bluuebunny/crossref_metadata_2025_split huggingface dataset:
Two Mann-Whitney Type Rank Tests
Authors: Eplett W. J. R. 
Published: December 2018

Summary
Two Mann-Whitney type rank tests are introduced and their test statistics related to the test statistics of the Smirnov tests. The null distributions of the test statistics are studied both for small sample sizes and in terms of limiting distributions. A lower bound for the power of these tests is obtained. Monte Carlo methods are employed to assess the power of the tests against competitors; the Mann-Whitney type tests perform well. Bahadur efficiency is also used to assess the performance of the tests. Their efficiency properties are good.
Belief Functions and Parametric Models
Authors: Shafer Glenn 
Published: December 2018

Summary
The theory of belief functions assesses evidence by fitting it to a scale of canonical examples in which the meaning of a message depends on chance. In order to analyse parametric statistical problems within the framework of this theory, we must specify the evidence on which the parametric model is based. This article gives several examples to show how the nature of this evidence affects the analysis. These examples also illustrate how the theory of belief functions can deal with problems where the evidence is too weak to support a parametric model.
The Distributions of Smirnov Type Two-Sample Rank Tests for Discontinuous Distribution Functions
Authors: Eplett W. J. R. 
Published: December 2018

Summary
An important area of application for rank tests occurs when there are ties in the data which may happen when the observations are drawn from a discrete population or are grouped. The standard theory for the two-sample Smirnov test as to whether two samples have been drawn from the same population assumes continuous distributions in which case ties only arise with probability zero. The null distribution of the test statistic for large sample sizes is obtained here for discontinuous distributions. Since this depends upon the (unknown) population distribution a procedure for estimating the null probabilities is discussed. One application of the resulting test is for testing association in a 2 × C contingency table for ordinal data when there is a large total entry, but several cells have small entries. The distribution of a competitor to the Smirnov test introduced by the author is also discussed in the case of discontinuous distribution functions.
Bayes Factors for Linear and Log‐Linear Models with Vague Prior Information
Authors: Spiegelhalter D. J. , Smith A. F. M. 
Published: December 2018

SummaryThe Bayes factor, or integrated likelihood ratio, provides a possible Bayesian alternative to the standard F‐test procedure for comparing two linear models. However, if vague prior information for the model parameters is represented by limiting improper prior forms, it is well known that the resulting Bayes factor involves an arbitrary, unspecified constant, and is thus not well defined. A method of assigning this constant is proposed and illustrated for a number of standard problems. The approach is then extended to the analysis of contingency tables using log‐linear models.
Transient Behaviour of the Interrupted Poisson Process
Authors: Milne Claire 
Published: December 2018

Summary
Kuczura (1973) introduced the use of the Interrupted Poisson Process (IPP) as a simplified model for overflow telephone traffic, and derived some of its equilibrium properties. This paper presents the time-dependent factorial-moment generating function for the IPP. From this function are derived the joint moments of the numbers of calls in progress at any number of instants in time. In particular, the covariance of the numbers of calls in progress at any two instants leads to a formula for the variance of scan-measured traffic. The results make it possible to calculate the moments of various estimators of the variance of traffic.
The paper also gives a new decomposition of interarrival times, and displays one limiting form of the IPP as a batch arrival process with geometrically distributed number of arrivals per batch.
All these results are of perfectly general applicability. They add to the repertory of analytically tractable queuing processes. Likely fields of application are sickness insurance, equipment maintenance, transportation, neurophysiology and nuclear physics.
Bivariate Cox Processes: Some Models for Bivariate Spatial Point Patterns
Authors: Diggle Peter J. , Milne Robin K. 
Published: December 2018

SUMMARY
From certain points of view, the range of probability models currently available for describing the joint behaviour of two point processes is rather limited. In this paper we explore the structure of some further models and apply our results to the statistical analysis of bivariate spatial point patterns.
The One-Sided Lagrange Multiplier Test of the AR (p) Model vs the AR (p) Model with Measurement Error
Authors: Tanaka Katsuto 
Published: December 2018

SUMMARY
The one-sided Lagrange multiplier test is suggested for testing the null autoregressive (AR) model against the AR model with measurement error. The test statistic is shown to be asymptotically N(0, 1) under the null. Finite sample properties of the test both under the null and under the alternative are examined briefly by simulations.
Serial Dependence in Contingency Tables
Authors: Tavaré Simon 
Published: December 2018

SUMMARY
A simple and useful representation is given for the asymptotic behaviour of the Pearson χ 2 test of independence in two-way contingency tables. This is used to analyse the statistic when the data are generated by Markov chains. A robustness result, showing when the Markov dependence has no effect on the usual limiting χ2 distribution, is also given.
On Estimating Time Series Parameters Using Sample Autocorrelations
Authors: Kabaila Paul 
Published: December 2018

SUMMARY
Consider a scalar linear process {xt} whose spectral density is σ 2 k(λ, θ 0) where σ2 is the innovation variance and k(⋅,θ0)∈{k(⋅,θ):θ∈S⊂ℝq}. We introduce a class of estimators of θ0 based only on the sample autocorrelations. These estimators are shown to be consistent and asymptotically normally distributed with a covariance matrix which is independent of the distributions of the innovations. A lower bound to the asymptotic covariances of these estimators is derived and is shown to be achieved by the least-squares estimator. We also consider the extent to which these results generalize to the multivariate case. In particular, we present a multivariate generalization of the main result presented by Kabaila (1980).
Sequential Estimation Saving Sampling Operations
Authors: Hall Peter 
Published: December 2018

SUMMARY
A method is proposed for accelerating the sequential estimation procedure due to Anscombe, Chow and Robbins. It enables the number of sampling operations to be reduced by any predetermined factor, at the expense of only a slight increase in the expected sample size. The large sample theory is outlined, and some numerical computations provided to demonstrate the practicality of the procedure for smaller samples.
An Exact Test on the Goodman–Kruskal λ for Prediction on a Dichotomy
Authors: Turek Richard J. , Suich Ronald C. 
Published: December 2018

Summary
Goodman and Kruskal (1954) introduced a measure λ of predictive association when predicting the category of a variable B from a category of a variable A. The measure λ is such that 0 ≤ λ ≤ 1 with a zero value meaning no predictive gain while λ = 1 indicates a perfect predictive association between A and B. Thus, the test of H 0: λ = 0 versus H 1: λ &gt; 0 is of prime importance, since it is entirely analogous to a test for significance of regression or correlation. We present an exact test, developed through a reparameterization scheme, of the above hypothesis when B is dichotomous. The testing procedure is quite simple, requiring few calculations. In addition, this paper presents the method of calculation of power for any point in the resulting parameter space and relates the power to the original parameter λ.
Improving the Precision of Estimation by Fitting a Model
Authors: Altham P. M. E. 
Published: December 2018

SUMMARY
Suppose we have a random sample of size n from a distribution with parameters (p l, …,pk) Then, for large n, if (p 1,…, pk) satisfy any model ω of dimension less than k, any function of (p 1, …, pk) can be estimated more precisely by using this model than by using the general model with all k parameters. This result will not be at all surprising to experienced statisticians, but a formal statement and proof of it should be useful in teaching prospective statisticians.
A Note on Least-Squares Approximation in the Bayesian Analysis of Regression Models
Authors: Mouchart M. , Simar L. 
Published: December 2018

SUMMARY
Least-Squares approximation of the parameters in a regression model are worked out in a Bayesian framework and shown to provide, at a low computational cost, a setup to handle non-normal models and/or non-natural conjugate prior distributions. This allows one to balance an approximate solution to a reasonable model against an exact solution to a simplified model.
Iteratively Reweighted Least Squares for Maximum Likelihood Estimation, and Some Robust and Resistant Alternatives
Authors: Green P. J. 
Published: December 2018

SUMMARY
The scope of application of iteratively reweighted least squares to statistical estimation problems is considerably wider than is generally appreciated. It extends beyond the exponential-family-type generalized linear models to other distributions, to non-linear parameterizations, and to dependent observations. Various criteria for estimation other than maximum likelihood, including resistant alternatives, may be used. The algorithms are generally numerically stable, easily programmed without the aid of packages, and highly suited to interactive computation.
Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models
Authors: Davis M. H. A. 
Published: December 2018

SUMMARY
A general class of non-diffusion stochastic models is introduced with a view to providing a framework for studying optimization problems arising in queueing systems, inventory theory, resource allocation and other areas. The corresponding stochastic processes are Markov processes consisting of a mixture of deterministic motion and random jumps. Stochastic calculus for these processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper. The relevance of the extended generator concept in applied problems is discussed and some recent results on optimal control of piecewise-deterministic processes are described.
Sensitivity of Principal Components
Authors: Krzanowski W. J. 
Published: December 2018

SUMMARY
Simple analytical expressions are derived for the maximum changes in the coefficients of any principal component that are associated with a given (small) change in the variance of the component. This enables a sensitivity analysis to be conducted simultaneously with any principal component analysis, to investigate the stability of the derived components. This has implications for the interpretation of any set of components. A brief illustration is provided, and possible extensions to other multivariate techniques are outlined.
Some Methods of Inclusion Probability Proportional to Size Sampling
Authors: Nigam A. K. , Kumar Pranesh , Gupta V. K. 
Published: December 2018

SUMMARY
This article proposes a sampling scheme which involves creating a sampling design to ensure inclusion probability proportional to size selection. The sampling design is created through constructing a sample space in which the population units occur in proportion to their sizes and every pair of units occurs in such a way as to provide a non-negative and stable variance estimator. The selection procedure is then extremely simple and the values of the inclusion probabilities of pairs of units can be computed easily. The methods of constructing the sample space are demonstrated through typical examples.
Group Sequential Sampling with Variable Group Sizes
Authors: Hayre Lakhbir S. 
Published: December 2018

SUMMARY
In applications of sequential methods, it is often advantageous from a practical point of view to sample in bulk, or groups, rather than one at a time. We propose and study two adaptive methods of choosing the group size at each stage. These attempt to reach the stopping boundaries in as few groups as possible, but without overshooting the boundary by too much. Simulation results for the SPRT for a normal mean show that the methods work very well, requiring only a few groups to cross the boundary and leading to only a moderate increase in sample size Some asymptotic results are also given for the two methods.
Variance Component Models with Binary Response: Interviewer Variability
Authors: Anderson Dorothy A. , Aitkin Murray 
Published: December 2018

SUMMARY
Interviewer variability in a binary response is an example of a problem requiring variance component estimation in a non-normal family. The maximum likelihood estimation procedure is derived and used to examine some binary items on a large questionnaire. This raises some interesting questions about the use of unbalanced ANOVA methods with these data.
Maximum Likelihood Estimation of the Lower Tail of a Probability Distribution
Authors: Smith Richard L. , Weissman Ishay 
Published: December 2018

SUMMARY
We consider the estimation of the three parameters of the lower tail of a distribution function based on the k smallest out of n observations. The likelihood function has a singularity but it is argued that a local maximum, when it exists, should be taken as the m.l.e. Asymptotic results as k → ∞, n → ∞, k/n → 0 show that such a local maximum does exist, and provides consistent estimators whenever the shape parameter is greater than one; otherwise there is no local maximum and likelihood inference fails. We also discuss interval estimation and propose a test to distinguish between the Type I and Weibull limit laws.
Spherical Medians
Authors: Fisher N. I. 
Published: December 2018

SUMMARY
Spherical analogues of the linear and spatial medians are proposed for unimodal, bipolar axial and girdle distributions on the sphere. For unimodal data, the statistical properties of the sample spherical median direction are studied, including comparison with the sample mean direction in the case of Fisher's distribution. Spherical analogues of the one- and k-sample sign test are suggested. The paper parallels the discussion by Brown (1983) for the spatial median.
Bounds on Reciprocal Moments with Applications and Developments in Stein Estimation and Post-Stratification
Authors: Wooff David A. 
Published: December 2018

SUMMARY
Bounds on the kth reciprocal moment of a distribution are given in terms of the mean, variance and left extremity of the distribution. A methodology for obtaining distribution-specific bounds, with improved accuracy, is outlined. Some natural approximations are noted. Applications are given in Stein estimation, and in classical and Bayesian post-stratification.
On the Polynomial Functional Relationship
Authors: Chan Lai K. , Mak Tak K. 
Published: December 2018

SUMMARY
A method for obtaining consistent estimators of the coefficients in a polynomial functional relationship model with normal errors is proposed when the error covariance matrix is either completely known or known up to a proportionality factor. For quadratic functional relationships with possibly non-normal errors, we present a consistent estimator when the error covariance matrix is known. A large sample test of the quadratic against the linear functional relationship is also suggested in this case.
Asymptotic Expansions for Confidence Limits in the Presence of Nuisance Parameters, with Applications
Authors: Peers H. W. , Iqbal Mohammad 
Published: December 2018

SUMMARY
Series expansions for confidence limits based on consistent estimators are obtained in the presence of nuisance parameters. The maximum likelihood estimator is treated as a special case and the necessary characteristics of its sampling distribution are obtained in terms of basic quantities derivable from the likelihood function. The theory is applied to the problem of setting separate confidence limits for the scale and shape parameters of the Weibull distribution. Comparisons are made with earlier simulation studies.
Fitting Logistic Models Under Case-Control or Choice Based Sampling
Authors: Scott A. J. , Wild C. J. 
Published: December 2018

SUMMARY
There has been a great deal of interest in recent years in fitting logistic and log-linear models to tables of population counts estimated from survey data. Since maximum likelihood methods are not available in general for complex survey designs, most work has concentrated on adapting standard methods developed for multinomial sampling. Maximum likelihood methods have been developed for some special designs, however, and we might expect ad hoc methods to be less efficient in these cases. We compare the two approaches in the important special case of fitting logistic regression models under case-control or choice-based sampling, where the population is stratified by values of the (categorical) response variable.
A Test of Exponentiality Vs. Monotone-Hazard Alternatives Derived from the Empirical Characteristic Function
Authors: Epps T. W. , Pulley L. B. 
Published: December 2018

SUMMARY
A test of exponentiality is proposed which is consistent for alternatives with monotone failure rate. Derived as a weighted integral of the difference between the characteristic functions of the sample and of the exponential distribution, the scale-invariant statistic depends on the mean value of the exponential density function, evaluated at the sample observations. The power of the test is similar to that of the Gini test of Gail and Gastwirth (1978b), and both compare favourably with other leading tests of exponentiality.
An Exact Maximum Likelihood Estimation Procedure for Regression-ARMA Time Series Models with Possibly Nonconsecutive Data
Authors: Wincek Michael A. , Reinsel Gregory C. 
Published: December 2018

SUMMARY
An explicit procedure is given to obtain the exact maximum likelihood estimates of the parameters in a regression model with ARMA time series errors with possibly nonconsecutive data. The method is based on an innovation transformation approach from which an explicit recursive procedure is derived for the efficient calculation of the exact likelihood function and associated derivatives. The innovations and associated derivatives are used to develop a modified Newton-Raphson procedure for computation of the estimates. A weighted nonlinear least squares interpretation of the estimator is also given. A numerical example is provided to illustrate the method.
Bayes Factors for Non-Homogeneous Poisson Processes with Vague Prior Information
Authors: Akman V. E. , Raftery A. E. 
Published: December 2018

SUMMARY
The calculation of Bayes factors for rival parametric models of non-homogeneous Poisson processes is considered. If vague prior information for the model parameters is represented by limiting improper prior forms, then the resulting Bayes factor is defined only up to a multiplicative constant. It is noted that the procedure proposed by Spiegelhalter and Smith (1982) does not provide any solution to the problem of assigning the constant if the priors are inappropriately specified, and sufficient conditions for it to provide a solution are derived. It is shown that priors which satisfy the conditions exist in most situations. The case of monotonic log-polynomial intensity models is then considered in some detail.
Distance Based Ranking Models
Authors: Fligner M. A. , Verducci J. S. 
Published: December 2018

SUMMARY
A class of ranking models is proposed for which the probability of a ranking decreases with increasing distance from a modal ranking. Some special distances, namely those associated with Kendall and Cayley, decompose into a sum of independent components under the uniform distribution. These distances lead to multiparameter generalizations whose parameters may be interpreted as information at various stages in a ranking process. Estimation of model parameters is described, and the results are applied to an example of word associations. A censoring argument motivates simple extensions of these models to include partial rankings. The generalized Cayley distance model is illustrated for random arrangements arising from mechanisms other than ranking.
Chebyshev Polynomial Approximations and Characteristic Function Estimation
Authors: Madan D. B. , Seneta E. 
Published: December 2018

SUMMARY
A new procedure for estimating characteristic functions based on a Chebyshev polynomial expansion for the density of the Cosine is developed. Simulation results confirm the usefulness of the method. It is applied to the estimation of two stochastic process models for daily stock returns. The Press compound events model is also estimated by maximum likelihood methods. Results are suggestive of the adequacy of the compound events model and the vg model (a variant of the Praetz t distribution), and the superiority of these models over the normal and symmetric stable.
Adjustments for Kurtosis in Factor Analysis with Elliptically Distributed Errors
Authors: Browne M. W. , Shapiro A. 
Published: December 2018

SUMMARY
Simple corrections to normal theory tests of fit of the factor analysis model are provided for the situation where common factors have arbitrary distributions and errors have a distribution from the elliptical class. It is shown that normal theory estimators are asymptotically efficient in this situation and appropriate modifications for the asymptotic covariance matrix of estimators are provided. Factor analysis models with structured error covariance matrices are also considered.
On Symmetric Bootstrap Confidence Intervals
Authors: Hall Peter 
Published: December 2018

SUMMARY
It is shown that in quite general circumstances, symmetric percentile-t bootstrap confidence intervals have coverage error O(n –2), where n denotes sample size. This compares with an error of roughly constant n –1 for equal-tailed percentile-t confidence intervals. It is also proved that symmetric intervals are not necessarily any longer than equal-tailed intervals. Arguments based on Edgeworth and Cornish–Fisher expansions are used to predict circumstances in which symmetric intervals will have at once shorter length and smaller coverage error than equal-tailed intervals. The effect of number of replications on interval length and coverage error is discussed. Theoretical conclusions are illustrated in a simulation study.
Estimating Subgroup Means with Misclassification
Authors: Mak Tak K. 
Published: December 2018

SUMMARY
The present paper considers the estimation of subgroup means in the presence of misclassification errors in allocating individuals to the subgroups. A simple non-iterative estimator resulting from modifying Selen's (1986) estimator is studied when the probabilities of misclassification are independently estimated. In contrast to Selen (1986), an explicit expression for the covariance matrix of the suggested estimator is obtained using special matrix products and matrix differentiation theories. The result is useful in developing large sample theories for hypothesis testing and interval estimation. For the case of double sampling, the problem of deriving a more efficient estimator is considered and a method for allocating sample sizes suggested.