bluuebunny/crossref_metadata_2025 huggingface dataset:
CREDIBILITY THEORY: A CONCISE PARTIAL SURVEY1
Authors: Zehnwirth Ben
Published: February 2008

Developments in credibility theory in the last seventy years or so are outlined. Particular attention is paid to early work in the field and to more recent developments showing some of the many connections between credibility theory and other fields including linear Bayesian theory, linear filtering theory and constant coefficient regression.
REMARKS ON OPTIMAL INFERENCE FOR MARKOV BRANCHING PROCESSES: A SEQUENTIAL APPROACH
Authors: Basawa I. V. , Becker Niels
Published: February 2008

Use of a suitable stopping rule yields exact uniformly most powerful tests and minimum variance unbiased estimators of various parameters of a Markov branching model with or without immigration. The population model discussed includes the pure birth, simple epidemic, immigration‐death, M/M/ 1 queue, linear birth‐death and a branching diffusion process, among others, as special cases.
REDUCED DISTANCE MEASURES AND TRANSFORMATIONS IN PROCESSING MULTIVARIATE OUTLIERS
Authors: Barnett Vic
Published: February 2008

The study of multivariate outliers raises many problems of definition, principle and manipulation. Well‐authenticated tests of discordancy exist only for the multivariate normal distribution. Detection of outliers in non‐normal distributions involves the adoption of appropriate criteria to represent ‘extremeness' of observations in a sample; corresponding tests of discordancy usually require tedious, or even intractable, distributional and computational manipulations. A class of transformations of the data is considered with a view of transferring some of the familiar and desirable features of discordancy tests for normal samples to non‐normal situations.
AN ESTIMATE OF THE ASYMPTOTIC STANDARD ERROR OF THE SAMPLE MEDIAN
Authors: Sheather S. J. , Maritz J. S.
Published: February 2008

A method for estimating the asymptotic standard error of the sample median based on generalized least squares is outlined. The practical problems of implementing this new estimate along with those associated with two existing estimates are discussed. Finally a simulation study is presented to compare the three estimates.
A STOCHASTIC LOGISTIC MODEL WITH TIME DELAY
Authors: Prajneshu
Published: February 2008

The stochastic version of the logistic model for population growth is generalized to take account of continuously distributed time delay with an exponentially decaying kernel. The theory of diffusion processes is used to analyse the probability density function of the population size. The explicit expression for the stationary distribution is worked out and the effect of time delay on various statistics is discussed.
JACKKNIFING THE GENERAL LINEAR MODEL
Authors: Weber N. C. , Welsh A. H.
Published: February 2008

The aim of this paper is to investigate the problems of estimating a smooth function of the parameters in a general linear model and to clarify some of the points raised by Hinkley (1977) in connection with this problem. An example of the type of problem at hand is that of estimating the maximum (or minimum) mean value in a quadratic regression model. The estimator based on the least squares estimator of the parameters in the linear model is compared to the jackknife estimator and the weighted jackknife estimator proposed by Hinkley (1977). The asymptotic properties of the estimators are examined and their small sample properties are compared through simulation studies.
GIL‐PELAEZ‐ROSÉN TRANSFORMATION OF DATA
Authors: Csörcö Sándor
Published: February 2008

Several statistics based on the empirical characteristic function have been proposed for testing the simple goodness‐of‐fit hypothesis that the data come from a population with a completely specified characteristic function which cannot be inverted in a closed form, the typical example being the class of stable characteristic functions. As an alternative approach, it is pointed out here that the inversion formula of Gil‐Pelaez and Rosén, as applied to the data and the hypothetical characteristic function via numerical integration, is the natural replacement of the probability integral transformation in the given situation. The transformed sample is from the uniform (0, l) distribution if and only if the null hypothesis is true, and for testing uniformity on (0,1) the whole arsenal of methods statistics so far produced can be used.
A NOTE ON THE MAXIMUM LIKELIHOOD ESTIMATION OF REGRESSION MODELS WITH FIRST ORDER MOVING AVERAGE ERRORS WITH ROOTS ON THE UNIT CIRCLE
Authors: Pesaran M. H.
Published: February 2008

This note gives an alternative derivation of Sargan and Bhargava’ s results concerning the probability of observing on the unit circle a local maximum of the likelihood function of regression models with first order moving average errors. The note also discusses the relevance of these results for the computation of the exact maximum likelihood estimation of regression models with moving average errors.
DIRECTION AND COLLINEARITY FACTORS OF WILK'S A ASSOCIATED WITH THE GROWTH CURVE MODEL
Authors: Kshirsagar Anant M. , Davis Thomas M.
Published: February 2008

Khatri (1966) has derived a Wilks' s A test of a general linear hypothesis in the growth curve model. In this paper we give the direction and collinearity factors and their null distributions when the hypothesis is not true but the noncentrality matrix is of rank one. Interpretation of these tests and their usefulness in discrimination in growth curve models are discussed.
INFERENCE FOR CENSORED MATCHED PAIRS USING SIGNED RANKS
Authors: Pettitt A. N.
Published: February 2008

Using the marginal likelihood based on the signed ranks derived from matched pairs data, inferences are made for regression parameters. Both members of a given pair are subject to the same censoring time, while different pairs are subject to different censoring times. Censoring is independent of the response and on the right. Easily calculated logistic density scores are used to provide an approximate analysis so that inferences can be made about a regression parameter in the presence of a difference within the matched pairs. Inference for the survival times of matched skin grafts is considered.
AN ANALYSIS OF CLASSICAL AND TIE‐BREAKER TENNIS
Authors: Pollard G. H.
Published: February 2008

Expressions for the probability that a player wins a game, set or match of classical or tie‐breaker tennis are obtained. Also, expressions for the distribution, the mean and the variance of the number of points in a game, set or match of classical or tie‐breaker tennis are obtained. These results explain the long matches often previously observed in classical tennis between two players each with very effective serves on fast grass‐court surfaces. The methodology used to derive these expressions could be used to obtain corresponding expressions for other “nested‐type” scoring systems. For example, tennis is 3‐nested (game, set, match) whereas squash is only 2‐nested (game, match).
BETTER PRIORS FOR BAYESIAN BETTORS
Authors: Isaacson Dean , Meeden Glen
Published: February 2008

summary

Consider the game where a Bayesian investor places a series of bets on the outcomes of a sequence of tosses of a coin with odds set by a Bayesian bookie. It is shown that at each toss the investor can have non‐negative expected winnings even though after many tosses the two posterior distributions are nearly equivalent.
THE CALCULATION OF CONFIDENCE REGIONS FOR EIGENVECTORS
Authors: Watson G. S.
Published: February 2008

summary

An explicit algorithm is given for constructing a confidence region on the appropriate unit sphere for an eigenvector, given a large sample. It is assumed the eigenvector corresponds to the largest eigenvalue of ExxT, a matrix with distinct eigenvalues, and that the estimation uses n‐1S̀xixixT. While the theory is generally applicable, the writer has in mind the special case where ∥x∥= 1 i.e. directional data.
EXACT FINITE‐SAMPLE PROPERTIES OF A PRE‐TEST ESTIMATOR IN RIDGE REGRESSION
Authors: Srivastava V. K. , Giles D. E. A.
Published: February 2008

summary

This paper discusses a pre‐test regression estimator which uses the least squares estimate when it is “large” and a ridge regression estimate for “small” regression coefficients, where the preliminary test is applied separately to each regression coefficient in turn to determine whether it is “large” or “small.” For orthogonal regressors, the exact finite‐sample bias and mean squared error of the pre‐test estimator are derived. The latter is less biased than a ridge estimator, and over much of the parameter space the pre‐test estimator has smaller mean squared error than least squares. A ridge estimator is found to be inferior to the pre‐test estimator in terms of mean squared error in many situations, and at worst the latter estimator is only slightly less efficient than the former at commonly used significance levels.
A NOTE ON THE ANALYSIS OF COVARIANCE IN BALANCED INCOMPLETE BLOCK DESIGNS
Authors: Ratcliff D. , Williams E. R. , Speed T. P.
Published: February 2008

summary

The Williams & Ratcliff (1980) and Zelen (1957) methods for the analysis of covariance in incomplete block designs with recovery of inter‐block information are compared using data from a balanced incomplete block design. The former is shown to be more efficient. Other advantages of the Williams & Ratcliff formulation are also presented.
GOODNESS‐OF‐FIT TESTS FOR FISHER'S DISTRIBUTION ON THE SPHERE
Authors: Fisher N. I. , Best D. J.
Published: February 2008

A set of three goodness‐of‐fit procedures is proposed to investigate the adequacy of fit of Fisher's distribution on the sphere as a model for a given sample of spherical data. The procedures are all based on standard tests using the empirical distribution function.
STEIN'S METHOD AND THE BERRY‐ESSÉEN THEOREM
Authors: Barbour A. D. , Hall Peter
Published: February 2008

Stein's method is used to prove the Lindeberg‐Feller theorem and a generalization of the Berry‐Esséen theorem. The arguments involve only manipulation of probability inequalities, and form an attractive alternative to the less direct Fourier‐analytic methods which are traditionally employed.
THE MONTE CARLO EVALUATION OF ORTHANT PROBABILITIES FOR MULTIVARIATE NORMAL DISTRIBUTIONS
Authors: Moran P. A. P.
Published: February 2008

The calculation of multivariate normal orthant probabilities is practically impossible when the number of variates is greater than five or six, except in very special cases. A transformation of the integral is obtained which enables quite accurate Monte Carlo estimates to be obtained for a fairly high number of dimensions, particularly if control variates are used.
ON THE USE OFX2 AS A TEST OF INDEPENDENCE IN CONTINGENCY TABLES WITH SMALL CELL EXPECTATIONS
Authors: Lawal H. Bayo , Upton Graham J. G.
Published: February 2008

When anr×ccontingency table has many cells having very small expectations, the usual χ2approximation to the upper tail of the Pearson χ2goodness‐of‐fit statistic becomes very conservative. The alternatives considered in this paper are to use either a lognormal approximation, or to scale the usual χ2approximation. The study involves thousands of tables with various sample sizes, and with tables whose sizes range from 2×2 through 2×10×10. Subject to certain restrictions the new scaled χ2approximations are recommended for use with tables having an average cell expectation as small as 0·5.
A GOODNESS OF FIT TEST BASED ON THE LINKED LINE CHART1
Authors: Shirahata S. , Wakimoto K. , Tarumi T.
Published: February 2008

In this paper, we propose a graphical representation of data and a test statistic based on it for testing the goodness of fit of a completely specified null distribution. The graph is constructed as a linked line chart given by vectors which reflect the pattern of order statistics. The test statistic is defined as an area defined by our chart and its asymptotic distribution is derived under the null hypothesis. Computer simulations performed to study the power properties of our chart indicate that the test is powerful for scale alternatives. Furthermore, it is shown that our test is closely related to the Watson test.
RECURSIVE ESTIMATION OF THE GENERAL LINEAR MODEL WITH DEPENDENT ERRORS AND MULTIPLE ADDITIONAL OBSERVATIONS1
Authors: Haslett Stephen
Published: February 2008

The techniques for recursive estimation of the general linear model with dependent errors and known second order properties, is generalised to allow for simultaneous addition of an arbitrary number of additional observations. Computational formulae for recursive updating of parameter estimates are derived, together with a sequence of univariate recursive residuals for testing the constancy of the regression relation over time.
A NOTE ON THE INVERSE COVARIANCE MATRIX OF THE AUTOREGRESSIVE PROCESS1
Authors: Verbyla A. P.
Published: February 2008

summary

The inverse covariance matrix of an autoregressive process of arbitrary order is found explicitly using the notion of the information matrix for the vector random variable, not the parameters. Any process for which a simple conditional representation exists, can be treated in the same way. The approach has merit in the teaching of statistics.
ANCILLARIES SUFFICIENT FOR THE SAMPLE SIZE1
Authors: Lloyd C. J.
Published: February 2008

The process of recovery of information proceeds by conditioning on ancillaries which are part of the minimal sufficient statistic (MSS), so‐called internal ancillaries. This is motivated by the notion that ancillaries function as precision indices. In some cases the ancillary can itself replace the sample size entirely in the model. It is decided that such ancillaries must be conditioned on if one of the sufficiency or conditionality principles is not to be violated.
THE EPIDEMIOLOGY OF A DISEASE USING HAZARD FUNCTIONS1
Authors: O'Neill Terence J. , Tallis G. M. , Leppard P.
Published: February 2008

A prime objective of this paper is to mathematically quantify certain epidemiological concepts and show how some of these can be applied to certain registry type data. Usually epidemiological quantities are expressed in terms of density functions. However it is often more natural to estimate hazard functions in practical situations. Hence the emphasis will be on expressing various measures in terms of hazard functions. This contrasts with the useful paper of Albert, Gertman & Louis (1978) where density functions are used throughout. The definitions of some key concepts such as cohort effect are also different which gives rise to an alternative analysis and some new results. Initially, incidence, mortality and prevalence are discussed and this is followed by a treatment of initiation which is a less commonly used measure. The results are applied to the lung cancer data in the South Australian Central Cancer Registry.
GOODNESS‐OF‐FIT AND DISCORDANCY TESTS FOR SAMPLES FROM THE WATSON DISTRIBUTION ON THE SPHERE
Authors: Best D. J. , Fisher N. I.
Published: February 2008

The only parametric model in current use for axial data from a rotationally symmetric bipolar or girdle distribution on the sphere is the Watson distribution. This paper develops methods for evaluating the model as a fit to data using graphical and formal goodness‐of‐fit tests, and tests of discordancy.
SOME ASYMPTOTIC PROPERTIES OF THE SIMPLE LOGLINEAR MODEL
Authors: Maller R. A.
Published: February 2008

Consistency and asymptotic normality of the maximum likelihood estimator of β in the loglinear model E(yi) = eα+βXi, where yiare independent Poisson observations, 1iaan, are proved under conditions which are near necessary and sufficient. The asymptotic distribution of the deviance test for β=β0is shown to be chi‐squared with 1 degree of freedom under the same conditions, and a second order correction to the deviance is derived. The exponential model for censored survival data is also treated by the same methods.
EQUINEIGHBOURED XPERIMENTAL DESIGNS
Authors: Ipinyomi R. A.
Published: February 2008

This paper introduces a new class of designs called equi‐neighboured designs. An equineighboured design has the property that every unordered pair of treatments occurs as nearest neighbours equally frequently at every level. These designs are defined in Section 4 and shown to be balanced when neighbouring observations are correlated. Some equineighboured designs are constructed using a complete set of orthogonal Latin squares. Cyclic equineighboured designs are also defined.
ON THE USE OF THE EMPIRICAL DISTRIBUTION AND CHARACTERISTIC FUNCTION TO ESTIMATE PARAMETERS OF REGULAR VARIATION
Authors: Welsh A. H.
Published: February 2008

In this paper we present two new classes of estimators of parameters of regular variation, one based on the empirical distribution function and the other on the empirical characteristic function. They achieve the same rates of mean square error convergence as the estimators proposed by Hall (1982). The estimator based on the empirical characteristic function, unlike the other estimators, utilises the whole sample and not just a few extreme order statistics.
UPPER BOUNDS FOR THE HARMONIC MEAN, WITH AN APPLICATION TO EXPERIMENTAL DESIGN
Authors: Fitzpatrick Simon , Jarrett Richard G.
Published: February 2008

For positive‐valued random variables, the paper provides a sequence of upper bounds for the harmonic mean, theith of these bounds being exact if and only if the random variable is essentiallyi‐valued. Sufficient conditions for the convergence of the bounds to the harmonic mean are given. The bounds have a number of applications, particularly in experimental design where they may be used to check how close a given design is toA‐optimality
ON LEVENE'S TESTS OF VARIANCE HOMOGENEITY
Authors: Yitnosumarto S. , O'Neill M. E.
Published: February 2008

Levene's tests of homogeneity of treatment variances in completely randomised and randomised complete block experiments are examined. These tests are essentially standard analysis of variance F‐tests performed on functions of the absolute values of residuals. It is found that in order to achieve (i) equality of component mean squares under the null hypothesis, and (ii) nominal significance levels, the various standard degrees of freedom need to be modified.
CONSTRUCTION OF BALANCED TERNARY DESIGNS
Authors: Agarwal G. G. , Kumar Sanjay
Published: February 2008

In this paper variance balanced ternary designs are constructed in unequal block sizes for situations when suitable BIB designs do not exist for a given number of treatments because of the constraints bk=vr,and λ(v ‐ 1) =r(k‐ 1).
Category Distinguishability and Observer Agreement
Authors: Darroch J. N. , McCloud P. I.
Published: February 2008

It is common in the medical, biological, and social sciences for the categories into which an object is classified not to have a fully objective definition. Theoretically speaking the categories are therefore not completely distinguishable. The practical extent of their distinguishability can be measured when two expert observers classify the same sample of objects. It is shown, under reasonable assumptions, that the matrix of joint classification probabilities is quasi‐symmetric, and that the symmetric matrix component is non‐negative definite. The degree of distinguishability between two categories is defined and is used to give a measure of overall category distinguishability. It is argued that the kappa measure of observer agreement is unsatisfactory as a measure of overall category distinguishability.
A Note on a Partition of the Likelihood Ratio Test for Autoregressive Covariance Structure
Authors: Verbyla A. P.
Published: February 2008

A sequence of nested hypotheses is presented for the examination of the assumption of autoregressive covariance structure in, for example, a repeated measures experiment. These hypotheses arise naturally by specifying the joint density of the underlying vector random variable as a product of conditional densities and the density of a subset of the vector random variable. The tests for all but one of the nested hypotheses are well known procedures, namely analysis of variance F‐tests and Bartlett's test of equality of variances. While the procedure is based on tests of hypotheses, it may be viewed as an exploratory tool which can lead to model identification. An example is presented to illustrate the method.
On Smoothing Sparse Multinomial Data
Authors: Hall Peter , Titterington D. M.
Published: February 2008

Asymptotic theory is developed for the problem of smoothing sparse multinomial data, with emphasis on the criterion of mean summed square error of estimators of the probability mass function. If the data are not too sparse, in a well‐defined sense, then the optimal rate of convergence is that achieved by the unsmoothed cell proportions. Otherwise, this rate can be improved upon by smoothing. Explicit results, including formulae for the optimal smoothing parameter, are presented for a kernel‐type estimator. Also for this case, a cross‐validatory choice procedure is shown to be asymptotically optimal.
The Construction of Optimal Balanced Incomplete Block Designs When Adjacent Observations are Correlated
Authors: Russell K. G. , Eccleston J. A.
Published: February 2008

An algorithm is described for the optimal rearrangement of the treatments within each block of a Balanced Incomplete Block Design when a specified “nearest neighbour” correlation structure exists among observations from plots in the same block. The procedure uses results obtained by Kiefer & Wynn (1981). Designs obtained using the algorithm are found to compare favourably with those produced by combinatorial methods given in Cheng (1983). The algorithm produces optimal designs for all BIBD parameter sets, including those not covered by the results of Kiefer & Wynn or Cheng.
On Permutation Tests in Multiple Regression and Analysis of Covariance Problems
Authors: Oja Hannu
Published: February 2008

We introduce distribution‐free permutation tests and corresponding estimates for studying the effect of a treatment variable x on a response y. The methods apply in the presence of a multivariate covariate z. They are based on the assumption that the treatment values are assigned randomly to the subjects.
Selection of the Transformation Variable in the Laplace Transform Method of Estimation
Authors: Laurence Alexa F. , Morgan Byron J. T.
Published: February 2008

The work of this paper is based on the innovative approach of Feiginet al.(1983), who estimate parameters of lifetime distributions by equating empirical and theoretical Laplace transforms. We show that the optimal choice of the transform variable depends critically upon the number of sampling times, the way they are spaced, and how the empirical transform is formed. Two new approaches for choosing the transform variable, viz. using cross‐validation or constrained optimisation, are introduced and shown to have potential for wide‐ranging use.
On the Optimality of Estimating the Tail Index and a Naive Estimator
Authors: Csörgö Miklós , Horváth Lnos , Révész Pál
Published: February 2008

Using a straightforward estimator for estimating the tail index of a distribution we illustrate the inherent difficulties of this problem. We prove strong and weak consistencies and central limit theorems for our naive estimator, and discuss its various rates of convergence under different conditions. We argue that, while optimal rates of convergence do exist under various conditions for a number of estimators of the tail index, the notion of an optimal sequence for this problem is bound to run into unsurmountable difficulties.
Regression Shrinkage Methods and Autoregressive Time Series Prediction
Authors: Copas J. B. , Jones M. C.
Published: February 2008

The pros and cons of applying regression shrinkage prediction arguments and methods to autoregressive time series forecasting are discussed. Simulation evidence of the performance of a Stein regression prediction formula suggests that the overall dominance of the shrunken predictor over least squares in regression no longer holds in time series samples of a reasonable length. Rather, shrinkage appears the better of the two, with respect to prediction mean squared error, only for weaker relationships and seems to be inferior to the least squares predictor when the autoregressive relationship is strong.
A Note on Change‐Over Designs
Authors: Williams E. R.
Published: February 2008

A change‐over model with correlated errors is discussed. In particular the results of Patterson (1950) and Lucas (1951) for balanced change‐over designs are extended to more than four treatments and more general variance matrices. A connection with recent work on neighbour models for field trials is made.
Incorporating Previous Results Into the Analysis of General Balanced Designed Experiments
Authors: Knuiman M. W. , Speed T. P.
Published: February 2008

When previous results are available about quantities of interest in a designed experiment they should be incorporated into the analysis. We suppose that estimates of treatment effects and variance components and their precisions are available from previous data but not necessarily the full data. A prior‐posterior method is described which incorporates these previous estimates directly into the analysis of a current set of data. General but concise formula are derived for the class of generally balanced designs. Previous results are represented by a multivariate normal prior for the treatment means and independent inverse chi‐squared distributions for the variance components. Joint and marginal posterior modes and a measure of dispersion are proposed as combined or updated estimates. These posterior summary statistics have highly interpretable forms and are readily computed.
THE FIRST EPIDEMIC MODEL: A HISTORICAL NOTE ON P.D. EN'KO
Authors: Dietz K.
Published: February 2008

summary

A summary of P. D. En'ko's contributions to the theory of epidemics is presented. This work appeared 1889 in Russian in St. Petersburg. En'ko actually fitted his discrete time model to several epidemics of measles which he observed in boarding‐schools in St. Petersburg. His remarkable contribution predates the Reed‐Frost model by nearly forty years.
CONVERGENCE OF KERNEL FUNCTIONS FOR CUBIC SMOOTHING SPLINES ON NON‐EQUISPACED GRIDS
Authors: de Hoog F.R. , Anderssen R.S.
Published: February 2008

summary

Numerical experimentation with data, which is quite noisy and on a highly non‐even grid, shows that cubic smoothing splines give a visually pleasing fit to the data, even when the interpolating spline oscillates wildly. In part, Silverman (1984) has explained this fact by showing that the cubic smoothing spline converges, to a certain kernel approximation as the number of data points is increased. In this paper, we examine the convergence of the kernel functions which generate the cubic smoothing spline fit to data, under weaker conditions on the non‐even grid than imposed by Silverman.
POINT PROCESSES WITH A CLUSTERING TRANSITION
Authors: And David Gates , Westcott Mark
Published: February 2008

summary

The paper examines the properties of a simple pairwise interaction point process or distribution, when the potential is attractive. This leads to various degrees of clustering. Using measures such as the normalizing constant, number of close pairs and a generalized scan statistic, it is found that there are effectively three regimes for the model, determined by the relative magnitudes of numbers of pointsN, the point domainVand strength of interactionv.AsN vincreases, abrupt transitions between these regimes occur with the middle “critical” one holding for only a relatively small range ofN v‐values. It is possible to simulate the process reliably in one dimension, unlike the planar version, and confirmatory results are reported. A discrete version of the model, more susceptible to analysis, is introduced; it leads to the same conclusions and exhibits a criticality resembling, but distinct from, that in processes with phase transitions. Possible application of the discrete model to urbanization is described.
ON THE VARIANCE PROPERTIES OF STRESS RELEASE MODELS
Authors: Vere‐Jones D.
Published: February 2008

summary

A class of piece‐wise linear stochastic processes is described, which can be used to model the gradual accumulation and sudden release of stress in earthquake models. Interest centres on the variance properties of the sequence of time points at which the sudden release (earthquakes) occur. Some general conditions are derived for the existence of moments, and under these conditions the variance properties are examined. It is shown that the point process of such events can have a bounded variance function, as is known to happen in the case of constant stress releases, only in this degenerate case. In the final section an example is examined which is closely related to the classical collective risk model.
THE ROLE OF CONDITIONAL INFERENCE
Authors: Becker Niels
Published: February 2008

summary

The fact that unconditional sampling theoretic inference is sometimes misleading is illustrated with some examples. Each of these examples involves a sequential sampling procedure and it is suggested here that meaningful inferences can be obtained in these examples by viewing the sequential components of the experiment as though they are separate and independent experiments. Inferences are then made with reference to hypothetical repetitions of the components of the current experiment, rather than referring to hypothetical repetitions of the experiment as a whole. In essence this involves combining the conditional inferences from the components as though they are independent. The approach involves the same likelihood and asymptotic likelihood inference remains essentially the same. However, the finite sampling properties of estimators and tests are changed. A by‐product of the use of this alternative reference set is that it resolves problems arising from the arbitrariness of stopping rules. This approach to sampling theoretic inference is not merely a device for overcoming difficulties arising in a few examples, it has relevance in all problems of statistical inference.
EFFECTS OF ERRORS IN INSPECTION ON A BINARY METHOD FOR ISOLATING NONCONFORMING ITEMS
Authors: Johnson Norman L. , Kotz Samuel
Published: February 2008

summary

The effects of inspection errors on the well‐known method of “successive halving” to determine nonconforming items is studied. The method is known to be near‐optimal when no more than one nonconforming item is present. We also study the properties of the procedure when there are two or more nonconforming items among those to be tested.
BIAS IN THE ESTIMATION OF MULTIVARIATE AUTOREGRESSIONS
Authors: Nicholls D. F. , Pope A. L.
Published: February 2008

summary

A derivation of the bias of the least squares estimate of the coefficients of a multivariate autoregressive model is presented. The explicit expression obtained is of use when, in the case of small samples, one needs to make a bias correction prior to bootstrapping.
SOME SERIES OF EFFICIENCY BALANCED DESIGNS
Authors: Ghosh D.K. , KARMAKAR P.K.
Published: February 2008

Two series of efficiency balanced designs with v*+ 1 treatments have been constructed using balanced incomplete block designs having v* treatments.
PARAMETER ESTIMATION AND APPLICATIONS FOR A GENERALISATION OF THE BETA‐BINOMIAL DISTRIBUTION
Authors: Danaher P.J.
Published: February 2008

A three‐parameter generalisation of the beta‐binomial distribution (BBD) derived by Chandon (1976) is examined. We obtain the maximum likelihood estimates of the parameters and give the elements of the information matrix. To exhibit the applicability of the generalised distribution we show how it gives an improved fit over the BBD for magazine exposure and consumer purchasing data. Finally we derive an empirical Bayes estimate of a binomial proportion based on the generalised beta distribution used in this study.
THE RELATIONSHIPS BETWEEN SKEWNESS AND KURTOSIS
Authors: MacGillivray H.L. , Balanda K.P.
Published: February 2008

Theoretical considerations of kurtosis, whether of partial orderings of distributions with respect to kurtosis or of measures of kurtosis, have tended to focus only on symmetric distributions. With reference to historical points and recent work on skewness and kurtosis, this paper defines anti‐skewness and uses it as a tool to discuss the concept of kurtosis in asymmetric univariate distributions. The discussion indicates that while kurtosis is best considered as a property of symmetrised versions of distributions, symmetrisation does not simply remove skewness. Skewness, anti‐skewness and kurtosis are all inter‐related aspects of shape. The Tukey g and h family and the Johnson Su family are considered as examples.
BOOTSTRAPPED MULTI‐DIMENSIONAL PRODUCT LIMIT PROCESS
Authors: Yandell Brian S. , Horváth Lajos
Published: February 2008

We approximate the limit process for a multivariate censored survival distribution using the bootstrap. The empirical process has a complicated covariance structure depending on the survival and censoring. The bootstrapped process provides a means to develop distribution‐free procedures including simultaneous confidence bands. Results extend to comparison of multivariate survival distributions. A gallstone study is examined in some detail.
RATIO‐TO‐SIZE ESTIMATORS OF MEAN PER SUBUNIT IN TWO‐STAGE SAMPLING OVER TWO OCCASIONS
Authors: Okafor Fabian C.
Published: February 2008

We propose here some strategies for estimating the population mean per subunit at the current occasion and change in mean from one occasion to the next based on two‐stage sampling on two successive occasions.

Estimators of the mean in two‐stage sampling over successive occasions have so far been based on the knowledge of the total number of subunits (elements),M0in the population or on assumed equal sizes for the primary units. We have therefore given the ratio‐to‐size estimators for the population mean per subunit on the current occasion and the change in mean over the two occasions whereM0is not known. The results obtained also apply to the situation whereM1is correlated with the variable of interesty.
SOME MODELS FOR OVERDISPERSED BINOMIAL DATA
Authors: Anderson Dorothy A.
Published: February 2008

Various models are currently used to model overdispersed binomial data. It is not always clear which model is appropriate for a given situation. Here we examine the assumptions and discuss the problems and pitfalls of some of these models. We focus on clustered data with one level of nesting, briefly touching on more complex strata and longitudinal data. The estimation procedures are illustrated and some critical comments are made about the various models. We indicate which models are restrictive and how and which can be extended to model more complex situations. In addition some inadequacies in testing procedures are noted. Recommendations as to which models should be used, and when, are made.
MAXIMUM LIKELIHOOD ESTIMATION OF GROSS FLOWS
Authors: Chambers R.L. , Woyzbun L. , Pillig R.
Published: February 2008

A method of maximum likelihood estimation of gross flows from overlapping stratified sample data is developed. The approach taken is model‐based and the EM algorithm is used to solve the estimation problem. Inference is thus based on information from the total sample at each time period. This can be contrasted with the conventional approach to gross flows estimation which only uses information from the overlapping sub‐sample. An application to estimation of flows of Australian cropping and livestock industries farms into and out of an “at risk” situation over the period 1979–84 is presented, as well as a discussion of extensions to more complex sampling situations.
ON THE HILDRETH‐HOUCK ESTIMATOR FOR RANDOM COEFFICIENT REGRESSION MODELS
Authors: Anh V. V.
Published: February 2008

This paper is concerned with the linear regression model in which the coefficients are random variables. The Hildreth‐Houck method is considered for estimating the model. Sufficient conditions for the consistency of the Hildreth‐Houck estimator are discussed and its asymptotic normality is established.
CHOLESKY DECOMPOSITION OF A VARIANCE MATRIX IN REPEATED MEASURES ANALYSIS
Authors: Lianto S. , McGilchrist C.A.
Published: February 2008

The Cholesky decomposition is given for the inverse of a variance matrix occurring in repeated measures problems where observations have a correlation structure both within and between experimental units. The use of this decomposition is outlined for ML and REML estimation procedures.
ON COMPONENTS OF VARIANCE and MODELLING EXCEEDANCES OVER A THRESHOLD
Authors: Solomon P. J.
Published: February 2008

summary

Variance component estimates from a simple hierarchical model are used to model the distribution of large data values exceeding a threshold. The advantages of interrelating the components of variance and the exceedances are stressed. The theory is outlined and an analysis of some data on blood pressure is discussed.
ANALYSIS OF VARIATIONS IN AN INFECTION RATE
Authors: Becker Niels , Yip Paul
Published: February 2008

summary

In a previous analysis of data from a smallpox epidemic in Abakaliki, Nigeria, it was found that the epidemic model based on uniform mixing was able to give an adequate description only when the infection rate was taken to be a function of time. Here we demonstrate that an alternative, and plausible, explanation is that the infection rate acting upon each given susceptible is constant over time, but that it varies between susceptibles. This variation in susceptibility of individuals can give the impression that the infection rate is declining over time, because highly susceptible individuals tend to be infected earlier so that the mean susceptibility of the remaining susceptibles is declining over time.

The above example reveals that there is interest in exploring the nature of the dependence of the infection rate upon time. To this end we propose the nonparametric estimation of the infection rate and illustrate it with reference to the Abakaliki data.
COVARIANCE MODELS FOR LATTICE DATA
Authors: Kiivefu H. T. , Campbell N. A.
Published: February 2008

summary

Given observations on an m × n lattice, approximate maximum likelihood estimates are derived for a family of models including direct covariance, spatial moving average, conditional autoregressive and simultaneous autoregressive models. The approach involves expressing the (approximate) covariance matrix of the observed variables in terms of a linear combination of neighbour relationship matrices, raised to a power. The structure is such that the eigenvectors of the covariance matrix are independent of the parameters of interest. This result leads to a simple Fisher scoring type algorithm for estimating the parameters. The ideas are illustrated by fitting models to some remotely sensed data.
PARTIALLY EQUINEIGHBOURED DESIGNS
Authors: Ipinyomi R. A.
Published: February 2008

summary

This paper presents further results on a class of designs called equineighboured designs, ED. These designs are intended for field and related experiments, especially whenever there is evidence that observations in the same block are correlated.

An ED has the property that every unordered pair of treatments occurs as nearest neighbours equally frequently at each level. Ipinyomi (1986) has defined and shown that ED are balanced designs when neighbouring observations are correlated. He has also presented ED as a continuation of the development of optimal block designs.

An ED would often require many times the number of experimental materials needed for the construction of an ordinary balanced incomplete block, BIB, design for the same number of treatments and block sizes. Thus for a relatively large number of treatments and block sizes the required minimum number of blocks may be excessively large for practical use of ED.

In this paper we shall define and examine partially equineighboured designs with n concurrences, PED (n), as alternatives where ED are practically unachievable. Particular attention will be given to designs with smaller numbers of blocks and for which only as little balance as possible may be lost.
THE SOJOURN TIME DISTRIBUTION OF AN ALTERNATING RENEWAL PROCESS
Authors: Rossiter M.H.
Published: February 2008

summary

Ordinary, modified, and equilibrium alternating renewal processes are defined in such a way that the distribution of the sojourn time in one state of a two‐state system may be considered conditional on the starting state. The double Laplace transform of a non‐negative stochastic process is also defined, and used to express a result of Takacs (1957) on sojourn time distributions.
ON SPLINE SMOOTHING WITH AUTOCORRELATED ERRORS
Authors: Diggle Peter J. , Hutchinson Michael F.
Published: February 2008

summary

The generalised cross‐validation criterion for choosing the degree of smoothing in spline regression is extended to accommodate an autocorrelated error sequence. It is demonstrated via simulation that the minimum generalised cross‐validation smoothing spline is an inconsistent estimator in the presence of autocorrelated errors and that ignoring even moderate autocorrelation structure can seriously affect the performance of the cross‐validated smoothing spline. The method of penalised maximum likelihood is used to develop an efficient algorithm for the case in which the autocorrelation decays exponentially. An application of the method to a published data‐set is described. The method does not require the data to be equally spaced in time.
A SELECTED BIBLIOGRAPHY ON THE ANALYSIS OF REPEATED MEASUREMENTSandRELATED AREAS
Authors: Diggle Peter J. , Donnelly John B.
Published: February 2008

summary

Different approaches to the analysis of repeated measurements are outlined. For each approach, a few key references are given as a possible basis for further reading. Related methodological areas are mentioned, again accompanied by key references in each case.
LIMIT THEOREMS FOR STANDARDIZED PARTIAL SUMS OF WEAKLY EXCHANGEABLE ARRAYS
Authors: Robinson J.
Published: February 2008

summary

A symmetric array of random variables is weakly exchangeable if, when the same arbitrary permutation is applied to rows and columns, the joint distribution remains the same. We consider the asymptotic distribution of the standardized sums of the elements of the upper left hand corner of the partitioned array, generalizing results on U‐statistics. In general, the asymptotic distribution is normal, but if the array is first standardized by subtracting row and column means, then it is a linear form in a normal variable and independent squares of normal variables with coefficients depending on the limits of the eigenvalues of the array.
A Discrete Time Parametric Model for the Analysis of Failure Time Data
Authors: Adams Geoff , Watson Ray
Published: February 2008

This paper introduces a parametric discrete failure time model which allows a variety of smooth hazard function shapes, including shapes which are not readily available with continuous failure time models. The model is easy to fit, and statistical inference is simple. Further, it is readily extended to allow for differences between subjects while retaining the ease of fit and simplicity of statistical inference. The performance of the discrete time analysis is demonstrated by application to several data sets.
SMALL SAMPLE VARIANCE ESTIMATORS FOR U‐STATISTICS
Authors: Schucany William R. , Bankson Daniel M.
Published: February 2008

New unbiased estimators are presented for the dominant and lower‐order terms of the variance expansion for U‐statistics. In small samples these provide important corrections to the usual estimate of asymptotic standard error which is based on the leading term in the expansion. The new estimators for the first term cannot be recommended. The ordinary jackknife estimator is found to be more effective than the direct estimates of the separate terms.
AN APPROACH TO THE SAMPLING THEOREM FOR CONTINUOUS TIME PROCESSES
Authors: Pogány Tibor
Published: February 2008

In this paper we extend the sampling theorem to the full spectrum of weakly stationary stochastic processes. The mean square approximation error bound is also given.
QUANTILES OF SUMS AND EXPECTED VALUES OF ORDERED SUMS
Authors: Liu Jingyu , David H.A.
Published: February 2008

Watson & Gordon (1986) investigated the relationship between the quantiles of a sum of independent continuous random variables and the sum of the individual quantiles. In this note some further results are obtained. Also corresponding relationships are developed for the expected values of the order statistics of a sum, and for the sum of the expected values of the individual order statistics.
TEST FOR TREATMENT EFFECT BASED ON BINARY DATA WITH RANDOM SAMPLE SIZES
Authors: Shao Jun , Chow Shein‐Chung
Published: February 2008

The problem of testing for treatment effect based on binary response data is considered, assuming that the sample size for each experimental unit and treatment combination is random. It is assumed that the sample size follows a distribution that belongs to a parametric family. The uniformly most powerful unbiased tests, which are equivalent to the likelihood ratio tests, are obtained when the probability of the sample size being zero is positive. For the situation where the sample sizes are always positive, the likelihood ratio tests are derived. These test procedures, which are unconditional on the random sample sizes, are useful even when the random sample sizes are not observed. Some examples are presented as illustration.
THE CONSTRUCTION OF EQUILEVERAGE DESIGNS FOR MULTIPLE LINEAR REGRESSION
Authors: Dollinger Michael B. , Staudte Robert G.
Published: February 2008

The hat matrix is widely used as a diagnostic tool in linear regression because it contains the leverages which the independent variables exert on the fitted values. In some experiments, cases with high leverage may be avoided by judicious choice of design for the independent variables. A variety of methods for constructing equileverage designs for linear regression are discussed. Such designs remove one of the factors, namely large leverage points, which can lead to nonrobust estimators and tests. In addition, a method is given for combining equileverage designs to test for lack of fit of the linear model.
ON THE VARIANCE‐COVARIANCE MATRIX IN MARKOVIAN MANPOWER SYSTEMS IN CONTINUOUS TIME
Authors: Gerontidis Ioannis I.
Published: February 2008

The variability of the grade sizes in Markovian manpower systems in continuous time is considered. The differential equations describing the evolution of the variance‐covariance matrix are derived and the associated generator is determined in a closed form. The limiting variability of an expanding system is studied via two theorems which provide conditions for the limit to exist independently of the initial distribution and for the rate of convergence to be exponentially fast. A numerical illustration of the theory is given.
TESTING THE STABILITY OF REGRESSION COEFFICIENTS USING GENERALIZED RECURSIVE RESIDUALS
Authors: Michels Paul , Trenkler Götz
Published: February 2008

Simple but flexible methods to detect deviations from the assumption of constant coefficients in linear regression are presented. Based on recursive residuals a runs test is developed as an alternative to CUSUM‐ and MOSUM‐techniques. Finally a simulation study gives insight into the new method.
TABLES OF SMALL OPTIMAL REPEATED MEASUREMENTS DESIGNS
Authors: Street Deborah J. , Eccleston J.A. , Wilson William H.
Published: February 2008

This paper presents tables of the optimal repeated measurements designs for the estimation of direct effects and of residual effects for a model with independent errors, for up to n = 10 experimental units, for t= 2 treatments and p= 2, 3 or 4 periods, and for t= 3 treatments and p= 2 or 3 periods.
VARIABLE KERNEL DENSITY ESTIMATES AND VARIABLE KERNEL DENSITY ESTIMATES
Authors: Jones M.C.
Published: February 2008

The term “variable kernel density estimate” is sometimes used to mean a kernel density estimate employing a different bandwidth for each data point, and sometimes to denote a kernel density estimate with bandwidth a function of estimation location. This expository article stresses the importance of the distinction between these two definitions, both via an introductory description of the ideas involved and in terms of their comparative theoretical performance.