briefly discussed with an anticipation of an application to goodness-of-fit tests.
A Model for Association in Bivariate Survival Data
Authors: Oakes David 
Published: December 2018

Summary
A reparameterization of a model introduced by D. G. Clayton for association in bivariate life-tables is discussed. Inference for the parameter governing the association is considered when the marginal distributions are specified up to Lehmann alternatives. The information matrix is derived explicitly and it is shown that the parameterization is moderately successful in introducing orthogonality between the association parameter and the two scale parameters. The likelihood proposed by Clayton for the case that the marginal distributions are completely unknown is criticized. An alternative nonparametric estimator based on Kendall's coefficient of concordance is proposed and its asymptotic variance evaluated.
Rounding Error in Regression: The Appropriateness of Sheppard's Corrections
Authors: Dempster Arthur P. , Rubin Donald B. 
Published: December 2018

SUMMARY
We consider three simple approaches to rounding error in least squares regression. The first treats the rounded data as if they were unrounded, the second adds an adjustment to the diagonal of the covariance matrix of the variables and the third subtracts an adjustment from the diagonal. The third, Sheppard's corrections, can be motivated as maximum likelihood with small rounding error and either (1) joint normal data or (2) normal residuals, “regular” independent variables, and large samples. Although an example and theory suggest that the third approach is usually preferable to the first two, a generally satisfactory attack on rounding error in regression requires the specification of the full distribution of variables, and convenient computational methods for this problem are not currently available.
Upper Bounds for Average Efficiency Factors of Two-Factor Interactions
Authors: Dean A. M. , Lewis S. M. 
Published: December 2018

SUMMARY
An upper bound is derived for the average efficiency factor of a two-factor interaction when an experiment is arranged as an incomplete block design. Attention is restricted to designs which have orthogonal factorial structure and which allow one or both main effects to be estimated with full efficiency. It is shown that several designs may be compared simultaneously using a graphical interpretation of the bound.
Outlier Resistant Distributions: Where Does the Probability Go?
Authors: Goldstein Michael 
Published: December 2018

Summary
For a single observation x from a distribution with unknown location parameter θ, we investigate the relationship between the prior probability that θ lies in an interval I and the posterior probability that θ lies in I, given x, as x tends to infinity. In the case when the likelihood function is strictly unimodal, and thus outlier resistant, we give sufficient conditions to ensure that the limiting posterior probability is not greater than the prior probability, by exploiting dispersion properties of the distribution.
On the Optimality and Usage of Reinforced Block Designs for Comparing Test Treatments with a Standard Treatment
Authors: Jacroux Mike 
Published: December 2018

SUMMARY
In this paper we consider the problem of determining optimal reinforced block designs for estimating the differences in effects between a set of test treatments of interest and some standard treatment. The optimality criterion considered is the average variance with which elementary treatment differences involving the standard treatment are estimated. A design is said to be reinforced with the standard treatment if each block of the design contains the standard treatment once, and we refer to such designs as SR-designs. Some sufficient conditions are derived for an SR-design to be optimal within the entire class of available SR-designs and some SR-designs which can be obtained by reinforcing each block of certain types of group divisible designs are shown to satisfy the conditions given. An efficiency criterion is also defined which can be used to compare arbitrary SR-designs with respect to how well they estimate treatment differences involving the standard treatment.
A Note on Restricted Maximum Likelihood Estimation with an Alternative Outlier Model
Authors: Thompson R. 
Published: December 2018

SUMMARY
For single outliers in normal theory fixed effects models a mean slippage model is commonly used. An alternative is to model the outlier as arising from an unknown observation with inflated variance. Maximum likelihood estimates for the position of the outlier under the two models need not agree. This paper considers maximizing a restricted part of the likelihood to estimate the variance parameters and characterizes these estimates in terms of standard least squares parameters. It is shown that the residual variance and outlier position are the same under both models.
Monotonicity of the Probability of Correct Selection or are Bigger Samples Better?
Authors: Bofinger Eve 
Published: December 2018

SUMMARY
The problem of selecting the normal population with largest mean when variances and sample sizes may be unequal is considered and conditions on the variances which ensure that the probability of correct selection increases when any sample size is increased are investigated. It is shown that the related probability of choosing a population with mean “close” to the largest does not have such a monotonic property while subset selection probabilities do. We conclude that “bigger samples are usually better”.
On the Estimation of Residual Variance and Order in Autoregressive Time Series
Authors: Paulsen Jostein , Tjøstheim Dag 
Published: December 2018

SUMMARY
We study the bias of Yule-Walker, least squares and Burg-type estimates of the residual variance of autoregressive processes. Both simulations and theory indicate that Yule-Walker estimates are inferior to least squares and Burg-type estimates. The effect on order determination is also studied, and we extend the results on overestimation of the AIC criterion to the general multivariate case. For strongly autocorrelated processes, Yule-Walker estimates of residual variance and order may be severely biased even for comparatively large sample sizes.
Re-Weighted Least Squares Estimation with Censored and Grouped Data: An Application of the EM Algorithm
Authors: Pettitt A. N. 
Published: December 2018

SUMMARY
We consider the problem of adapting weighted least squares estimation so that estimates can be found with censored or grouped data. The EM algorithm is implemented for the linear model where the errors are assumed to be generated by a scale mixture of normal distributions. In particular, explicit results are given for the case where the marginal distribution of the error is Student-t with an even number of degrees of freedom. Expressions for the observed information are found, relating grouped data results to those for right censored data. Some ad hoc rules for the identification of outliers are given. An example involving the lifetimes of motorettes is considered.
Perturbation Theory for Generalized Procrustes Analysis
Authors: Langron S. P. , Collins A. J. 
Published: December 2018

SUMMARY
Perturbation theory for Procrustes statistics is developed when both configurations are subject to independent normal errors. The total sum of squares is shown to partition into sums of squares for translation, rotation/reflection and scaling, plus a residual. These results are extended to generalized Procrustes analysis. This gives a theoretical justification to Gower's analysis of variance summary of the results from a generalized Procrustes analysis.
A Criterion for the Construction of Optimal Neighbour Designs
Authors: Williams E. R. 
Published: December 2018

SUMMARY
The model of Williams (1986) for the neighbour analysis of field trials is investigated in order to derive a criterion for the comparison of neighbour designs and hence the construction of optimal neighbour designs. A two-stage procedure is given whereby an efficient resolvable incomplete block design can be used as a starting point for the construction of an efficient neighbour design. A definition of balance for neighbour designs is presented. A comparison with the method of Wilkinson et al. (1983) is discussed.
A Model for High-Order Markov Chains
Authors: Raftery Adrian E. 
Published: December 2018

SUMMARY
A model for Markov chains of order higher than one is introduced which involves only one additional parameter for each extra lag. Asymptotic properties and the autocorrelation structure are investigated. Three examples are given in which the model appears to model data more successfully than both the usual high-order Markov chain and the alternative models of Jacobs and Lewis (1978), Pegram (1980) and Logan (1981).
Testing Collapsibility in Contingency Tables
Authors: Ducharme Gilles R. , Lepage Yves 
Published: December 2018

SUMMARY
In this article, the problem of testing for the collapsibility of a contingency table is studied. The notion of collapsibility is first discussed and three aspects of this property are distinguished. Tests for these three forms are presented, with attention focussed on 2 × 2 × K tables. Finally, it is shown that in a collapsible table, the marginal odds-ratio is more efficient than the usual estimators of the common odds-ratio.