bluuebunny/crossref_metadata_2025 huggingface dataset:
THE THEORY OF COMPETING RISKS1
Authors: David H. A.
Published: February 2008

The 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

This 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.
USING THE SYDNEY AREA TRANSPORTATION STUDY DATA FOR SOCIAL RESEARCH
Authors: Davis J. R.
Published: February 2008

Abstract  A large scale survey conducted for the 1971 Sydney Area Transportation Study (SATS) provides one of the richest sources of urban social data in Australia. This paper tests two characteristics of the sample—the residents' age distribution and the location of the workforce—against the population distribution of these characteristics obtained from the 1971 Census. It is concluded that, whilst the sample does differ significantly from the population, the difference is not so great as to negate the usefulness of this data for social research. Of the possible causes of the difference the most likely is the large nonresponse and noncontact rate encountered by the survey. Finally, given the dearth of basic income information in Australia, some limitations on the application of the SATS household income data for this purpose are discussed.
BEST PREDICTION OF EXPONENTIAL FAILURE TIMES WHEN ITEMS MAY BE REPLACED2
Authors: Kaminsky Kenneth S.
Published: February 2008

Best unbiased and best invariant predictors for exponential failure times are found when items may be replaced as they fail. The best predictors are linear.
BAYESIAN TEST OF HYPOTHESIS IN THE MULTINOMIAL DISTRIBUTION
Authors: Samiuddin M. , Hanif Muhammad
Published: February 2008

For 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.
ON THE DISTRIBUTION OF SPHERICITY TEST CRITERION IN THE MULTIVARIATE GAUSSIAN DISTRIBUTION
Authors: Gupta A. K.
Published: February 2008

In this paper, the exact distribution of the likelihood‐ratio criterion for testing the hypothesis of sphericity in a multivariate normal distribution is derived as a mixture of incomplete beta functions. Some advantages of the present derivation are also indicated.
ASYMPTOTIC THEORY FOR PRINCIPAL COMPONENT ANALYSIS: NON‐NORMAL CASE1
Authors: Davis A. W.
Published: February 2008

This 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.
THE CRAMÉR‐RAO INEQUALITY
Authors: Pitman E. J. G.
Published: February 2008

The essential significance of the Cram‐Rao inequality is investigated. This inequality states a relation between the rate of change of a mean value and a rate of change of the probability measure. Simple, general regularity conditions are obtained.
ON THE ESTIMATION OF TOTAL WEIGHT IN CHEMICAL BALANCE WEXGHING DESIGNS1
Authors: Chacko Annie , Dey A.
Published: February 2008

This 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

An 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

Numerical 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

Given 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

In 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

Pearson (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

Matrix 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

It 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

The 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

A 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

A 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

It 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

Summary

Estimates 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

The 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

The 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

The 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

The 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

Procedures 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

In 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.
Optimal Estimating Equations with Applications to Insect Development Times
Authors: Morton R.
Published: February 2008

This paper proposes a general method of estimation when a function of data and parameters is to be modelled, which is most efficient in a certain sense. It is applied to the following situation. If X(t) is the temperature at time t, the time Y taken for an insect to complete a stage of growth is assumed to satisfy the model.
Anomalies in the Gambling Market
Authors: Tuckwell R. H.
Published: February 2008

Apparent irregularities between the win and the place betting markets in Australian horseracing are examined. Win odds are used to predict win probabilities from which place probabilities are estimated and compared with the place odds on offer. It is concluded that anomalies do in fact exist and are capable, in theory at least, of profitable exploitation.
On Non‐Normal Invariance Principles for Multi‐Response Permutation Procedures
Authors: Brockwell Peter J. , Mielke Paul W. , Robinson John
Published: February 2008

A non‐normal invariance principle is established for a restricted class of univariate multi‐response permutation procedures whose distance measure is the square of Euclidean distance. For observations from a distribution with finite second moment, the test statistic is found asymptotically to have a centered chi‐squared distribution. Spectral expansions are used to determine the asymptotic distribution for more general distance measures d, and it is shown that if d(x, y) = |x — y|u, u† 2, the asymptotic distribution is not invariant (i.e. it is dependent on the distribution of the observations).
Bayes Risk Consistency of Nonparametric Bayes Density Estimates2
Authors: Ghorai J. K. , Rubin H. , Rubin H.
Published: February 2008

Even though the literature on nonparametric density estimation is large, the literature on Bayesian estimation of the density function is relatively small. The reason is the lack of a suitable prior over the space of probability density functions. There have been attempts to define priors over the space of probability measures, but they have not yielded any workable prior for the purpose of density estimation. Dubins & Freedman (1963) have denned random distribution functions which are singular with probability one. Kraft (1964) has denned a class of distribution functions which have derivatives but not continuous derivatives and hence are not suitable for density estimation. The only really convenient prior is the Dirichlet process prior due to Ferguson (1973), but unfortunately this prior concentrates all its mass over the discrete distribution with a dense set of jumps. Recently Lo (1978) has overcome this difficulty by taking convolution of the Dirichlet process with a fixed continuous kernel.

In Section 2, the existence of a version of the posterior distribution and the conditional expectation for arbitrary prior over the space of continuous density functions are discussed. The Bayes risk consistency of the Bayes estimator is discussed in Section 3. The Bayes estimator and its properties with respect to two specific prior distributions are discussed in Section 4. In Section 5 some negative results are presented. Finally a numerical example is given in Section 6.
The Use of Multiplicity in a Household Survey of Disabilities
Authors: Jones Roger G.
Published: February 2008

The multiplicity technique has been proposed (Sirken, 1970) as a means of improving estimates of the number of rare “events” in a population. This paper describes one use of this technique, namely estimation of the number of persons with certain types of disability living in private dwellings in Canberra. The results are taken from three household surveys conducted in Canberra during 1978–79 in which a multiplicity rule linking parents, siblings and children of residents of sample households who were also living in private dwellings in Canberra was used. While no direct evidence on the level of non‐sampling error is available here, it appears that net response errors at least are not substantial using this multiplicity rule and that a reasonable gain in sampling efficiency results from the use of multiplicity.
On the Convergence of the Horvitz‐Thompson Estimator
Authors: Robinson P. M.
Published: February 2008

We investigate the degree to which the Horvitz‐Thompson estimator approximates the population mean in survey sampling. Specifically, conditions for (mean square) consistency are given, along with rates of convergence. The conditions involve only first and second‐order inclusion probabilities, and for various sampling designs they are easy to check.
Estimated Generalized Least Squares for a Heteroscedastic Regression Model
Authors: Anh V. V.
Published: February 2008

This paper considers the general linear regression model yc = X1β+ut under the heteroscedastic structure E(ut) = 0, E(u2) =σ2‐ (Xtβ)2, E(ut us) = 0, tæs, t, s= 1, T. It is shown that any estimated GLS estimator for β is asymptotically equivalent to the GLS estimator under some regularity conditions. A three‐step GLS estimator, which calls upon the assumption E(ut2) =s̀2(X,β)2 for the estimation of the disturbance covariance matrix, is considered.
On Incomplete U‐Statistics Having Minimum Variance
Authors: Lee Alan J.
Published: February 2008

The problem of choosing a design for an incomplete U‐statistic is discussed. Designs yielding minimum variance U‐statistics are presented, and their efficiencies relative to complete U‐statistics studied.
An Investigation of two Sequence‐Comparison Statistics
Authors: Gordon A. D.
Published: February 2008

This paper describes an investigation of two statistics which compare two ordered sequences of objects by providing a measure of the discordance when the sequences are slotted together. Configurations having zero discordance are described. Plausible null models for data are postulated, and an account is given of a simulation study which investigated the distribution of the statistics when these models were used in the analysis of physical logging data from two wells.
Bibliography of Vital Statistics in Australia: a Third List
Authors: Lancaster H. O.
Published: February 2008

This list brings up to date the references in my “Bibliography of Vital Statistics in Australia and New Zealand” Austral. J. Statist. 6 (1964) 33–99 and the “Bibliography of Vital Statistics in Australia: a second list” ibid (1973) 1–26. The cover of the Journals remains the same as listed on page 33 of the original bibliography and continues up to the end of 1980 in most cases. As mentioned in the second list, there are few references to New Zealand sources because of the publication of the bibliography of Dr. J. W. Donovan. Some references are given to works devoted to the health of the aboriginal population but this field is more completely done by Moodie & Pedersen (1971).
ANALYSIS OF DATA FROM A SINGLE EPIDEMIC1
Authors: Becker Niels G.
Published: February 2008

A model with nonrandom latent and infectious periods is suggested for epidemics in a large community. This permits a relatively complete statistical analysis of data from the spread of a single epidemic. An attractive feature of such models is the possibility of exploring how the rate of spread of the disease depends on the number of susceptibles and infectives. An application to smallpox data is included.
ON THE CONVERGENCE RESULT FOR THE SUPERCRITICAL BELLMAN‐HARRIS PROCESS1
Authors: Cohn Harry
Published: February 2008

It was proved in Cohn (1982) that for any finite offspring mean, supercritical Bellman‐Harris process {Z(t)} there exist some norming constants {C(t)} such that {Z(t)/C(t)} converges almost surely to a non‐degenerate random variable W. {C(t)} were defined to be the μ‐quantiles of {Z(t)}. Schuh (1982) has given an alternative proof of this result, identifying C(t) as “the Seneta constants” 1/(‐log Ft(‐1)(γ)), where F1(γ) = E(γZ(t)). Both proofs are long and complicated. It will be shown here that a much simpler proof can be devised from Cohn (1982), if use is made of an elementarily proved property given in Schuh (1982).
WEIGHTED AREA TECHNIQUES FOR THE ESTIMATION OF THE PARAMETERS OF A GROWTH CURVE1
Authors: Leedow M. I. , Tweedie R. L.
Published: February 2008

A weighted area estimation technique which allows explicit estimation of the parameters of the growth curve

lt= L∞[1‐exp(‐K(t‐t0))]

is introduced.

Simulated data are used to compare an optimal weighted area method with that of maximum likelihood. Length at age data from fisheries field studies are used to compare the weighted area and maximum likelihood techniques with the “graphical” method of Ford‐Walford.

The weighted area methods achieve 80–90% efficiency on simulated data, and are shown to provide robust and sensible estimates on field data.
GENERALIZED INVERSES USED IN RECURSIVE ESTIMATION OF THE GENERAL LINEAR MODEL1
Authors: McGilchrist C. A. , Sandland R. L. , Hennessy J. L.
Published: February 2008

Recursive methods in regression have proved useful in providing diagnostic tools for checking the model as well as checking the stability of the model over time. Such methods are now extended to deal with the problems of singularity that arise when one variable is completely confounded with previously fitted variables up to a particular time point. The problem is solved by setting it in the framework of the general linear model with dependent errors.
A NEW EXPANSION FOR THE MULTIVARIATE NORMAL DISTRIBUTION1
Authors: Moran P. A. P.
Published: February 2008

A new expansion is given for the integral of the multivariate normal distribution over a region of the form (V1, m) ×.× (uk, ∞). The regions of convergence and divergence are partially identified and shown to be different from those of the tetrachoric expansion.
APPROXIMATIONS TO SOME TEST STATISTICS FOR PERMUTATION TESTS IN A COMPLETELY RANDOMIZED DESIGN1
Authors: Robinson J.
Published: February 2008

Under a randomization model for a completely randomized design permutation tests are considered based on the usual F statistic and on a multi‐response permutation procedure statistic. For the first statistic the first two moments are obtained so a comparision with the distribution under the normal theory model can be made. The second statistic is shown to converge in distribution to an infinite weighted sum of chi‐squared variates, the weights being the limits of the eigenvalues of a matrix depending on the distance measure used and the order statistics of the observations.
CUMULANTS AND PARTITION LATTICES1
Authors: Speed T. P.
Published: February 2008

The (joint) cumulant of a set of (possibly coincident) random variables is defined as an alternating sum of moments with appropriate integral coefficients. By exploiting properties of the Mobius function of a partition lattice some basic results concerning cumulants are derived and illustrations of their use given.
SOME STATISTICAL DISTRIBUTIONS OF USE IN ANALYSING BIRD COUNT DATA1
Authors: Watterson G. A.
Published: February 2008

The following report arose from an enquiry by a zoologist, J. M. Cullen, concerning various possible ways of analysing bird count data. He was particularly interested in two questions: (i) What is the best way to estimate abundances of various species?, and (ii) What evidence is there that birds occur randomly (in particular, as a Poisson process) as opposed to in flocks or according to some mutual repulsion process?
TESTING FOR MOVING AVERAGE REGRESSION DISTURBANCES
Authors: King Maxwell L.
Published: February 2008

This paper considers a locally optimal procedure for testing for first order moving average disturbances in the linear regression model. For this hypothesis testing problem, the Durbin‐Watson test is shown to be approximately locally best invariant while the new test is most powerful invariant in a given neighbourhood of the alternative hypothesis. Two versions of the test procedure are recommended for general use; one for problems involving positively correlated disturbances and one for negatively correlated disturbances. An empirical comparison of powers shows the clear superiority of the recommended tests over the Durbin‐Watson test. Selected bounds for the tests' significance points are tabulated.
TESTS FOR INDEPENDENCE IN THE PRESENCE OF MISSING VALUES
Authors: Wei L. J.
Published: February 2008

The locally most powerful rank test is derived for testing independence of two random variables with possible missing observations on both responses. The test statistic has a simple form and can be easily obtained. For the purpose of practical use, the asymptotic null distribution of the test statistic is also provided.
TESTING THE CONCORDANCE OF EVENTS WITH THEIR PROBABILITIES
Authors: Moran P. A. P.
Published: February 2008

A test due to D. R. Cox (1958a, 1958b) for the agreement between an observed set of independent events and independently prescribed probabilities is considered. Although the exact distribution can be found for small numbers of events this is often not possible. A method of modifying the scoring system slightly is shown to result in much simpler calculation with very little loss in power. The exact distribution is desirable because of slow convergence to normality. The logic of using a simulation test is considered.
MINIMAX ESTIMATION OF A MULTIVARIATE NORMAL MEAN UNDER A CONVEX LOSS FUNCTION
Authors: Lin Pi‐Erh , Mousa Amany
Published: February 2008

Let X = (X1, ‐ Xp)prime; ˜ Np (μ, Σ) where μ= (μ1, ‐, μp)′ and Σ= diag (Σ21, ‐, Σ2p) are both unknown and p3. Let (ni ‐ 2) wi/Σ2i! X2ni, independent. of wi (I ≠ j = 1, ‐, p). Assume that (w1, ‐, wp) and X are independent. Define W = diag (w1, ‐, wp) and ¶ X ¶2w= X′W‐1Q‐1W‐1X where Q = diag (q1, ‐,n qp), qi > 0, i = 1, ‐, p. In this paper, the minimax estimator of Berger & Bock (1976), given by δ (X, W) = [Ip ‐ r(X, W) ¶ X ¶‐2w Q‐1W‐1] X, is shown to be minimax relative to the convex loss (δ ‐ μ)′[αQ + (1 ‐ α) Σ‐1] δ ‐ μ)/C, where C =α tr (Σ) + (1 ‐ α)p and 0 α 1, under certain conditions on r(X, W). This generalizes the above mentioned result of Berger & Bock.
ADMISSIBILITY OF LIKELIHOOD RATIO RULES IN COVARIATE CLASSIFICATION USING DEPENDENT SAMPLES
Authors: Bandyopadhyay Shibdas
Published: February 2008

The two populations considered for this study are two distinct time points. Samples consist of observations made at both the time points on every sampling unit. The unit to be classified is observed at one of the two time points. The observation vectors contain covariates, having same expectation at both the time points. In this set‐up admissibility of some likelihood ratio rules is established.
ON A STOCHASTIC MODEL FOR AN IRREVERSIBLE SYSTEM OF COMPARTMENTS
Authors: Becker Niels , Finch Caroline
Published: February 2008

summary

A continuous time stochastic model for an irreversible system of kcompartments with nonhomogeneous Poisson inputs is considered. The model allows an arbitrary residence time for each of the compartments. Individuals may enter the system through any compartment and may depart from the system via any compartment.
A New STATISTIC FOR DETECTING INFLUENTIAL OBSERVATIONS IN A SCHEFFE‘ TYPE CALIBRATION CURVE
Authors: Spiegelman Clifford H.
Published: February 2008

summary

A statistic for identifying influential observations in calibration is given. The statistic is easy to interpret, and provides a useful measure of influence for Scheffé type calibration curves.
STRATEGY, NONTRANSITIVE DOMINANCE AND THE EXPONENTIAL DISTRIBUTION
Authors: Kaminsky K. S. , Luks E. M. , Nelson P. I.
Published: February 2008

An easily programmed recursive formula for the evaluation of the distribution function of ratios of linear combinations of independent exponential random variables is developed. This formula is shown to yield the probability that one team beats another in a contest we call the special gladiator game. This game generates tournaments which exhibit nontransitive dominance and have some surprising consequences. Similar results are obtained for a recursive formula based on the geometric distribution.
A K‐SAMPLE EXTENSION TO FLIGNER'S CLASS OF TESTS FOR SCALE
Authors: Koffler Stephen L. , Penfield Douglas A.
Published: February 2008

The parameteric tests for equality of variance are well known. The classical F‐test is typically used to test the hypothesis of equality of two variances, while tests such as those developed by Bartlett (1937) are commonly used for the k‐sample hypothesis. These tests assume an underlying normal distribution and are quite sensitive to departures from normality (Box, 1953). Thus, when considering data that are from non‐normal distributions, alternative nonparametric tests must be employed.

Fligner (1979) has proposed a class of two‐sample distribution‐free tests which possess very desirable properties and are attractive alternatives to other nonparametric tests for scale. The present paper extends the Fligner class of tests to the more general k‐sample case.
A GROUP OF SPLIT‐PLOT DESIGNS WITH A HETEROSCEDASTIC MODEL
Authors: Bhuyan K. C.
Published: February 2008

For a group of split‐plot designs it is assumed that the error variance is constant for a particular experiment but it varies from experiment to experiment. Assuming error variances to be known, estimators of the treatment parameters are obtained by weighted (generalised) least squares method and the corresponding analysis is given. For unknown error variances, an adjustment of the statistics using estimated weights is proposed for removing much of the resulting bias. The adjustment stems from a theorem due to Meier (1953).
GENERATING MECHANISMS OF, AND PARAMETER ESTIMATORS FOR, THE EXTREME VALUE DISTRIBUTION
Authors: Revfeim K. J. A.
Published: February 2008

Identified types of extreme value distributions are obtained from a basic form by variable transformation or truncation. The truncated distribution form is naturally generated as the extreme of a Poisson process with a randomly distributed size of each point event. If the size has a Negative Exponential distribution then, for moderate rates of the Poisson process, the extreme value distribution is of the type often called the Gumbel distribution. A Pareto distribution of size gives a second type which has natural association with a recurrence process of threshold exceedance.

This specification of the extreme value distribution generates the identified distribution types in terms of physically meaningful parameters. The natural two parameter format provides the basis for a three parameter model which allows a more realistic description of the distribution of event sizes.

Extreme values are often associated with data censoring due to some observations being out of range. Equations are given which demonstrate the simple association between estimators of the physically meaningful parameters in censored and uncensored situations.
COMBINING INFORMATION FROM LINEAR MODELS ON POSSIBLY DIFFERENT SCALES
Authors: Berman Mark
Published: February 2008

This paper examines the joint statistical analysis of M independent data sets, the jth of which satisfies the model λjYj=XjB +εj, where the λjare unknown and the εiare normally distributed with a known correlation structure. The maximum likelihood equations, their asymptotic covariance matrix, and the likelihood ratio test of the hypothesis that the λjs are all equal are derived. These results are applied to two examples.
CHANGE‐OVER DESIGNS WITH ERRORS FOLLOWING A FIRST ORDER AUTOREGRESSIVE PROCESS
Authors: Bora A. C.
Published: February 2008

This paper deals with the problem of analysing the change over design in the context of a first order autoregressive process for the error terms. The method of maximum likelihood has been adopted for estimating treatment effects. The conditions derived for obtaining a balanced change over design show that a change over design balanced in the absence of autocorrelation is not necessarily balanced in the presence of autocorrelation. Also, it is observed that the autocorrelation co‐efficient and the treatment effect when p≠0 can be tested as usual with the likelihood ratio test criterion.
CHARACTERIZATIONS OF MULTINOMIAL AND NEGATIVE MULTINOMIAL MIXTURES BY REGRESSION
Authors: Papageorgiou H.
Published: February 2008

Characterizations are given for mixtures of multinomial and negative multinomial distributions with respect to their index parameter. Several well known multivariate discrete distributions are used as illustrative examples.
SURVEY DESIGN
Authors: Foreman E. K.
Published: February 2008

summary

Survey design involves planning and documenting questionnaires, sample selection and survey operations. It constitutes a simultaneous solution to numerous interrelated conceptual and practical design issues, more than may usually be settled effectively, or even recognised, in any reasonable time by contemplation alone. The alternative is an iterative approach, making a trial plan, testing and then improving it, and, if necessary, repeating it until a satisfactory plan is evolved. Pilot testing can then become the focus of design decisions by providing relevant data and operating experience, and by using experimental methods, as a basis for adroit revision of trial survey plans. This paper concerns the planning of efficient survey design processes along these lines.
DELIBERATELY BIASING SURVEY QUESTIONS
Authors: Fischer A. J. , Lewis R. D.
Published: February 2008

summary

In “before” and “after” surveys of Attitudes Towards Random Breath Testing in South Australia, three basic versions of the questionnaire were used. In the first, a set of “lead‐up” questions, which were designed to deliberately bias the results towards acceptance of the tests, was included before the main questions; in the second, there were no lead‐up questions; in the third, a different set of lead‐up questions was used, and was aimed at deliberately biasing the results against the tests. The results in two out of the four attempts to influence the answers (compared with no lead‐up questions) were significant in the expected direction, and in the other two cases were in the correct direction but not significant. The difference between the positive‐and negative‐biasing versions was highly significant in both cases. It is important to be aware that changes in context rather than in question wording per se can give rise to effects which dwarf the sampling error.
A NEW PROCEDURE FOR ASSESSING LARGE SETS OF CORRELATIONS
Authors: Cameron M. A. , Eagleson G. K.
Published: February 2008

In this paper, a new test of the hypothesis that all the correlations between a set of variables are zero is proposed. It is based on the asymptotic behaviour of the largest of the observed correlation coefficients. Here “asymptotic” refers to the size of the correlation matrix considered. Simulations show that the critical levels, calculated using the asymptotic theory, are conservative but quite accurate, even for small correlation matrices.
ON THE INVARIANCE OF ISOMETRY UNDER UNEQUAL SCALE CHANGES
Authors: James Ian R.
Published: February 2008

Isometry is the independence of a size variable G(X) and shape. This note characterizes G(X) =γΦXb1i as the only continuous size variable for which isometry with respect to G can continue to hold for all unequal changes of scale of the variables Xi, assuming some conditions on the ranges of the Xi.
GROUPING PROBLEMS IN DISTRIBUTION‐FREE REGRESSION1
Authors: Brown B. M.
Published: February 2008

In regression models having symmetric errors, exact distribution‐free inference about individual parameters may be carried out by grouping observations, eliminating unwanted parameters within groups, and applying distribution free techniques for the symmetric location parameter problem. Models whose errors have identical but not symmetric distributions may obtain symmetry by taking differences between pairs of observations. Both grouping and differencing involve potential efficiency loss. The choice of an optimal scheme to minimize efficiency loss is expressible as a multi–assignment type of problem, whose solutions, exact and approximate, are discussed.
THE EFFECTS OF CORRELATION AMONG OBSERVATIONS ON THE ACCURACY OF APPROXIMATING THE DISTRIBUTION OF SAMPLE MEAN BY ITS ASYMPTOTIC DISTRIBUTION1
Authors: Sharma Subhash C.
Published: February 2008

In this paper, we investigate the effects of correlation among observations on the accuracy of approximating the distribution of sample mean by its asymptotic distribution. The accuracy is investigated by the Berry‐Esseen bound (BEB), which gives an upper bound on the error of approximation of the distribution function of the sample mean from its asymptotic distribution for independent observations. For a given sample size (n0) the BEB is obtained when the observations are independent. Let this be BEB. We then find the sample size (n*) required to have BEB below BEB0, when the observations are dependent. Comparison of n* with n0 reveals the effects of correlation among observations on the accuracy of the asymptotic distribution as an approximation. It is shown that the effects of correlation among observations are not appreciable if the correlation is moderate to small but it can be severe for extreme correlations.
THE MULTIPLE CORRELATION COEFFICIENT AND FISHER'S A STATISTIC1
Authors: Venable W.N.
Published: February 2008

Fisher's A statistic, often called the adjusted R2 statistic, is shown to be a close approximation to the maximum likelihood estimate of the multiple correlation coefficient, p2, based on the marginal distribution of R2. Expansions for the estimate are obtained. The same methods lead to maximum marginal likelihood estimators for the noncentrality parameters for noncentral X2 and F.
MINIMUM MSE ESTIMATION BY LINEAR COMBINATIONS OF ORDER STATISTICS1
Authors: Samanta M.
Published: February 2008

In this paper we assume that in a random sample of size ndrawn from a population having the pdf f(x; θ) the smallest r1 observations and the largest r2 observations are censored (r1≥0, r2≥0). We consider the problem of estimating θ on the basis of the middle n‐r1‐r2 observations when either f(x;θ)=θ‐1f(x/θ) or f(x;θ) = (aθ)1f(x‐θ)/aθ) where f(·) is a known pdf, a (<0) is known and θ (>0) is unknown. The minimum mean square error (MSE) linear estimator of θ proposed in this paper is a “shrinkage” of the minimum variance linear unbiased estimator of θ. We obtain explicit expressions of these estimators and their mean square errors when (i) f(·) is the uniform pdf defined on an interval of length one and (ii) f(·) is the standard exponential pdf, i.e., f(x) = exp(–x), x≥0. Various special cases of censoring from the left (right) and no censoring are considered.
ON ESTIMATING THE SPREAD OF A DISTRIBUTION ABOUT ITS REGRESSION SLOPES1
Authors: Breth M.
Published: February 2008

Nonparametric tolerance regions are used to estimate the spread of a distribution about known regression slopes. When the slopes are not known their sample estimates are employed.
ERROR RATES FOR ORTHOGONAL CONTRASTS AFTER A SIGNIFICANT F‐TEST1
Authors: Gordon Ian
Published: February 2008

Tables are given for the experiment‐wise error rate when orthogonal contrasts are tested following a significant F test in a balanced one‐way classification.
A TEST OF HOMOGENEITY AGAINST SCALE ALTERNATIVES USING SUBSAMPLE EXTREMA1
Authors: Gore A. P. , Shanubhogue Ashok
Published: February 2008

In this paper a new class of non‐parametric tests for testing homogeneity of several populations against scale alternatives is proposed. For this, independent samples of fixed sizes are drawn from each population and from these samples, all possible sub‐samples of the same size are drawn and their maxima and minima are computed. Using these extreme the class of tests is obtained. Tests of this type have been offered for the two‐sample slippage problem by Kochar (1978). Under certain conditions, this class of tests is shown to be consistent against ‘difference in scale’ alternatives. The test has been compared with Bhapkar's V‐test (1961), Deshpande's D‐test (1965), Sugiura's Drs‐test (1965) and with a classical test given by Lehmann (1959, pp. 273–275). It is shown that some members of this proposed class of tests are more efficient than the first three tests in the case of uniform, Laplace and normal distributions, when the number of populations compared is small.
ON THE PERFORMANCE OF KOLMOGOROV‐SMIRNOV TESTS ON STABLE RANDOM VARIABLES1
Authors: Hua Tsushung A.
Published: February 2008

This paper provides two procedures to perform the Kolmogorov–Smirnov (K‐S) tests on stable random variables. One utilizes the integral representation of the cumulative distribution function of this random variable to perform the K‐S test; the other utilizes the Gil‐Pelaez‐Roseń transformation of data (Csörg(1983)) to test uniformity on (0,1) for the transformed sample. Both procedures are examined and evaluated by a simulation study.