bluuebunny/crossref_metadata_2025 huggingface dataset:
Smooth Estimates for the Hazard Function
Authors: Anderson J. A. , Senthilselvan A.
Published: December 2018

Consideration is given to the piecewise smooth estimation of hazard functions given by Cox's (1972) proportional hazards model. The smoothest estimate available hitherto is a step-function which is not continuous. The method used is penalized maximum likelihood estimation introduced by Good and Gaskins (1971) and developed by Silverman (1978). This gives a quadratic spline with discontinuities in the slope at the times of death. The knot points are at times of death and censoring. The hazard function and corresponding survival curves are estimated for a group of 51 women with carcinoma of the vulva. The estimated survival curve is compared with those given by Breslow's (1972) and Kalbfleisch and Prentice's (1973) methods.
Exchange and Interchange Procedures to Search for Optimal Row-And-Column Designs
Authors: Eccleston John A. , Jones Byron
Published: December 2018

An algorithm to search for optimal row-and-column designs is described. It is similar to the one for block designs described by Jones and Eccleston (1980). The algorithm determines the treatment replications and searches for an optimal set of treatment concurrences. The optimality criterion is the sum of the weighted variances of a set of treatment contrasts of interest. Examples which illustrate the use of the algorithm are given and discussed.
A Note on the Admissibility of Some Non-Negative Quadratic Estimators
Authors: Sankaranarayanan K.
Published: December 2018

A certain estimator of the finite population variance and the Sen—Yates—Grundy variance estimator of the Horvitz—Thompson estimator of total are shown to be admissible in the class of all non-negative unbiased quadratic estimators.
Population Algebras
Authors: Holgate P.
Published: December 2018

The use of non-associative algebras to describe the dependence of the composition of a population on two (possibly identical) populations in a previous generation, which has been exploited in the genetics context, is extended to deal with stochastic population processes.

Aspects of the theory brought into focus by the new applications are investigated. A number of specific examples are studied with a view to exploring the kind of problems that can be handled by the algebraic approach. Lastly, the interaction between population and classical genetic algebras is studied.
On the Efficiency of Empirical Characteristic Function Procedures
Authors: Feuerverger Andrey , McDunnough Philip
Published: December 2018

The asymptotic normality and arbitrarily high efficiency of some new statistical procedures based on the empirical characteristic function is established under general conditions.
Maximum Likelihood Estimation for a Class of Multinomial Distributions Arising in Reliability
Authors: Samaniego F. J. , Jones L. E.
Published: December 2018

Let Xi, i = 1, …,k be independent Bernoulli variables, with Xi ~ B(1, pi). Let Y = σ Xi, and consider a multinomial experiment based on n independent, identically distributed observations Y  1,…, Yn. This model is identifiable in the ordered parameter vector (p  (1),…, p  (k)), where p(i  -1) ≤ p(i), and arises in reliability experiments in which k components in parallel have potentially different probabilities of failure. The family of multinomial distributions with the structure described above is properly contained in the family of general multinomial distributions with (k + 1) classes. Maximum likelihood estimation for this family is considered, and it is shown that for sufficiently large n, the maximum likelihood estimate of (p  (1),…, p  (k)) may be identified with high probability from the roots of a kth degree polynomial whose coefficients are consistent estimates of the elementary symmetric functions of the ratios θ(i) = p  (i)/(1 - p  (i)). A probability computation for the case k = 2 sheds light on the sample size required for our asymptotic results to take hold.
Empirical Bayes Analysis of Survival Time Data
Authors: Urridge J. B
Published: December 2018

An empirical Bayes analysis of life-time data is described. The paper examines and extends the model discussed by Kalbfleisch (1978) in which the cumulative hazard function is treated as a gamma process. It is shown that the results obtained from the model by using grouped data (the usual case in practice) are more satisfactory than those obtained using continuous data. The paper also shows that a parameter representing the variability of the underlying gamma process can be estimated from such data. A further feature is that the analysis considers more general processes than the gamma process using the latter for illustrative purposes only.
On the Bayesian Steady Forecasting Model
Authors: Key P. B. , Godolphin E. J.
Published: December 2018

A recent criterion of Smith (1979) seeks to generalize the steady forecasting model of Harrison and Stevens (1976) to take account of non-normality in the observation and system variables. In this note, predictive distributions and forecasts corresponding to quadratic and step loss functions are examined when the observation variable has a distribution belonging to the exponential family. It is shown that Smith's generalized model does not always yield forecasts which satisfy constraints obtained from the more familiar forms of steady forecasting. Two particular cases of the exponential family are used to illustrate the point.
The Circular Structural Model
Authors: Anderson Dorothy A.
Published: December 2018

This paper deals with consistent estimation of the structural parameters of the circular structural model. Identifiability is proved and the difficulties of dealing with the structural model in practice mentioned. A uniform distribution is then assumed for the angular variables and maximum likelihood estimation of the parameters examined. Also discussed are use of an approximation to the ratio of modified Bessel functions, asymptotic behaviour of the estimators as the ratio of the circle radius to the underlying structural variance parameter increases, and efficiency of other estimators of the parameters. The circular functional model, and the difficulties associated with it, is briefly mentioned.
A Method for Constructing Valid Restricted Randomization Schemes Using the Theory of D-Optimal Design of Experiments
Authors: White L. V. , Welch W. J.
Published: December 2018

Complete randomization of a one-way layout design may lead to problems if the resulting choice of layout is considered unsuitable by the experimenter. Valid restricted randomization is an attempt to retain the mathematical properties of complete randomization while ensuring that the probability of selection of an unsuitable layout is zero. The problem of constructing valid restricted randomization schemes, when these exist, is shown to be equivalent to a particular problem in the theory of optimal design of experiments.
A Goodness-Of-Fit Test Based on the Empirical Characteristic Function When Parameters Must be Estimated
Authors: Koutrouvelis I. A. , Kellermeier John
Published: December 2018

The goodness-of-fit test using the empirical characteristic function proposed by Koutrouvelis (1980) is extended to the case where parameters must be estimated. The proposed test statistic is shown to have an asymptotic chi-squared distribution with degrees of freedom reduced by the number of parameters estimated.
A Family of Distributions for Modelling Non-Elliptically Symmetric Multivariate Data
Authors: Cook R. Dennis , Johnson Mark E.
Published: December 2018

The paucity of distributions that can be used as an aid to modelling the structure of multivariate data is a recognized limitation. We present a relatively simple family of distributions for use in describing data which are not elliptically symmetric. Properties of the family are discussed and it is shown that multivariate Pareto, Burr and Logistic distributions are special cases. In addition, simulation methods for applications in Monte Carlo robustness studies are outlined and, finally, the fit to a data set on uranium exploration is compared to that obtained using the usual bivariate normal distribution.
Randomized Allocation of Treatments in Sequential Experiments
Authors: Bather J. A.
Published: December 2018

Since the idea of sequential allocation was first studied, in a version of what is now called the multi-armed bandit problem, the results of many investigations have shown that, even when an optimal allocation rule can be found, its form depends on the parameters of the model and no single rule has emerged that is widely acceptable in practice. On the other hand, it can be shown that conventional methods, using equal allocations of the treatments under comparison, involve many unnecessary applications of inferior treatments even if the final choice of the “best” treatment relies on a sequential test. The evidence for this claim is based on an investigation of randomized allocation rules, where the choice of the next treatment is randomized in such a way that some preference is given to the “favourite” at any stage, but other treatments are not permanently excluded.
Further Results on Quasi-Complete Latin Squares
Authors: Freeman G. H.
Published: December 2018

Further results are given for quasi-complete latin squares. These are latin squares which have the property that every unordered pair of elements occurs next to each other exactly twice in rows and twice in columns. All possible squares with first row in natural order are considered up to size 6, while possible squares for sizes 7 to 9 are increasingly numerous so are considered progressively less exhaustively. Pairs of squares which together have equality of concurrences of ordered pairs of elements are also examined. The uses of quasi-complete squares for the practical design of field experiments requiring equality of occurrences of unordered pairs of neighbours are discussed.
A Two-Variety Square Lattice Design Balanced Under Besag's Coding Scheme
Authors: Veevers A. , Zafar-Yab M.
Published: December 2018

Experimental designs for planting a mixture of two varieties on a square lattice of sites are available which possess a certain balance property. The additional property of being balanced within each set of sites obtained using Besag's first-order coding scheme is evident in just one of these designs.
On Ali's Characterization of the Spherical Normal Distribution
Authors: Arnold Steven F. , Lynch James
Published: December 2018

Recently Ali (1980) showed that the independence of the sample mean and the sample variance characterizes the spherical normal distribution in the class of absolutely continuous spherically symmetric distributions. Here, using invariance considerations, we give a proof of this characterization without the absolute continuity assumption.
Parametrizations of Non-Linear Models
Authors: Hougaard Philip
Published: December 2018

summary

in the literature there have been many suggestions on how to parametrize models. some properties you can seek are (1) stability of variance of the mle; (2) normal likelihood; (3) zero asymptotic skewness of the mle; (4) asymptotic unbiasedness of the mle.

the parametrizations corresponding to these demands are found in the one-dimensional curved exponential family. they all belong to a general class of transformations, but they are in general not identical. the transformations in this class are characterized by a differential equation. the transformations are identical in the nonlinear normal regression model.
Some E-Optimal Designs for the One-Way and Two-Way Elimination of Heterogeneity
Authors: Jacroux Mike
Published: December 2018

In exploratory experiments aimed at providing as much information as possible on the effects of the treatments being studied and where heterogeneity needs to be eliminated in one or two directions, use of an equally replicated block or row-column design may mean wasting some of the available experimental units. In this paper we prove the E-optimality of several different types of block and row-column designs that have unequally replicated treatments; such unequally replicated designs can maximize the information on treatment effects without wasting units.
Two Mann-Whitney Type Rank Tests
Authors: Eplett W. J. R.
Published: December 2018

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

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

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

The 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

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

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

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

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

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).
Outlier Discordancy Tests in the Normal Linear Model
Authors: Butler R.
Published: December 2018

Outlier discordancy tests are motivated by considering the residual pattern recognition approach of Daniel and the approaches of cross-validation and maximum likelihood. Various optimality properties of the significance tests for the most outlying subset of data are shown and a multivariate two-way layout example is given.
Sequential Estimation Saving Sampling Operations
Authors: Hall Peter
Published: December 2018

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

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 > 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

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

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

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.
A Comparison of Upper Bounds for Efficiency Factors of Block Designs
Authors: Dean A. M. , Lewis S. M.
Published: December 2018

A comparison is made of four competing upper bounds for the efficiency factor of an incomplete block design, in the case of connected designs with equal treatment replication and equal block size. It is shown that one of the four bounds is generally the tightest over a wide range of parameter values.
Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models
Authors: Davis M. H. A.
Published: December 2018

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.
Multiple Hypothesis Testing
Authors: Sawyer K. R.
Published: December 2018

The concept of multiple comparisons between a set of competing hypotheses is examined. A statistic is developed for testing a maintained hypothesis against a series of separate alternatives. This statistic is an extension of the binary Cox test.
Sensitivity of Principal Components
Authors: Krzanowski W. J.
Published: December 2018

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

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

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

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.
Estimating a Multivariate Linear Structural Relationship with Replication
Authors: Isogawa Yoshiko
Published: December 2018

We derive maximum likelihood estimators for parameters of a multivariate linear structural relationship in the replicated case. The asymptotic covariance matrix of the maximum likelihood estimator of the coefficient of the relationship is obtained by using the delta method when the sample size tends to infinity.
Maximum Likelihood Estimation of the Lower Tail of a Probability Distribution
Authors: Smith Richard L. , Weissman Ishay
Published: December 2018

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

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

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.
A Note on Spherical Splines
Authors: Fisher Nicholas I. , Lewis Toby
Published: December 2018

This paper presents two families of curves for interpolating and smoothing sequences of points on the surface of the unit sphere. One family is a natural analogue of the usual splines for curve-fitting in the plane; the other is slightly less optimal but more convenient from a computational viewpoint.
On the Polynomial Functional Relationship
Authors: Chan Lai K. , Mak Tak K.
Published: December 2018

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

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

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

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

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

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

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.
Decision-Theoretic Measures of Influence in Regression
Authors: Kempthorne Peter J.
Published: December 2018

A Bayesian decision-theoretic framework is used to define the influence of observations when fitting a regression model to data. Measures assessing an observation's influence on the posterior risk depend on the specification of the underlying loss function and prior assumptions. Illustrations are given for normal linear regression models.
Chebyshev Polynomial Approximations and Characteristic Function Estimation
Authors: Madan D. B. , Seneta E.
Published: December 2018

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

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

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

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.
Inference from Accelerated Life Tests Using Filtering in Coloured Noise
Authors: Blackwell Louis M. , Singpurwalla Nozer D.
Published: December 2018

We present a new approach for inference from accelerated life tests. Our approach formulates such problems as inference under Kalman filter models with correlated observation errors. We restrict attention to exponential life distributions, and the power rule as a time transformation function. Extensions to other time transformation functions are straightforward; however, extensions to other distributions involve nonlinear filtering and are not considered. The advantages of our formulation are that we are able to incorporate uncertainty in the time transformation function and also are able to allow it to change with the stress. to validate our approach we consider some simulated data; to give it a sense of reality we apply it to actual data.
Bootstrap Methods
Authors: Hinkley David V.
Published: December 2018

A survey of some developments in bootstrap methodology is given. Topics include confidence limits, significance tests, empirical likelihoods, conditioning, double bootstrapping, and numerical techniques. Special attention is given to regression problems. There are brief remarks about more complex problems, including variance component problems, time series and nonparametric regression.
On the Use of Marginal Likelihood in Time Series Model Estimation
Authors: Wilson G. Tunnicliffe
Published: December 2018

In the context of time series regression, with an error model of the ARIMA type, the fitting of the regression can seriously bias the ARIMA model parameter estimates. Moreover, choosing between different error models on the basis of the smallest residual variance may lead to incorrect selection with a high probability, even in samples of moderate size. The marginal likelihood procedure is considered as a solution to these problems and examples are presented in the context of trend estimation, seasonal forecasting and mixed spectrum analysis.
Model Specification in Multivariate Time Series
Authors: Tiao George C. , Tsay Ruey S.
Published: December 2018

We propose a method to specify an appropriate yet parsimonious vector autoregressive moving average (ARMA) model for a given multivariate time series. By considering contemporaneous linear transformations of the vector process, we introduce the concept of scalar component models within the vector ARMA framework (a) to reveal possibly hidden simplifying structures of the process, (b) to achieve parsimony in parameterization and (c) to identify the exchangeable models. The simplifying structures are of particular importance in the analysis of multivariate time series because they are often not obvious from the observed data but can be used to gain insights to the process under study. The analytical tool used to search for scalar component models is a canonical correlation analysis of vector processes and the proposed procedures are illustrated via two real examples.
Embedded Models in Three-Parameter Distributions and Their Estimation
Authors: Cheng R. C. H. , Iles T. C.
Published: December 2018

Two distinct problems can arise in maximum likelihood estimation in certain three-parameter problems. One problem, associated with the fitting of a threshold parameter, occurs if the fitted distribution has to be very positively skewed. This problem is well known. However, there is a second and unrelated difficulty which occurs quite often in practice and which arises when the distribution is not at all skew. This problem is not so well understood. It is shown in this paper that, within the three-parameter model, there is an embedded two-parameter special case which corresponds to infinite parameter values in the original model. The problem arises when this embedded model is the best fit to the data. The problem is shown to be easily resolved by first carrying out a check to see whether the embedded model should be fitted instead of the three-parameter model. Formal tests for this are discussed. The gamma, inverse Gaussian, log-normal and Weibull distributions are examples where the problem occurs. Numerical examples are provided for illustration.
The Conditional Predictive Ordinate for the Normal Distribution
Authors: Pettit L. I.
Published: December 2018

The conditional predictive ordinate (CPO) is a Bayesian diagnostic which detects surprising observations. It has been used in a variety of situations such as univariate samples, the multivariate normal distribution and regression models. Results are presented about the most surprising observation which has minimum CPO. For the multivariate normal distribution it is shown that the most surprising observation must lie at one of the vertices of the convex hull. It is also shown that the observation with maximum Mahalanobis distance from the sample mean must lie on the convex hull. Results are given for the expected number of vertices on the convex hull when the sample is contaminated. An alternative, closely related diagnostic, the ratio ordinate measure, is presented. A numerical comparison of the two measures is given.
A Simple Method for the Adjustment of Profile Likelihoods
Authors: McCullagh Peter , Tibshirani Robert
Published: December 2018

We propose a simple adjustment for profile likelihoods. The aim of the adjustment is to alleviate some of the problems inherent in the use of profile likelihoods, such as bias, inconsistency and overoptimistic variance estimates. The adjustment is applied to the profile log-likelihood score function at each parameter value so that its mean is zero and its variance is the negative expected derivative matrix of the adjusted score function. For cases in which explicit calculation of the adjustments is difficult, we give two methods to simplify their computation: An ‘automatic’ simulation method that requires as input only the profile log-likelihood and its first few derivatives; first-order asymptotic expressions. Some examples are provided and a comparison is made with the conditional profile log-likelihood of Cox and Reid.
On Use of the Em Algorithm for Penalized Likelihood Estimation
Authors: Green Peter J.
Published: December 2018

The EM algorithm is a popular approach to maximum likelihood estimation but has not been much used for penalized likelihood or maximum a posteriori estimation. This paper discusses properties of the EM algorithm in such contexts, concentrating on rates of convergence, and presents an alternative that is usually more practical and converges at least as quickly.
Alternative Smoothed Bootstraps
Authors: Young G. A.
Published: December 2018

Bootstrap estimation of simple population functionals is considered. The smoothed bootstrap (Efron, 1979, 1982) is compared with an alternative estimation procedure based on resampling ideas of Kendall and Kendall (1980). Specific examples of the estimation problem are considered, showing that the competing estimators may display different qualitative behaviours.
Construction of Block Designs Using Mathematical Programming
Authors: Whitaker D. , Triggs C. M. , John J. A.
Published: December 2018

The construction of optimal or nearly optimal block designs, using the A-optimality criterion, is formulated as a non-linear 0–1 programme. An approach which ignores the 0–1 constraint is suggested and its feasibility is examined by constructing block designs using the non-linear programming computer package MINOS.
Fisherian Inference in Likelihood and Prequential Frames of Reference
Authors: Dawid A. P.
Published: December 2018

In celebration of the centenary of the birth of Sir Ronald Fisher, this paper explores Fisher's conception of statistical inference, with special attention to the importance he placed on choosing an appropriate frame of reference to define the inferential model. In particular, we investigate inferential models which respect the likelihood principle or the prequential principle, and argue that these will typically have an asymptotic sampling theory justification.
Kernel Regression Estimation with Time Series Errors
Authors: Hart Jeffrey D.
Published: December 2018

Suppose that data y  1, ..., yn are observed according to the model yi=f((i−12)/n)+ϵi,i=1,…,n, where f is a smooth function and {ϵ1,…,ϵn} is a sample from a zero-mean, covariance stationary time series. The problem of objectively choosing the bandwidth of a kernel estimate for f is addressed. It is shown both theoretically and by simulation that cross-validation produces extremely rough kernel estimates when the data are sufficiently positively correlated. This makes it inadvisable to use residuals from a cross-validated kernel estimate as a means of estimating the covariance function of the errors. Alternative methods of estimating the covariance function are proposed. In a simulation study, incorporating these estimated covariances into a risk estimation procedure leads to more efficient smoothing of positively correlated data.
Bivariate Distributions with Conditionals in Prescribed Exponential Families
Authors: Arnold B. C. , Strauss D. J.
Published: December 2018

We characterize the class of bivariate distributions such that the conditional distributions belong to any specified exponential families. The result leads at once to several bivariate families derived by Castillo and Galambos and by Arnold and Strauss, as well as to distributions with Poisson, geometric and other conditionals. We indicate methods to simulate samples from the distributions and estimate their parameters.
An Approximate Bartlett Adjustment for Testing the Goodness of Fit of Multinomial Regression Models
Authors: Lugtenburg D.
Published: December 2018

For up to four categories and given sufficient replications per design point (eight or more seem to be enough), an adjusted likelihood ratio statistic for testing the goodness of fit of multinomial regression models is proposed. This adjustment does not depend on the multinomial model used and therefore will have a wide range of applications. It is certainly useful for the proportional odds model, introduced by McCullagh. This proportional odds model is used in some simulation studies to investigate the performance of the new statistic.