bluuebunny/crossref_metadata_2025_split huggingface dataset:
EXACT TWO‐SAMPLE MEDIAN TESTS WHEN ONE “SAMPLE” VALUE POSSIBLY FROM A DIFFERENT POPULATION
Authors: Kelleher Grace J. 
Published: February 2008

AbstractRandom samples are assumed for the univariate two‐sample problem. Sometimes this assumption may be violated in that an observation in one “sample”, of size m, is from a population different from that yielding the remaining m—1 observations (which are a random sample). Then, the interest is in whether this random sample of size m—1 is from the same population as the other random sample. If such a violation occurs and can be recognized, and also the non‐conforming observation can be identified (without imposing conditional effects), then that observation could be removed and a two‐sample test applied to the remaining samples. Unfortunately, satisfactory procedures for such a removal do not seem to exist. An alternative approach is to use two‐sample tests whose significance levels remain the same when a non‐conforming observation occurs, and is removed, as for the case where the samples were both truly random. The equal‐tail median test is shown to have this property when the two “samples” are of the same size (and ties do not occur).
CHARLES HENRY WICKENS: 1872–1939
Authors: Lancaster H. O. 
Published: February 2008

SummaryAn account of the life of the second Commonwealth Statistician, Charles Henry Wickens (1872–1939), has been given. After a primary school education in a Victorian country centre, Wickens became Associate of the Institute of Actuaries. Having joined the public service of Western Australia in 1897, he was appointed Compiler in the Commonwealth Bureau of Census and Statistics in 1906; he served as Commonwealth Statistician and Actuary, 1922 to 1932, giving outstanding service as government adviser and head of an important government department. He was a leader among theoretical and practical economists. His contributions to the study of Australian demography, especially life tables and vital statistics, were of the highest quality and permanent value. He made also scholarly contributions to actuarial theory and to the popularization of the work of the Bureau.
THE FUNDAMENTAL FORMULA OF BLASCHKE IN INTEGRAL GEOMETRY AND GEOMETRICAL PROBABILITY, AND ITS ITERATION, FOR DOMAINS WITH FIXED ORIENTATIONS
Authors: Miles R. E. 
Published: February 2008

AbstractThe so‐called “principal formulae” of planar integral geometry are conventionally couched in terms of the “kinematic density”dxdydθ. Here a corresponding theory with respect to the “Lebesgue density”dxdy, that is with rotations suppressed, is developed. The only real difference is that the new “fundamental formula of Blaschke”contains a term depending upon the relative orientations of the two domains involved. In particular, the remarkable iteration property of these formulae carries over. The usual principal formulae follow as a corollary of the formulae given here, upon, averaging over orientations.
ALIGNING OF ESTIMATES: AN ALTERNATIVE TO EMPIRICAL BAYES METHODS
Authors: Maritz J. S. 
Published: February 2008

SummaryThe data that are used in constructing empirical Bayes estimates can properly be regarded as arising in a two‐stage sampling scheme. In this setting it is possible to modify the conventional parameter estimates so that a reduction in expected squared error is effected. In the empirical Bayes approach this is done through the use of Bayes's theorem. The alternative approach proposed in this paper specifies a class of modified estimates and then seeks to identify that member of the class which yields the minimum squared error. One advantage of this approach relative to the empirical Bayes approach is that certain problems involving multiple parameters are easily overcome. Further, it permits the use of relatively efficient methods of non‐parametric estimation, such as those based on quantiles or ranks; this has not been achieved by empirical Bayes methods.
RELATIONS BETWEEN ERGODICITY AND MEAN DRIFT FOR MARKOV CHAINS1
Authors: Tweedie Richard L. 
Published: February 2008

AbstractIf {Xn} is an irreducible aperiodic Markov chain on a state apace denote the mean one step change of position, or “drift”, of {Xn} at j. The main result of this note is to show that, when |µ(j)| is bounded, {Xn} admits a stationary distribution {πj}if and only if for some N > 0 and some state i, lim inf ∑when this holds, the limit infimum is in fact . Many of the known sufficient or necessary criteria for the existence of a stationary distribution can then be derived easily from this and related results.
A LINEAR MODEL WITH ERRORS LACKING A VARIANCE1
Authors: Chambers E. L. , Heathcote C. E. 
Published: February 2008

SummaryThe problem discussed is that of estimating β= (β1, …, βk) in the model Y=βX +ε when X has a specified multivariate distribution and the error ε does not necessarily have a finite second moment, for example, ε symmetric stable. We construct a moment estimator based on the empirical characteristic function and establish asymptotic unbiassedness and normality. Most of the paper is concerned with the case when X is normal. Forms of the suggested estimator are given in (2.5), (4.6) and (5.5).
RANKED SET SAMPLING THEORY WITH SELECTIVE PROBABILITY MATRIX1
Authors: Yanagawa T. , Shirahata S. 
Published: February 2008

AbstractBanked set sampling theory introduced by Mclntyre (1952) is generalized by introducing a Selective Probability Matrix. The theory is intended to make full use of available information and is most useful in situations ‐where a random sample of small size can be readily ordered by visual inspection or other rough gauging methods, and the exact measurement of the sample is costly in time or effort.In this paper an estimator of the population mean is constructed and several properties of it are investigated to demonstrate the advantages of the theory. The cases of perfect ranking and errors in ranking are discussed in detail and it is made clear that errors in ranking do not destroy the usefulness of the method.
THE THEORY OF COMPETING RISKS1
Authors: David H. A. 
Published: February 2008

SummaryThe theory of competing risks is motivated, certain aspects are reviewed critically, and some extensions are indicated. A unified formulation of the theory is given covering dependent as well as independent risks. The relations between various functions useful in the theory are made explicit. In a historical note a valuable early result is put into modern notation. The currently controversial subject of identifiability when risks are dependent is discussed and it is indicated under what conditions some of the difficulties raised can be overcome. Consequences of assuming proportional hazard rates are set out. New conditions are provided under which this assumption holds and it is shown how the assumption may be tested. Some concluding remarks deal with limitations of the theory and point out areas needing further work.
A BIVARIATE BINOMIAL DISTRIBUTION AND SOME APPLICATIONS1
Authors: Hamdan M. A. , Jensen D. R. 
Published: February 2008

SummaryThis study is concerned with the joint distribution of the total numbers of occurrences of binary characters A and B, given three independent samples in which both characters, A but not B, and B but not A, are observed. The distribution function is given; its conditional distributions and regression functions are found; bounds on certain joint probabilities are established; and conditions for bivariate Poisson and Gaussian limits are studied. An application yields the joint distribution of sign statistics for the pair‐wise comparison of treatments with a control.
BAYESIAN TEST OF HYPOTHESIS IN THE MULTINOMIAL DISTRIBUTION
Authors: Samiuddin M. , Hanif Muhammad 
Published: February 2008

SummaryFor Dirichlet priors in a multinomial distribution the Bayesian test of a simple hypothesis parallels the Bartlett test of homogeneity of variances in normal samples. This parallelism enables a correction factor to be developed for a particular test statistic along the lines of Bartlett's correction. The performance of the corrected test statistic is studied numerically.
ASYMPTOTIC THEORY FOR PRINCIPAL COMPONENT ANALYSIS: NON‐NORMAL CASE1
Authors: Davis A. W. 
Published: February 2008

SummaryThis paper considers the asymptotic distributions of latent roots and vectors in principal components analysis when the parent population is non‐normal. It is shown that sufficient of T. W. Anderson's asymptotic theory in the multivariate normal case carries over for some results to be obtained.
ON THE ESTIMATION OF TOTAL WEIGHT IN CHEMICAL BALANCE WEXGHING DESIGNS1
Authors: Chacko Annie , Dey A. 
Published: February 2008

SummaryThis paper is concerned with the problem of estimation of total weight in a chemical balance weighing design. Some results regarding the estimability of the total weight are obtained and a lower bound for the variance of the estimated total weight is given. Finally, a series of weighing designs estimating the total weight in an ‘optimum’ manner is reported.
TWO‐SPECIES SYSTEMS IN RANDOM ENVIRONMENT
Authors: Prajneshu  
Published: February 2008

AbstractAn exactly solvable model for two interacting species with stochastic parameters is investigated. The parameter describing the interaction is assumed to be characterized by a dichotomic Markov process. It is remarkable that in contrast to the usual oscillatory behaviour in the deterministic case the expected value of the logarithm of each population size, as a consequence of parametric stochastic perturbations, attains a stable value as time increases. check that in their absence the damping term vanishes, leading to the deterministic model of Gomatam.
A LINEAR MODEL WITH ERRORS LACKING A VARIANCE II1
Authors: Chambers R. L. , Heathcote C. R. 
Published: February 2008

SummaryNumerical results are presented for estimates of the parameters in the linear model Y =βX +ε in which X is normally distributed and ε is symmetric stable. The study complements an earlier paper of the same title and the main concern is with numerical comparisons between four estimates of β; the least squares estimate, the minimum absolute deviations estimate, and two moment estimates of the form derived in Chambers and Heathcote (1975). The generation of fifty independent sets of observations (Xj, Yj), j = 1,2, …, n for each of n = 100, 500 and selected combinations of parameter values provided the basis of the results. It is indicated that the moment estimators and the minimum absolute deviation estimator performed comparably, and are a significant improvement on the least squares estimator. The main conclusion is that one of the moment estimates, based on a two stage adaptive procedure and denoted by β¯n(ta) below, is generally the most useful of the four.
OPTIMAL CRITICAL VALUES FOR A PRELIMINARY TEST IN POOLING MEANS
Authors: Ohtani Kazuhiro , Toyoda Toshihisa 
Published: February 2008

SummaryGiven two random samples from normal populations with the same known variance, the experimenter wishes to estimate the mean of the fist population. Whether to pool the two samples or not is made to depend on the result of a preliminary normal test. The bias and mean square error of the pre‐test estimator are presented. Based on two different criteria, a minimax regret and a minimum expected regret ones, the optimal critical values for the pre‐test are given. The minimax regret value is unique (about 1.37), while the alternative values vary depending on the mean and precision included in the prior distribution.
ON ASSESSING THE POTENTIAL SEVERITY OF AN OUTBREAK OF A RARE INFECTIOUS DISEASE: A BAYESIAN APPROACH
Authors: Heyde C. C. 
Published: February 2008

SummaryIn this paper an infective population, during the early stages of the outbreak of a disease, is approximated by a Galton‐Watson process. Attention is focused on the threshold theorem which assesses an epidemic as major if the associated Galton‐Watson process is supercritical (i.e. the mean μ of the offspring distribution is greater than one). A Bayesian formulation is adopted together with the assumption of a power series offspring distribution and an approximate form is found for P(μ >1) computed from the posterior distribution of μ. Exact results are given for the case of a Poisson offspring distribution. The results are illustrated with applications to three sets of data on smallpox outbreaks. The Bayesian approach has a number of advantages over classical methods and in particular allows the cases μ < 1, μ > 1 to be treated without distinction.
ON THE STRUCTURE OF PEARSON'S BISERIAL CORRELATION
Authors: Hamdan M. A. 
Published: February 2008

AbstractPearson (1909) introduced a special method for estimating the correlation coefficient between a two‐level variate X and a c‐level variate Y, where it is assumed that the regression of Y on X is linear. Pearson's estimator, called biserial correlation, is thus obtained from a sample of size n from a 2 ×c table. On the other hand, Lancaster and Hamdan (1964) introduced the polychoric estimator of the correlation between two variates X and Y from a sample available in the form of an r×c contingency table. Later, Hamdan (1968) proved that Pearson's (1900) tetrachoric estimator is a special case of Lancaster and Hamdan polychoric estimator. The present paper applies the orthonor‐mal technique which underlies Lancaster's partition of chi‐squared (1949) to show that Pearson's biserial correlation is a special form of Lancaster and Hamdan's polychoric estimator.
MATRIX ANALYSIS OF THE CASH FLOWS AND RESERVES OF A LIFE OFFICE
Authors: Pollard J. H. 
Published: February 2008

SummaryMatrix projection methods have been used by demographers to prove a number of powerful general theorems concerning population growth and development. The methods have also been applied to the study of graded social systems and to problems of manpower planning. The policy‐holders of a life office and the members of a superannuation fund belong to graded systems with age as the important hierarchical variable. The abovementioned methods can therefore be used to study the growth and development of the membership of these institutions.Recent articles by Sherris (1977), and Pollard and Sherris (1979a, 1979b) have shown that matrix analysis is also very useful for projecting the cash flows and reserves of life assurance companies and superannuation funds.In this paper the use of these methods is illustrated by the projection of the reserves of a life office writing whole‐life assurance contracts. We find that as the fund matures, it grows exponentially.
SCREENING FOR BREAST CANCER
Authors: Tallis G.M. , O'Neu T. J. , Leppard P. , Sarfaty G. 
Published: February 2008

SummaryIt is widely recognized that early detection of malignant cancer is associated with increased survival prospects. If regular examinations are given, then in the case of breast cancer, there is a high chance of locating lesions before they would normally be found by the patient. Such examinations are called screenings and may involve several detection modalities. The two main parameters in the design of a screening program are the frequency of examination and the sensitivity of the detection modality. Models are developed in this paper to examine the effect of screening on the sue of tumors at the time of detection. They are then used to assess the effect of the frequency and sensitivity of the screening program on the non‐recurrence rate for breast cancer. As a result of the modelling, various recommendations on screening design are given.
SAMPLING ERRORS IN THE ELECTORAL PROCESS FOR THE AUSTRALIAN SENATE
Authors: FISCHER A. J. 
Published: February 2008

SummaryThe Australian Senate is elected using a form of proportional representation in each of the six States and two Territories. Those candidates who receive more than a “quota” of votes are elected. In those cases where not enough candidates receive a quota of votes, the surplus votes of each elected candidate (that is, votes over and above the quota) are transferred to the remaining candidates, according to preferences expressed by the voters. These surplus votes are chosen at random and although constraints are placed in order to reduce the sampling error, there is nevertheless a small error introduced in most elections due to sampling. ‐The method of calculating this error has several unusual features and is therefore given in detail for one case, that of the 1974 Senate election for Victoria. Results are tabulated for all States for the elections of 1970, 1974 and 1975. An estimate of how often the wrong candidate will be elected by chance is given. Finally, a simple method for avoiding the sampling problem is suggested.
RANDOM PATHS ORIGINATING WITHIN A CONVEX REGION AND TERMINATING ON ITS SURFACE
Authors: Enns E. G. , Ehlers P. F. 
Published: February 2008

SummaryA ray is defined as a straight line originating within an arbitrary convex body K in n‐dimensional Euclidean space and terminating on the surface of K. The distributions of ray length are derived for three types of randomness. The results are expressed as functions of the overlap volume and overlap surface content of K with its translated self.
NECESSARY AND SUFFICIENT CONDITION FOR A BALANCED ARRAY OF STRENGTH 21 TO BE A BALANCED FRACTIONAL 2 FACTORIAL DESIGN OF RESOLUTION 2l
Authors: Shirakura Teruhiro 
Published: February 2008

SummaryA necessary and sufficient condition for a balanced array of strength 2l to be a balanced fractional 2m factorial design of resolution 2l is given. This design has the property that the main effects, two‐factor interactions,.and (l‐1)‐factor interactions are estimable ignoring the (l + 1)‐factor and higher order interactions, and that the covariance matrix of their estimates is invariant under any permutation of m factors. The above condition includes sufficient conditions given in earlier works of Shirakura (1976b, 1977).
A NOTE ON THE MULTIVARIATE LINEAR MODEL WITH CONSTRAINTS ON THE DEPENDENT VECTOR
Authors: Fisher N.I. , Hudson H. M. 
Published: February 2008

SummaryIt is shown that the least squares estimators of B and Σ in the multivariate linear model {EYi=X1B, D(Yi) =Σ, 1 ≤i≤n, Y1Yn uncorrelated} subject to the constraints YiM=XiN are just the usual least squares estimators B̂= (X'X)‐1X'Y and ΣC = 1/n(Y‐XB̂)(Y‐XB̂) in the unconstrained model where Σ has full rank. Tests of hypotheses concerning B are discussed for situations in which each Yi has a multivariate normal distribution, and examples of the applicability of the model reviewed.
MEDIAN ESTIMATES IN SIMPLE LINEAR REGRESSION
Authors: Brown B. M. 
Published: February 2008

SummaryEstimates in simple linear regression which minimize the sum of absolute values of residuals are discussed. These estimates, called median‐estimates, are an analogue of the sample median, and their properties reflect this. A simple graphical procedure, related to an early (1923) one of Edgeworth, is outlined for computing median estimates. This method works well in small or moderate samples, and is demonstrated on two examples. The small sample distribution of the median estimates is examined by conditioning on the pattern of signs of the residuals, and the resulting conditional distribution gives qualitative information on the adequacy of the approximation of the exact distribution by the (known) asymptotic distibution.
THE BOTTOMLESS DAM WITH SEASONAL INPUTS
Authors: Phatarfod Ravindra M. 
Published: February 2008

SummaryThe stationary distribution of the depletion (from the maximum content) of a bottomless dam is derived for the case where the inputs and releases are seasonal. The method used is an extension of the method of Wishart for a problem in queueing theory (without involving seasonality). A numerical example is given illustrating the method for the case of two seasons.In some recent work on dams (see Phatarfod, 1979; Pakes & Phatarfod, 1978), it was shown that it was more appropriate to consider the bottomless (or the infinitely deep) dam model rather than the topless (or the infinitely high) dam model as an approximation to the finite dam. The main consideration is that in real‐life reservoir situations, the planned release or draft is almost always less than the mean inflow. It is obvious that with this condition the content of a topless dam will not have a stationary distribution, whereas if we consider the depletion of a dam from its top, this will have a stationary distribution. An additional reason for considering the bottomless dam model is that the model is mathematically more tractable; this property was noticed before for continuous time models (see e.g. Hasofer, 1966)
MINIMUM VARIANCE UNBIASED ESTIMATION OF PROBABILITY DENSITIES
Authors: Singh Jagbir 
Published: February 2008

SummaryThe purpose of this note is to point out an elementary method for deriving the minimum variance unbiased (mvu) estimators of probability densities. The method is illustrated by estimating the densities of some well known important distributions. We believe that this note would be of interest especially to both teachers and students of a first course in mathematical statistics.
Looking Forward into the 1980's: A Personal View of the Problems and Prospects for the Statistical Profession
Authors: Heyde C. C. 
Published: February 2008

SummaryThe paper begins with a discussion of the state of research and development in Australia, and the effect of technological change, and then provides an assessment of consequent Government policy on the funding of research and development and of tertiary educational institutions. This is then related to likely consequences for the statistical profession.Various issues facing the Statistical Society and statisticians in general are discussed. These include public responsibility in the face of scepticism resulting from widespread statistical misrepresentation, employment opportunities for graduates, the relationships between theoreticians and practitioners, and the state of the statistical literature.
On Estimating Internal Migration for Open Populations
Authors: Brosnan Peter 
Published: February 2008

SummaryThe purpose of this note is to review the case for using the forward census survival ratio (FCSR) method for estimating internal migration. Though this technique seems likely, on certain criteria, to offer usable estimates of migration, it suffers from what some critics regard as a crucial weakness, namely a sensitivity to international migration. It is argued here, however, that this deficiency is less damaging than others have made it out to be. Consequently, a case can be made for preferring the FCSR method to other methods.
Graphical Comparison of Covariance Matrices
Authors: Campbell N. A. 
Published: February 2008

SummaryProcedures for comparing within‐group covariance matrices are developed, based on separate analyses of the variances and of the correlations. The variances and the correlations are represented as two two‐way tables, with the columns representing groups. Graphical procedures based on comparisons of linear regressions are presented, by considering a multiplicative columns‐regression model for the interaction of groups x variances and of groups x correlations. A multivariate comparison leads to the use of a generalized eigenanalysis to display any differences in covariance structure.
Discriminating Between the Von Mises and Wrapped Normal Distributions
Authors: Collett D. , Lewis T. 
Published: February 2008

SummaryIn the analysis of circular data, we encounter two models which lay claim to the title of normal distribution: the von Mises and wrapped normal distributions. In this paper, we consider whether it is possible to distinguish between them in a practical situation. More specifically, given data from a circular distribution which may be either von Mises or wrapped normal, we enquire as to how large a sample is required in order to tell them apart.