bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Multi-Sample Uniform Scores Test on a Circle and its Parametric Competitor
Authors: Mardia K. V. 
Published: December 2018

Summary
We propose a c-sample non-parametric test W on a circle based on uniform scores. The test can be regarded as an extension of Wheeler and Watson's test (1964). This test is constructed with the help of a variant of a c-sample test for von Mises populations under the shift-type of alternatives. We indicate the relationship of the W-test with a test given by Mardia (1970). This result solves the problem of critical values of this test and of approximations to the null distribution of W. The asymptotic distribution of this test and of its parametric competitor test S are obtained. Bahadur's efficiency of the W-test relative to the S-test is derived and some important particular cases are considered. The tests are applied to a numerical example.
Convex Loss Applied to Design in Regression Problems
Authors: Laycock P. J. 
Published: December 2018

Summary
A general linear regression function is to be observed at n points in order to estimate a known linear combination of the unknown parameters. The n points and the estimator are to be optimum in some sense and in this paper the main criterion for optimality involves uniformly minimizing certain convex loss functions. Three main sets of results are obtained, followed by some further results for normally distributed errors.
Some Power Comparisons between Bivariate Tests and a Twofold Univariate Test
Authors: Genizi Abraham 
Published: December 2018

Summary
The paper describes a comparative study of the power of four bivariate tests of linear hypotheses and of a “twofold univariate” test equivalent to applying separate F-tests to the two variables. The powers of the multivariate tests are estimated by Monte Carlo methods, and that of the twofold univariate test is derived by a method using characteristic functions. Graphs describing the powers are given, leading to practical recommendations in terms of parameters which have a simple intuitive meaning.
Mean-Value Formulae for a Class of Random Sets
Authors: Streit F. 
Published: December 2018

Summary
Mean-value formulae for important characteristics (e.g. volume, surface area, etc.) of the common intersection of randomly placed point-sets are derived under the condition that the basic probability distribution of the underlying model is either motion-invariant or translation-invariant (the orientation of the generating sets in this latter case being known). Various special cases are discussed, some of them leading to a new derivation of known results of geometrical probability theory. The expected value of the probability that an arbitrary point is covered by the random intersection-set is also determined.
A Test of Fit for Bivariate Distributions
Authors: Dahiya Ram C. , Gurland John 
Published: December 2018

Summary
Tests of fit based on generalized minimum χ2 techniques are developed for bivariate distributions. The asymptotic null distribution of the test statistic is χ2 while the asymptotic non-null distribution turns out to be that of a weighted sum of independent non-central χ2 variates. The special case of testing the fit of a bivariate normal distribution is investigated in detail and the power is obtained for several alternative families of bivariate distributions.
Scale Mixtures of Normal Distributions
Authors: Andrews D. F. , Mallows C. L. 
Published: December 2018

Summary
This paper presents necessary and sufficient conditions under which a random variable X may be generated as the ratio Z/V where Z and V are independent and Z has a standard normal distribution. This representation is useful in Monte Carlo calculations. It is established that when 1/2V 2 is exponential, X is double exponential; and that when 1/2V has the asymptotic distribution of the Kolmogorov distance statistic, X is logistic.
Partial Confounding in Symmetrical Factorial Experiments
Authors: Cotter Sarah C. 
Published: December 2018

Summary
A new method is given for partial confounding with any block size in symmetrical factorial experiments. The method combines the techniques of confounding and incomplete block design, so that some factorial effects are completely confounded and some are partially confounded. A list of useful balanced incomplete block designs and group divisible designs is given, showing the wide range of available block sizes.
A Test for Normality Based on Sample Entropy
Authors: Vasicek Oldrich 
Published: December 2018

Summary
A test of the composite hypothesis of normality is introduced. The test is based on the property of the normal distribution that its entropy exceeds that of any other distribution with a density that has the same variance. The test statistic is based on a class of estimators of entropy constructed here. The test is shown to be a consistent test of the null hypothesis for all alternatives without a singular continuous part. The power of the test is estimated against several alternatives. It is observed that the test compares favourably with other tests for normality.
Estimation of the Second-Order Intensities of a Bivariate Stationary Point Process
Authors: Brillinger David R. 
Published: December 2018

Summary
We consider histogram and smoothed histogram type estimates of the auto and cross intensity functions of a bivariate stationary point process. The asymptotic distributions are found to be multiples of Poissons in the histogram case and linear combinations of Poissons in the smoothed case. These asymptotic distributions suggest the plotting of the square roots of the estimates in order to stabilize the variance and to make the distributions more nearly normal. Two examples of such plots are presented in the paper.
Forecasting Transformed Series
Authors: Granger C. W. J. , Newbold P. 
Published: December 2018

Summary
Suppose that a forecasting model is available for the process Xt but that interest centres on the instantaneous transformation Yt = T(Xt). On the assumption that Xt is Gaussian and stationary, or can be reduced to stationarity by differencing, this paper examines the autocovariance structure of and methods for forecasting the transformed series. The development employs the Hermite polynomial expansion, thus allowing results to be derived for a very general class of instantaneous transformations.
Sampling Theory for Opaque Spatial Specimens
Authors: Davy Pamela , Miles R. E. 
Published: December 2018

Summary
Procedures for inferring the internal geometric structure of an opaque bounded n-dimensional set by random sectioning are discussed. General conditions are given (evidently for the first time) for the validity of the so-called “fundamental formulae” of stereology (the science of inferring spatial structure from lower dimensional data). In technical terms, a wide class of unbiased ratio estimators, based on the traces of embedded features in appropriately weighted random sections, is presented.
Modelling Spatial Patterns
Authors: Ripley B. D. 
Published: December 2018

Summary
Spatial point processes may be analysed at two levels. Quadrat and distance methods were designed for the sampling of a population in the field. In this paper we consider those situations in which a map of a spatial pattern has been produced at some cost and we wish to extract the maximum possible information. We review the stochastic models which have been proposed for spatial point patterns and discuss methods by which the fit of such a model can be tested. Certain models are shown to be the equilibrium distributions of spatial–temporal stochastic processes. The theory is illustrated by several case studies.
A Large-Sample Test for Detecting Gaps in Moving Average Models
Authors: Godolphin E. J. 
Published: December 2018

Summary
A procedure is given in the paper for testing the hypothesis that a specified set of parameters in a moving average process assumes the value zero. In particular, the method is applicable for detecting whether a moving average process is seasonal or not. This large-sample test, which operates entirely in the time domain, is based on the estimated asymptotic covariance matrix of improved estimates of the autocorrelation function and is derived from the results of Walker (1961) and Godolphin (1977). The procedure is illustrated and compared favourably on the basis of test power with the identification approach of Box and Jenkins (1970).
A Scale-Free Goodness-Of-Fit Test for the Exponential Distribution Based on the Gini Statistic
Authors: Gail M. H. , Gastwirth J. L. 
Published: December 2018

Summary
The sample Gini index is shown to be a powerful scale-free test of exponentiality against a variety of alternatives. Compared to the maximum likelihood test, the asymptotic relative efficiency of the Gini statistic is 0·69 against gamma and 0·88 against Weibull alternatives. Exact and asymptotic distribution theory is developed. On the basis of good power compared to competing tests, ease of computation, availability of exact critical values and robustness to measurement error, we recommend the Gini statistic as a scale-free goodness-of-fit test for the exponential distribution.
Studies in the Robustness of Multidimensional Scaling: Procrustes Statistics
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 first paper is concerned to provide a simple but clear and convincing development of procrustes analysis, the technique used for assessing the goodness-of-fit between two configurations. Although some of the results offered are new, it is largely a review paper designed to provide a basis for further work
Comparison of Two Sequential Tests for Two-Sided Alternatives
Authors: Borgan Ørnulf 
Published: December 2018

Summary
Wald's method based on weight functions provides sequential tests for two-sided alternatives. In this paper, this method is compared with a test due to Sobel and Wald for three decision problems used for two-sided alternatives. The boundaries of acceptance and rejection of the tests are compared, and it is shown that for the usual choice of stopping bounds, the region of continued observation for Wald's test is included in that of Sobel and Wald's test. The difference between the region of rejection and acceptance of the two tests is also discussed.
Relative Curvature Measures of Nonlinearity
Authors: Bates Douglas M. , Watts Donald G. 
Published: December 2018

Summary
Simple relative curvature measures of nonlinearity are developed to measure the extent of the nonlinearity in a model-experimental design-parameterization combination. We review the geometric aspects of linear and nonlinear least squares and, using the geometric concept of curvature, compute the maximum relative intrinsic curvature of the solution locus as well as the maximum relative parameter-effects curvature. The relative curvatures are independent of scale changes of the data and of the parameters so they can be used to compare different data sets as well as different parameterizations of the same data set. The methods are applied to 24 published nonlinear data sets, and in all cases it is found that the intrinsic curvature is less than the parameter-effects curvature. The nonlinearity measures of Beale (1960) and the bias expressions developed by Box (1971) are shown to be related to the curvature measures.
A Simple Method for Testing Goodness of Fit in the Presence of Nuisance Parameters
Authors: Braun Henry 
Published: December 2018

Summary
This paper presents a method, based on the empirical distribution function, for testing goodness of fit (gf) under composite null hypotheses. After the unknown parameters are estimated from the entire data set, the procedure calls for the transformed sample to be randomly partitioned into a large number of groups, and a gf statistic calculated for each group. These statistics are used to construct a test which can attain, asymptotically, any desired level α, and which requires for its implementation only standard tables of critical values. The procedure is particularly recommended when an a priori grouping of the sample can be employed and, hence, heterogeneous alternatives are quite plausible. It is shown that, under these alternatives, the power of the procedure compares favourably with that of other methods.
Regression Models for Ordinal Data
Authors: McCullagh Peter 
Published: December 2018

Summary
A general class of regression models for ordinal data is developed and discussed. These models utilize the ordinal nature of the data by describing various modes of stochastic ordering and this eliminates the need for assigning scores or otherwise assuming cardinality instead of ordinality. Two models in particular, the proportional odds and the proportional hazards models are likely to be most useful in practice because of the simplicity of their interpretation. These linear models are shown to be multivariate extensions of generalized linear models. Extensions to non-linear models are discussed and it is shown that even here the method of iteratively reweighted least squares converges to the maximum likelihood estimate, a property which greatly simplifies the necessary computation. Applications are discussed with the aid of examples.
Bayes Factors and Choice Criteria for Linear Models
Authors: Smith A. F. M. , Spiegelhalter D. J. 
Published: December 2018

Summary
Global and local Bayes factors are defined and their respective roles examined as choice criteria among alternative linear models. The global Bayes factor is seen to function, in appropriate contexts, as a fully automatic Occam's razor and to be closely related to the Schwarz model choice criterion. The local Bayes factor is shown to have a close relationship with the Akaike Information Criterion.
The Distribution of Higher-Order Interactions in Contingency Tables
Authors: O'Neill M. E. 
Published: December 2018

Summary
Lancaster's definition of the absence of second-order interactions in contingency tables produces test statistics which have asymptotic ***x 2 distributions under complete independence, but not (in general) otherwise. This paper obtains the asymptotic distributions of all interaction components in the partitioning of Pearson's x 2, and indicates a test procedure for higher-order interactions when lower-order interactions are found to be significant.
The Effect of Survey Design on Regression Analysis
Authors: Nathan G. , Holt D. 
Published: December 2018

Summary
Data arising from sample surveys are usually the result of complex survey design involving such techniques as stratification, multistage selection and the use of auxiliary information through unequal probability selection. These resulting data are often analysed using regression techniques without further regard to the sample design. This paper shows that, in general, ordinary least squares (OLS) regression will be biased in this situation even for large samples, although in the important class of most epsem designs asymptotic unbiasedness of least squares estimation is preserved. Alternative estimators are considered which yield unbiased estimates of the simple regression coefficient. Variances of all the estimators are derived and comparisons made. The usual OLS estimator of variance is also examined and found to be biased in general, even when used in conjunction with an epsem design for which the OLS estimator itself is unbiased.
A Note on Limit Theorems for Joint Distributions with Applications to Linear Signed Rank Statistics
Authors: Fligner Michael A. 
Published: December 2018

Summary
When investigating the limiting joint distribution of a pair of random variables, it is possible to proceed by studying the associated marginal and conditional distributions. A useful extension of some previous work in this area of Sethuraman is presented by considering the important case when one is conditioning on a lattice-type random variable. The results are applied to obtain, in a simple manner, the limiting distribution of a linear-signed rank statistic.
Permutation Probabilities as Models for Horse Races
Authors: Henery R. J. 
Published: December 2018

Summary
Some properties of models for the outcomes of races are described, these properties being consequences of a stochastic ordering of the permutations which define the outcomes of a race. Order statistics models which lead to stochastic ordering are also discussed—particular cases of these are the first-order model of Plackett (1975) and the normal model of Upton and Brook (1974). An approximation for the normal model is suggested.
Lagrange-Multiplier Tests of Multivariate Time-Series Models
Authors: Hosking J. R. M. 
Published: December 2018

SUMMARY
Generalizing Hosking (1980a), the Lagrange-multiplier test procedure is applied to hypotheses concerning multivariate autoregressive moving-average time-series models. The portmanteau and Quenouille goodness-of-fit tests for multivariate processes are derived in this manner and three other tests are obtained for multivariate moving-average models.
Distribution of the Residual Autocorrelations in Multivariate Arma Time Series Models
Authors: Li W. K. , McLeod A. I. 
Published: December 2018

SUMMARY
The large-sample distribution of the multivariate residual autocorrelations in the vector arma model is derived. This result is somewhat less complicated for the vector autoregressive model. A new multivariate portmanteau test for checking the adequacy of fitted vector arma models is developed. A simulation study shows that a simple modification of the portmanteau test improves its accuracy in small samples.
Multivariate Linear Relationships: Maximum Likelihood Estimation and Regression Bounds
Authors: Patefield W. M. 
Published: December 2018

Summary
The well known result that, when the ratio of error variances is specified in normal theory bivariate linear relationships, the maximum likelihood estimator of the slope parameter takes the same form for both structural and functional relationships is extended to the multivariate case. Furthermore, it is well known that in the bivariate case the estimator of the slope is bounded by the two regression estimators. Analogous results are derived for the multivariate case.
The asymptotic variance–covariance matrix of the maximum likelihood estimators of the coefficients of a multivariate linear relationship is determined, and an estimator of this matrix is proposed. Large sample confidence regions for the parameters are formulated and the relationship between these and normal theory regression confidence regions is discussed.
Regression Diagnostics, Transformations and Constructed Variables
Authors: Atkinson A. C. 
Published: December 2018

Summary
Two diagnostic displays for outlying and influential observations in multiple regression are reviewed. In some examples apparent outliers vanish after transformation of the data. Interpretation of the score statistic for transformations as regression on a constructed variable leads to partial residual plots for transformations and makes the two diagnostic displays available for detection of the influence of individual observations on the evidence for a transformation. Two forms of the partial residual plot are compared. A quick estimate of the transformation parameter is derived. This is shown to have poor properties and a superior sequence of estimates is found. The plots and estimates are studied for several examples using the power transformation for non-negative observations. The corresponding theory is developed for a “folded” transformation for proportions and percentages and an example given. The relationship with other constructed variables is explored, especially Tukey's one degeee of freedom for non-additivity. Pregibon's link test for generalized linear models is interpreted in terms of constructed variables and plots given for an example. This leads to the choice between two separate models for which a graphical Monte-Carlo procedure is suggested.
On Unequal Probability Sampling of Two Units Without Replacement
Authors: Agarwal S. K. , Kumar Pranesh , Dey A. 
Published: December 2018

Summary
A general class of unequal probability sampling schemes for selecting two units without replacement is given. Many known sampling schemes are shown to be members of this class. It is shown that for any member of this class, the Yates-Grundy estimator of variance of the Horvitz-Thompson estimator is always positive.
Finding the Observed Information Matrix When Using the EM Algorithm
Authors: Louis Thomas A. 
Published: December 2018

Summary
A procedure is derived for extracting the observed information matrix when the EM algorithm is used to find maximum likelihood estimates in incomplete data problems. The technique requires computation of a complete-data gradient vector or second derivative matrix, but not those associated with the incomplete data likelihood. In addition, a method useful in speeding up the convergence of the EM algorithm is developed. Two examples are presented.
Non-Parametric Bayesian Models for Samples from Finite Populations
Authors: Binder David A. 
Published: December 2018

Summary
Using Ferguson's (1973) non-parametric priors in a Bayesian analysis of finite populations, we show that asymptotically, at least, the usual estimates and confidence intervals for the population mean in simple and stratified random samples can be justified in Bayesian terms. We then apply these models for estimating population percentiles, and a new procedure for interval estimates in stratified sampling is developed.
Kernel-Based Density Estimates from Incomplete Data
Authors: Titterington D. M. , Mill G. M. 
Published: December 2018

SUMMARY
The problem of using non-parametric methods to estimate multivariate density functions from incomplete continuous data does not appear to have been considered before. Methods of producing kernel functions on incomplete observations are suggested involving averaging over the missing variables or substitution of them by simulated values. Consistency of the procedures in terms of integrated mean squared error is investigated and optimal choice of smoothing parameter is discussed. Application in terms of imputation for missing values is discussed.
A Kth Nearest Neighbour Clustering Procedure
Authors: Wong M. Anthony , Lane Tom 
Published: December 2018

Summary
Due to the lack of development in the probabilistic and statistical aspects of clustering research, clustering procedures are often regarded as heuristics generating artificial clusters from a given set of sample data. In this paper, a clustering procedure that is useful for drawing statistical inference about the underlying population from a random sample is developed. It is based on the uniformly consistent kth nearest neighbour density estimate, and is applicable to both case-by-variable data matrices and case-by-case dissimilarity matrices. The proposed clustering procedure is shown to be asymptotically consistent for high-density clusters in several dimensions, and its small-sample behaviour is illustrated by an empirical example.
Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin
Authors: Cheng R. C. H. , Amin N. A. K. 
Published: December 2018

Summary
A general method of estimating parameters in continuous univariate distributions is proposed. It is especially suited to cases where one of the parameters is an unknown shifted origin. This occurs, for example, in the three-parameter lognormal, gamma and Weibull models. For such distributions it is known that maximum likelihood (ML) estimation can break down because the likelihood is unbounded and this can lead to inconsistent estimators. Properties of the proposed method are described. In particular it is shown to give consistent estimators with asymptotic efficiency equal to ML estimators when these exist. Moreover it gives consistent, asymptotically efficient estimators in situations where ML fails. Examples are given including numerical ones showing the advantages of the method.