bluuebunny/crossref_metadata_2025_split huggingface dataset:
Nonparametric Analysis of Covariance with Ordered Alternatives
Authors: Marcus Ruth , Genizi Abraham 
Published: December 2018

SUMMARY
The problem of comparing k populations with respect to a univariate response variable Y against an ordered alternative is considered when a covariate X is taken into account using the matched-observations method of Quade (1982). Two test statistics are considered: one is Quade's statistic generalized for arbitrary k and the second is the Terpstra-Jonckheere statistic generalized for grouped data. Some simulations are carried out to study their small sample performance for different distributions of Y and X and for different sizes of the matched-observations classes. Finally, a general method of devising stepwise multiple testing procedures with fixed experiment wise error is applied to our problem of nonparametric analysis of covariance with ordered alternatives. An example of a neighbouring plots model is reanalyzed.
The Efficiency Factors of Particular Effects in Designs with Orthogonal Factorial Structure
Authors: Paterson L. J. 
Published: December 2018

SUMMARY
We investigate partial confounding which is not necessarily orthogonal to blocks. The efficiency factor of a main effect or interaction is related to the numbers of paths of a certain type in the treatment concurrence graph. From this we can derive combinatorial principles that help find designs with large efficiency factor for the effect or interaction. The principles are heuristically cogent and convenient, and are a natural generalisation of existing practice. Some illustration is given of their value in finding good generalised-cyclic designs.
On the Optimality of Some Tests of the Error Covariance Matrix in the Linear Regression Model
Authors: Honda Yuzo 
Published: December 2018

SUMMARY
This paper adopts the approach of conditional distributions to investigate the optimality of some tests of the error covariance matrix in the linear regression model. Specifically, we show that point optimal tests, advocated by King and Evans and King, are the most powerful similar test. We also derive the locally best similar and the locally best unbiased similar tests. Finding the latter cumbersome to apply, we then propose the asymptotically best similar and the asymptotically best unbiased similar (ABUS) tests as alternative criteria. We show that the two-sided Durbin–Watson test is ABUS against serial correlation and that the two-sided Lagrange multiplier test is ABUS against heteroscedastic disturbances.
Recursive Estimation of Autoregressions
Authors: Hannan E. J. , McDougall A. J. , Poskitt D. S. 
Published: December 2018

SUMMARY
This paper is concerned with the recursive estimation of autoregressive models, in particular the realtime determination of the order of such a specification. A model selection criterion based on the minimum description length principle due to Rissanen is discussed and strong consistency in the stationary situation is shown. Alternative criteria are also considered and modifications required to introduce forgetting when the procedures are implemented in the non-stationary case are presented. Some simulation evidence on the performance of the criteria when applied to stationary and non-stationary processes is given.
Median Estimation in the Presence of Auxiliary Information
Authors: Kuk Anthony Y. C. , Mak T. K. 
Published: December 2018

SUMMARY
This paper deals with the estimation, under simple random sampling, of a finite population median in the presence of an auxiliary variable. An estimator which is a simple modification of the ratio estimator for the mean is studied along with two other proposed estimators derived from a different approach. These estimators are applicable in situations where only the population median or a grouped frequency distribution of the auxiliary variable is known. On the basis of the asymptotic properties derived and some simulation results, the efficiencies of these estimators are compared. It is shown that the two estimators proposed, unlike that obtained from modifying the ratio estimator, always dominate the sample median in mean-squared error and that their efficiencies depend directly on the probability of ‘concordance’ rather than on the validity of a linearity assumption between the survey variable and the auxiliary variable. When the linearity assumption is approximately satisfied, the three estimators are seen to have comparable efficiencies, while the modified ratio estimator is found to be quite sensitive to departures from the linearity assumption.
On Substantive Research Hypotheses, Conditional Independence Graphs and Graphical Chain Models
Authors: Wermuth Nanny , Lauritzen Steffen Lilholt 
Published: December 2018

SUMMARY
Graphs consisting of points, and lines or arrows as connections between selected pairs of points, are used to formulate hypotheses about relations between variables. Points stand for variables, connections represent associations. When a missing connection is interpreted as a conditional independence, the graph characterizes a conditional independence structure as well. Statistical models, called graphical chain models, correspond to special types of graphs which are interpreted in this fashion. Examples are used to illustrate how conditional independences are reflected in summary statistics derived from the models and how the graphs help to identify analogies and equivalences between different models. Graphical chain models are shown to provide a unifying concept for many statistical techniques that in the past have proven to be useful in analyses of data. They also provide tools for new types of analysis.
Score Tests in Generalized Linear Measurement Error Models
Authors: Stefanski Leonard A. , Carroll Raymond J. 
Published: December 2018

SUMMARY
Hypothesis tests in generalized linear models are studied under the condition that a surrogate w is observed in place of the true predictor x. The efficient score test for the hypothesis of no association depends on the conditional expectation E(x|w) which is generally unknown. The usual test substitutes w for E(x|w) and is asymptotically valid but not efficient. We investigate two new test statistics appropriate when w = x + z where z is an independent measurement error. The first is a Wald test based on estimators corrected for measurement error. Despite the correction for attenuation in the estimator, this test has the same local power as the usual test. The second test employs an estimator of E(x|w) and is both asymptotically efficient for normal errors and approximately efficient when the measurement error variance is small.
Strata for Randomized Experiments
Authors: Bailey R. A. 
Published: December 2018

SUMMARY
Fisher argued that, for completely randomized designs, block designs and Latin square designs, his proposed randomization justified his proposed analysis of variance in that the latter gives valid estimates of experimental error even under very weak assumptions about the plot effects. In the succeeding 50 years a large number of more complicated experimental structures has been proposed and used. Randomization of these structures is rarely discussed in more than a cursory way, and its relationship with the analysis is mentioned even less frequently. Here I show that Fisher's ideas on validity and randomization may be set in a symmetry framework. Randomization is done by permuting the plot names, and that randomization procedure is used to justify the assumption of a relatively simple model for plot effects. Permutations are chosen at random from a specified permutation group. Except in the simplest cases, determination of the strata for the analysis of variance needs some knowledge of group theory. The relevant results from group theory are presented, together with some straightforward techniques which depend on them. The strata are then found for many large classes of examples, including the majority of experimental structures in current use.
Posterior Bayes Factors
Authors: Aitkin Murray 
Published: December 2018

SUMMARY
A general procedure for computing Bayes factors for the comparison of arbitrary models is described, based on the use of the posterior mean of the likelihood under each model rather than the usual prior mean. The use of the posterior mean has several advantages, including reduced sensitivity to variations in the prior and the avoidance of the Lindley paradox in testing point null hypotheses. The frequency properties of the new procedure are evaluated in standard examples, and a non-standard example is analysed to show the considerable differences possible between prior and posterior means of the likelihood. Several different justifications of the procedure are given, and a non-Bayesian direct likelihood interpretation is described.
Grouped Likelihood for the Shifted Power Transformation
Authors: Atkinson Anthony C. , Pericchi Luis R. , Smith Richard L. 
Published: December 2018

SUMMARY
Estimation of parameters is considered in the shifted power transformation family of models. The ordinary likelihood function is shown to behave poorly, often having no local maximum. It is argued that a grouped likelihood approach avoids these difficulties, and the practical implementation of this approach is considered. Bayesian inference is also considered, though more briefly, and it is argued that there are again difficulties with an ungrouped likelihood approach. The results provide further evidence of the utility of grouped likelihood approaches to inference in non-regular problems.
On the Relationship between Bayesian and Non-Bayesian Interval Estimates
Authors: Severini Thomas A. 
Published: December 2018

SUMMARY
Let Y 1, ..., Y n denote independent observations each distributed according to a density depending on a scalar parameter θ. Suppose that we are interested in constructing an interval estimate for 0. One approach is to construct a confidence region with a specified coverage probability based on the likelihood ratio test statistic. Another approach is to construct a highest posterior density region with a specified posterior probability. The goal of this paper is to study the relationship between these two approaches. In particular, we derive asymptotic expansions for the posterior probability of confidence regions based on the likelihood ratio test statistic and for the coverage probability of highest posterior density regions. Conditions under which the two methods lead to identical regions, at least approximately, are also given.
Testing Exponentiality Based on Kullback-Leibler Information
Authors: Ebrahimi Nader , Habibullah Mohamed , Soofi Ehsan S. 
Published: December 2018

SUMMARY
In this paper a test of fit for exponentiality based on the estimated Kullback-Leibler information is proposed. The procedure is applicable when the exponential parameter is or is not specified under the null hypothesis. The test uses the Vasicek entropy estimate, so to compute it a ‘window size’ m must first be fixed. A procedure for choosing m for various sample sizes is proposed and corresponding critical values are computed by Monte Carlo simulations. The use of the proposed test is shown in an illustrative example. Also, by means of Monte Carlo simulations, the power of the proposed test under various alternatives is compared with that of other standard tests. The results are impressive and the proposed test, almost always, has higher power than that of the other tests considered.
Non-Homogeneous Autoregressive Processes for Tracking (Software) Reliability Growth, and Their Bayesian Analysis
Authors: Singpurwalla Nozer D. , Soyer Refik 
Published: December 2018

SUMMARY
We motivate a non-homogeneous autoregressive process as a model for reliability growth and consider two formulations, both Bayesian, which alleviate a limitation that least squares estimators for such processes of order greater than 1 exist only when repeated measurements of the time series are available. In one formulation, the prior assumption involves exchangeability of coefficients, whereas in the other an autoregressive structure is imposed on them. Both formulations enable us to cast the resulting processes in state space form for which the Kalman filter algorithm can be used. The first formulation involves an adaptation of standard techniques whereas the second results in a new methodology for adaptive filtering which is facilitated by an approximation due to Lindley. The procedures are demonstrated via a consideration of some data on software failures.
On a Kernel Approach to a Screening Problem
Authors: Boys Richard J. 
Published: December 2018

SUMMARY
Screening methods are developed which raise the proportion of individuals possessing an attribute in the retained population to a predetermined level. A specification region for the screening variable is derived by using a kernel smoothing approach. The sensitivity of the procedure is assessed within a range of parametric models. Comparisons are also made with empirical and estimative solutions. The kernel method is illustrated by an example of screening within a medical context.
An Exact Cholesky Decomposition and the Generalized Inverse of the Variance–Covariance Matrix of the Multinomial Distribution, with Applications
Authors: Tanabe Kunio , Sagae Masahiko 
Published: December 2018

SUMMARY
A symbolic formula is given for the square-root-free Cholesky decomposition of the variance–covariance matrix of the multinomial distribution. The evaluation of the symbolic Cholesky factors requires much fewer arithmetic operations than does the general Cholesky algorithm. Since the symbolic formula is not affected by an ill-conditioned matrix, it is particularly useful when the elements of a probability vector are of quite different orders of magnitude. A simpler formula is obtained for Pederson's procedure of sampling from a multinomial population. An explicit formula of the Moore–Penrose inverse of the variance–covariance matrix is given as well as a symmetric representation of a multinomial density approximation to the multinomial distribution. These formulae facilitate symmetric manipulation of the matrix and are useful in statistical modelling and computation involving the logistic density transformation of the multinomial distribution and in computer simulations of dynamic models in population genetics. Each element of the Cholesky factors is given interesting probabilistic interpretations.
Local Lyapunov Exponents: Looking Closely at Chaos
Authors: Wolff Rodney C. L. 
Published: December 2018

SUMMARY
When a deterministic mechanism gives rise to an erratic time series, then under certain conditions the series is said to exhibit chaos. The catalogue of statistical methods for the analysis of time series is being augmented currently by methods for the detection and quantification of deterministic chaos. A hallmark of chaos is the tendency of nearby trajectories to diverge in the short term. A measure of the average rate of exponential divergence exhibited by a chaotic system is given by the Lyapunov exponents of that system; the values of such exponents can suggest the presence of chaos. In this paper, we give a brief exposition of a finite time version of the Lyapunov exponent which is state dependent, and to which we attach the epithet ‘local'. The local Lyapunov exponent is shown to be able to detect non-linearity in some cases, and to have other qualitative features. As defined, its success is limited, but this does not preclude its usefulness as a diagnostic tool.
Chance and Chaos in Measles Dynamics
Authors: Grenfell B. T. 
Published: December 2018

SUMMARY
This paper examines the impact of seasonality and chaotic dynamics in simple models for the population dynamics of measles on the probability of fade-out of infection. It uses Monte Carlo simulations of the seasonally forced SEIR model, with parameters appropriate to a city of 1 million people. The incidence of fade-out in a spatially homogeneous model is compared with simple spatial models involving various degrees of coupling between subareas. The results indicate a significant degree of fade-out of infection, which is not consistent with previously derived criteria for the persistence of measles. Lowering the degree of spatial coupling does not substantially reduce the extent of fade-out. A simple non-linear analysis of the simulated series is presented, and the epidemiological implications of these results are discussed.
Estimation of Parameters in Heteroscedastic Linear Models
Authors: Mak Tak K. 
Published: December 2018

SUMMARY
This paper deals with linear regression models with non-homogeneous error variances. The common situation where the error variance is a smooth function of the values of the regressor variables is considered. The error variance function is represented by a function of known form, but its expression involves the vector of unknown regression coefficients β and an additional vector parameter θ. Estimation of β by iterative weighted least squares (IWLS) therefore also requires updating the estimate of θ at each iteration. When the error variance function is misspecified, different methods of updating θ would yield IWLS estimators of varying degrees of efficiency. Under such situations, a method of updating θ is proposed, resulting in an iterative procedure for estimating β that is asymptotically optimal in the class of IWLS estimators. When the form of the error variance function is correctly specified, the estimation procedure proposed is asymptotically equivalent to weighted least squares with known optimal weights. A real example of its application is given and the extension to general non-linear models is briefly indicated.
Log-Linear Models for Survey Data with Non-Ignorable Non-Response
Authors: Chambers R. L. , Welsh A. H. 
Published: December 2018

SUMMARY
We demonstrate the feasibility of constructing, interpreting and fitting computable log-linear models to categorical survey data with arbitrary non-nested patterns of non-ignorable non-response. Under our approach, the non-response probability for each cell of the classification defined by the categories of interest is modelled separately from the classification probability itself, and we adopt a model formulation which allows the non-response model to depend on scores, discrete covariates, continuous covariates or a mixture of types of covariate. We obtain explicit expressions for the score and information functions generated by the observed data which allow us to compute approximate standard errors and test statistics based on these functions. Through illustrative examples we quantify the fact that inferences obtained from different non-ignorable non-response models can vary considerably. This lends support to the calls in the literature for caution in using such models.
Large Sample Theory of Spacings Statistics for Tests of Fit for the Composite Hypothesis
Authors: Wells Martin T. , Jammalamadaka S. Rao , Tiwari Ram C. 
Published: December 2018

SUMMARY
Let X 1,…, Xn be a sequence of independent and identically distributed random variables with an unknown underlying continuous cumulative distribution function F. Often we would like to test a null hypothesis concerning the goodness of fit of F to some distribution function which is fully specified or belongs to some parametric family, i.e. in some applications the null hypothesis is simple whereas in others it may be composite. In this paper we present the large sample theory of tests based on non-symmetric functions of sample spacings under composite null hypotheses as well as under contiguous alternatives. Goodness-of-fit tests which are optimal within this class are constructed.
On Edgeworth Expansion and Bootstrap Confidence Bands in Nonparametric Curve Estimation
Authors: Hall Peter 
Published: December 2018

SUMMARY
The notion of pivoting and techniques of Edgeworth expansion have become basic tools for using and understanding bootstrap methods in finite parameter problems. This paper shows that these ideas have important contributions to make to infinite parameter problems, e.g. in the construction of simultaneous confidence bands for nonparametric density estimators. We propose a bootstrap method for confidence band construction based on a pivotal function estimator and illustrate its use. We give an Edgeworth expansion argument which demonstrates the efficacy of the technique. The expansion is a power series in {(nh)-1(log h -1)3}1/2. where n is the sample size and h denotes the bandwidth. This should be compared with a power series in n -1/2 in more conventional, finite dimensional problems.
Modelling Variance Heterogeneity: Residual Maximum Likelihood and Diagnostics
Authors: Verbyla A. P. 
Published: December 2018

SUMMARY
The assumption of equal variance in the normal regression model is not always appropriate. to attempt to eliminate unequal variance a transformation is often used but if the transformation is not successful, or the variances are of intrinsic interest, it may be necessary to model the variances in some way. We consider the normal regression model when log-linear dependence of the variances on explanatory variables is suspected. Detection of the dependence, estimation and tests of homogeneity based on full and residual maximum likelihood are discussed as are regression diagnostic methods based on case deletion and log-likelihood displacement. Whereas the behaviour of full and residual maximum likelihood is similar under case deletion, changes in residual maximum likelihood estimates and log-likelihood displacements tend to be smaller than maximum likelihood.
Dynamic Hierarchical Models
Authors: Gamerman Dani , Migon Hélio S. 
Published: December 2018

SUMMARY
An analysis of a time series of cross-sectional data is considered under a Bayesian perspective. Information is modelled in terms of prior distributions and stratified parametric linear models developed by Lindley and Smith and dynamic linear models developed by Harrison and Stevens are merged into a general framework. This is shown to include many models proposed in econometrics and experimental design. Properties of the model are derived and shrinkage estimators reassessed. Evolution, smoothing and passage of data information through the levels of the hierarchy are discussed. Inference with an unknown scalar observation variance is drawn and an extension to the non-linear case is proposed.
On the Behaviour of Wald Statistics for the Disjunction of Two Regular Hypotheses
Authors: Glonek G. F. V. 
Published: December 2018

SUMMARY
Occasionally hypotheses arise which, although not themselves regular, have the logical structure of the disjunction of two, or in general several, regular hypotheses. An example of such a hypothesis is that of collapsibility in a three-way contingency table as defined by Whittemore. When such a hypothesis is to be tested, a Wald test appears, superficially, to offer a convenient solution. However, closer inspection reveals that the irregularity intrinsic to such problems precludes the regularity conditions required for the valid construction of a Wald test statistic. The purpose of this paper is to describe explicitly the nature of the irregularity and its effect on the asymptotic behaviour of the Wald test statistic.