bluuebunny/crossref_metadata_2025 huggingface dataset:
THE LIMITING FORM OF THE NON‐CENTRAL WISHART DISTRIBUTION1,2
Authors: Jensen D.B.
Published: February 2008

Let S (p×p) have a Wishart distribution ‐with v degrees of freedom and non‐centrality matrix θ= [θjK] (p×p). Define θ0= min {| θjk |}, let θ0→∞, and suppose that | θjK | = 0(θo). Then the limiting form of the standardized non‐central distribution, as θ while n̈ remains fixed, is a multivariate Gaussian distribution. This result in turn is used to obtain known asymptotic properties of multivariate chi‐square and Rayleigh distributions under somewhat weaker conditions.
CONFIDENTIALITY, PRIVACY AND SENSITIVITY IN HOUSEHOLD SURVEYS
Authors: Ware H. , Caldwell J. C.
Published: February 2008

Editorial Note: The personal nature of questions included in some surveys is a matter of interest and possibly concern to statisticians. At the Editor's request Dr. Ware and Professor Caldwell take up this issue, their comments being largely based on experience gained from a project carried out in 1971.
CONFIDENCE INTERVALS FOR POWER, WITH SPECIAL REFERENCE TO MEDICAL TRIALS*
Authors: Dudewicz Edward J.
Published: February 2008

A technique is given for drawing valid inferences in cases where performance characteristics of statistical procedures (e.g. power for a test, or probability of a correct selection for a selection procedure) depend upon unknown parameters (e.g. an unknown variance). The technique is especially useful in situations where sample sizes are small (e.g. in many medical trials); the “usual” approximate procedures are found to be misleading in such cases.
HORVITZ‐THOMPSON AND DES RAJ ESTIMATORS REVISITED
Authors: Rao T. J.
Published: February 2008

In this paper it is shown that the generalized πPS sampling strategy consisting of the design with πi, the probability of inclusion of the ith unit in the sample, proportional to the modified size together with the corresponding Horvitz‐Thompson estimator (Rao, 1971), is superior to the symmetrized Des Raj strategy under a general super‐population set‐up for all values of the super‐population parameter g, when the samples are of size two.
HOUSEHOLD CONSUMPTION OF FOOD IN AUSTRALIA
Authors: Podder N.
Published: February 2008

This paper is the second (see the first reference) in the series of studies entitled “Household Consumption and Income in Australia.” undertaken by the author to analyse data from an Australia‐wide consumption survey (Drane, Edwards and Gates, 1969). Whereas the first study was an investigation into the overall consumption patterns, the present study is devoted to analysing intensively the patterns of household food consumption. Food is especially important since it is the largest single consumption item in the family budget. In this paper the analysis is extended in two main directions. The first is the disaggregation of total food consumption into its components. The degree of disaggregation, however, is limited by the availability of detailed information. Accordingly, only five components of expenditure on food could be effectively considered. The second direction is the investigation of the possible differences in food consumption patterns among various sociological and demographic groups. To that end multivariate statistical techniques have been employed.

The first section of this paper gives a brief description of the scope and limitations of the study and sets out different hypotheses that could be tested. The second section discusses the appropriate statistical techniques and the estimation methods that would be useful, while the results and their exposition have been presented in the third section. The final section contains a short comparative study and a few concluding remarks.
ON THE CHOICE OF ESTIMATOR IN SURVERY SAMPLING*
Authors: Rao J. N. K. , Singh M. P.
Published: February 2008

We re‐examine the criteria of “hyper‐admissibility” and “necessary bestness”, for the choice of estimator, from the point of view of their relevance to the design of actual surveys. Both these criteria give rise to a unique choice of estimator (viz. the Horvitz‐Thompson estimator ỸHT) whatever be the character under investigation or sample design. However, we show here that the “principal hyper‐surfaces” (or “domains”) of dimension one (which are practically uninteresting)play the key role in arriving at the unique choice. A variance estimatorv1(ỸHT)(due to Horvitz‐Thompson), which takes negative values “often”, is shown to be uniquely “hyperadmissible” in a wide class of unbiased estimators of the variance ofỸHT. Extensive empirical evidence on the superiority of the Sen‐Yates‐Grundy variance estimatorv2(ỸHT)overv1(ỸHT)is presented.
BOOK REVIEWS
Authors: Vere‐Jones D.
Published: February 2008

Book reviewed in this article:

Winkler, Robert L.
An Introduction to Bayesian Inference and Decision.

Bliss, C. I.
Statistics in Biology.

Sard, A., and Weintraub, S.
A Book of Splines.

Kshirsagar, Anant M.
Multivariate Analysis.

Ghosh, B. K.
Sequential Tests of Statistical Hypotheses.

Rao, C. Radhakrishna, and Mitra, Sujit Kumar.
Generalised Inverse of Matrices and Its Applications.

Balaam, L. N.
Fundamentals of Biometry.

Simmons, Donald M.
Linear Programming for Operations Research.

Strum, Jay E.
Introduction to Linear Programming.

Newman, T. G., and Odell, P. L.
The Generation of Random Variates.

Rényi, Alfred.
Foundations of Probability.

Romanovsky, V. I.
Discrete Markov Chains.
COMPARISON OF THREE NON‐PARAMETRIC TESTS FOR BIVARIATE INTERCHANGEABILITY1
Authors: Ferguson Nancy Lo
Published: February 2008

Given a random sample(X1, Y1), …,(Xn, Yn) from a bivariate (BV) absolutely continuous c.d.f. H (x, y), we consider rank tests for the null hypothesis of interchangeability H0: H(x, y). Three linear rank test statistics, Wilcoxon (WN), sum of squared ranks (SSRN) and Savage (SN), are described in Section 1. In Section 2, asymptotic relative efficiency (ARE) comparisons of the three types of tests are made for Morgenstern (Plackett, 1965) and Moran (1969)BV alternatives with marginal distributions satisfying G(x) = F(x/θ) for some θ≠ 1. Both gamma and lognormal marginal distributions are used.
AN ASYMPTOTIC EXPANSION OF THE EXPECTATION OF THE ESTIMATED ERROR RATE IN DISCRIMINANT ANALYSIS1
Authors: Mclachlan G. J.
Published: February 2008

When a sample discriminant function is computed, it is desired to estimate the error rate using this function. This is often done by computing G(‐D/2), where G is the cumulative normal distribution and D2 is the estimated Mahalanobis' distance. In this paper an asymptotic expansion of the expectation of G(‐D/2) is derived and is compared with existing Monte Carlo estimates. The asymptotic bias of G(‐D/2) is derived also and the well‐known practical result that G(‐D/2) gives too favourable an estimate of the true error rate
A DISTRIBUTION‐FREE TEST FOR TWO‐WAY LAYOUT1
Authors: Tan K. C. , Gore A. P.
Published: February 2008

ABSTRCTS

Many nonparametric tests have been proposed for the hypothesis of no row (treatment) effect in a one‐way layout design. Examples of such tests are Kruskal‐Wallis H‐test, Bhapkar's (1961) V‐test and Deshpande's (1965) L‐test. However not many tests are available for testing the same hypothesis in a two‐way layout design without interaction. Perhaps the only “established” test is the one due to Friedman (1937). However, it applies to the case of one observation per cell only. In this paper, a new distribution‐free test is proposed for the hypothesis of row effect in a two‐way layout design. It applies to the case of several observations per cell, not necessarily equal. The asymptotic efficiency of the proposed test relative to other tests is studied.
ITERATIVE ANALYSIS OF GENERALIZED LATTICE DESIGNS
Authors: Williams E. R.
Published: February 2008

Generalized lattice designs are defined. They include as special cases the square and rectangular lattice designs, and the α‐designs defined by Patterson and Williams (1976). An iterative procedure is given for the combined estimation of variety effects in generalized lattice designs with optimal or near optimal efficiency factors. This procedure, together with an approximate variance matrix, enables the analysis of efficient generalized lattice designs to be carried out on mini computers.
FAMILY BUILDING DIFFERENCES BETWEEN SAME SEX AND MIXED SEX FAMILIES IN AUSTRALIA
Authors: Young Chrbtabel M.
Published: February 2008

From this investigation it seems that an aversion among some couples to a same sex family has some relevance in family building. However, although there are significant differences in the proportions of same sex and mixed sex families having an additional child, the overall effect on average family size of the (apparent) attempt to achieve a child of each sex appears to be slight—an increase of less than 3% in the case of the Melbourne data.

Despite the evidence that a significantly greater proportion of women with same sex families have another child, relatively few women admit that the sex structure of the children was the main factor in such a decision. Another insight into the relationship between sex structure and family building was that the desire for a child of each sex may have a negative effect on fertility in that couples who have already achieved such a configuration may decide not to have an additional child that they had originally planned to have.

Obviously, it is difficult to separate attitudes to the importance of having both sons and daughters from rationalisations associated with the sex structure of the respondent's own family. Nevertheless the desire for children of each sex seems to be related to traditional attitudes to woman's role, Southern European background, an earlier year of birth, and a lower level of education. However, at the same time women in these categories, particularly the last, seem to be relatively less likely to exhibit behaviour indicative of a controlled response to the sex structure of the family; thus among such groups the probability of same sex families having another child is found to be relatively similar to the proportion of mixed sex families having another child. In other words, they are less likely than other women, who care less about having both sons and daughters, to stop at two (or three) children when at least one son and one daughter have been attained.

What of the future relationship between proportions of same sex and mixed sex families having another child? Although it would seem that the combined effect of better educational opportunities and less traditional attitudes of each new generation would further reduce the importance attached to having both sons and daughters, at the same time one would expect an increase in a couple's ability to stop family building when two or three children of the desired sex structure had been achieved. Another factor is that possibly an increasing preference for smaller families will outweigh the wish to have a third (or fourth) child to achieve one child of each sex or for any other reason.
A NOTE ON THE USE OF INCOMPLETE MULTI‐AUXILIARY INFORMATION IN SAMPLE SURVEYS
Authors: Singh Randhir
Published: February 2008

In this paper an estimation procedure has been suggested making use of multivariate auxiliary information when information on some of the auxiliary variables is not available for the whole population, instead it is known for some parts of the population only.
EMPIRICAL BAYES ESTIMATION WITH NON‐IDENTICAL COMPONENTS. CONTINUOUS CASE.
Authors: O'Bryan Thomas E. , Susarla V.
Published: February 2008

In this paper a variant of the standard empirical Bayes estimation problem is considered where the component problems in the sequence are not identical in that the conditional distribution of the observations may vary with the component problems. Let {(Θn, Xn)} be a sequence of independent random vectors where Θn˜ G and, given Θn=Θn, Xn ‐PΘ,m(n) with {m(n)} a sequence of positive integers where m(n)≤m̄ < ∞ for all n. With PΘ,m in a continuous exponential family of distributions, asymptotically optimal empirical Bayes procedures are exhibited which depend on uniform approximations of certain functions on compact sets by polynomials in eΘ. Such approximations have been explicitly calculated in the case of normal and gamma families. In the case of normal families, asymptotically optimal linear empirical Bayes estimators in the class of all linear estimators are derived and shown to have rate O(n‐1/2).
A FOUR‐MOMENT APPROXIMATION BASED ON THE F DISTRIBUTION
Authors: Tiku M. L. , Yip D. Y. N.
Published: February 2008

In this note, a four‐moment approximation based on the F‐distribution is obtained by equating the first four moments on both sides of the equationF(X + g)/h, whereFhas the central F‐distribution having(v1v2)degrees of freedom. The usefulness of this approximation is illustrated.
A COMPONENT OF VARIANCE DUE TO COMPETITION1
Authors: Federer W. T. , Ladipo O. O.
Published: February 2008

Abstract and Summary

The existence of a component of variance for competition among sampling units or among individuals in a group was discussed by Yates and Zacopany in 1935. No procedure was suggested for estimating this component of variance. It is the purpose of this paper to give a procedure for estimating the component of variance due to competition and to apply the procedure to a set of data on weaning weights of pigs with 116 litters of various sizes and for Yorkshire, Chester‐White, and Berkshire breeds. The first problem was to define litter size. Within this definition then, litters sizes of 3 to 14 pigs per litter were obtained. The variation among pigs within a litter of size h was considered to have an expected value equal to Vs+ Vch where Vs is the sampling variance component and Vch is the competition variance component for a litter of size h. In order to obtain an estimate of Vch, a polynomial relation between h and Vch was postulated. In particular, it was postulated that where E(.) denotes expected value. This form states that Vch goes to zero for one pig per litter; it may be appropriate as long as small litter sizes (say 1 and 2 at least) are omitted from the analysis as was done in the present instance.

Using an iterative procedure of reestimating the weights at each stage, a form of weighted least squares analysis was performed. The procedure appears to converge after three to four steps of iteration. Solutions for some or all of the parameters Vp, Vs, β1 and β2 for h even, h odd, and all h = 3, 4, …, 14, were obtained using among litter mean squares, Ah, only, using within litter mean squares, Wh, only, and using both Ah, and Wh values. The Ah values for h = 3, 4, and 5 appeared to form a different group than for the other values of h. Both the Ah and Wh mean squares were from 56 day weights adjusted for birth weight.

The maximum value of Vch for odd h, was nine whereas it was six for even h. Using all h the maximum value for Vch occurred when h was equal to nine. It appeared that expressing Vch as a quadratic function of litter size was satisfactory for these litter sizes and mean squares.
A RANDOMIZATION PROBLEM IN FORMING DESIGNS WITH SUPERIMPOSED TREATMENTS1
Authors: Preece D. A. , Bailey R. A. , Patterson H. D.
Published: February 2008

Some programmes of experimentation require the superimposition of a new set of treatments on an existing experiment. Randomization of such treatments has received little attention in the literature but merits careful consideration. The present paper examines two apparently different theoretical approaches, one in effect randomizing the experiments together and the other randomizing the second experiment without reference to any randomization used in the first. In the simplest superimpositions the two methods give identical results in practice but problems arise when one Latin square is to be superimposed on another.
EXAMINATION OF REGRESSION RESIDUALS
Authors: Wilson S. R.
Published: February 2008

This article briefly reviews current literature on techniques for the examination of residuals in linear and nonlinear (including Time Series) models. Concentration is on graphical techniques and statistical test procedures (references involving a “routine” examination, computational aspects and discussion of model adequacy having not been included).
POWER ASPECTS OF ANALYSIS OF VARIANCE IN FIXED EFFECT MODEL ONE‐WAY CLASSIFICATION
Authors: Kanji G. K.
Published: February 2008

The sensitivity of the power in analysis of variance to the departure from the in‐built assumptions other than the normality of errors is discussed in Kanji (1975). To obtain the power values he considered the general linear hypothesis model.

Kanji (1976a) discussed a particular case of the above situation, that is fixed effect model two‐way classification. In this paper another particular case, that of the fixed effect model one‐way classification is discussed, the main purpose of which is to investigate whether it could show a different picture to the two‐way classification, especially for unequal replication. The results so obtained are presented in Tables 1A, 1B and 1C. They indicate that the power value is greatly affected by the inequality of error variances and unequal group sizes.
ESTIMATION FOR THE POSITIVE STABLE LAWS, I
Authors: Brockwell P. J. , Brown B. M.
Published: February 2008

Estimation of scale and index parameters of positive stable laws is considered. Maximum likelihood estimation is known to be efficient, but very difficult to compute, while methods based on the sample characteristic function are computationally easy, but have uncertain efficiency properties.

In this paper an estimation method is presented which is reasonably easy to compute, and which has good efficiency properties, at least when the index α (0, 0.5). The method is based on an expression for the characteristic function of the logarithm of a positive stable random variable, and is derived by relating the stable estimation problem to that of location/scale estimation in extreme‐value‐distribution families, for which efficient methods are known.

The proposed method has efficiency which →1 as α→,but on the other hand, efficiencies deteriorate after α >0.5, and in fact appear to →0 as α+ 1.
SOME CHARACTERIZATIONS OF THE CAUCHY DISTRIBUTION
Authors: Arnold B. C.
Published: February 2008

If X and Y are independent standard Cauchy random variables then (i) Y and (X+Y)/(1‐Xu) are independent, (ii) X and (X + Y)/(1 ‐XU) are identically distributed, and (iii) X and 2X/(1‐X2) are identically distributed. Each of these three properties is shown to characterize the Cauchy distribution among absolutely continuous distributions. Some related uniform characterizations are discussed.
ASPECTS OF CORRELATION IN BIVARIATE POISSON DISTRIBUTIONS AND PROCESSES
Authors: Griffiths R. C. , Milne R. K. , Wood R.
Published: February 2008

This paper reviews some interesting but scattered results that are known about correlation in bivariate Poisson distributions and processes and presents some new results. A particular concern in both contexts is with results and examples relating to negative correlation.
THE DESIGN OF CLINICAL TRIALS
Authors: Armitage P.
Published: February 2008

Clinical trials have grown in number and size since their introduction over 30 years ago. They embody Fisherian principles of experimentation, with emphasis on randomization rather than on complex structure. Randomization has recently come under attack, regrettably in the author's view. Much work has been done on methods of achieving balanced randomization, although the advantage of such schemes over post‐trial adjustment is not clear.

Trials are often too small to achieve sensible objects. Size is mainly determined by power considerations, decision‐theoretic models being difficult to relate to practical needs. Sequential methods are available, and have become more flexible.

Problems of planning and execution, on which the statistician's view is important, include the homogeneity or otherwise of patients, uniformity of treatment schedules, procedure for dealing with protocol departures and the avoidance of bias in assessment of response.

Cross‐over designs are useful for the study of short‐term alleviation of chronic disease symptoms, but more attention should be paid to the detection of treatment × period interaction, which is based on between‐subject comparisons. More use should be made of factorial designs, although they give rise to difficulties of interpretation when factors interact.
THE USE OF CORRELATION IN LARGE SAMPLES
Authors: Moran P. A. P.
Published: February 2008

The asymptotic relative efficiency of Kendall's and Spearman's coefficients of rank correlation are considered for samples from a bivariate normal distribution and comments are made on the calculation of their variances. For large samples it is suggested that one should use mean values of the coefficients calculated by splitting the sample into a fairly large number of smaller samples. This reduces the amount of calculation required and the asymptotic relative efficiency of this procedure is found both for ρ= 0 and ρ≠ 0.
OPTIMAL TESTS OF SIGNIFICANCE
Authors: Robinson J.
Published: February 2008

To perform a test of significance of a null hypothesis, a test statistic is chosen which is expected to be small if the hypothesis is false. Then the significance level of the test for an observed sample is the probability that the test statistic, under the assumptions of the hypothesis, is as small, or smaller than, its observed value. A “good” test statistic is taken to be one which is stochastically small when the null hypothesis is false. Optimal test statistics are defined using this criterion and the relationship of these methods to the Neyman‐Pearson theory of hypothesis testing is considered.
SOME LAW OF THE ITERATED LOGARITHM TYPE RESULTS FOR THE EMPIRICAL PROCESS
Authors: Shorack Galen R.
Published: February 2008

We consider Z±n= sup0< t ≤ 1/22 U±n (t)/(t(1‐ t))1/2, where + and ‐denote the positive and negative parts respectively of the sample paths of the empirical process Un. U±n and Un are seen to behave rather differently, which is tied to the asymmetry of the binomial distribution, or to the asymmetry of the distribution of small order statistics. Csáki (1975) showed that log Z±n/log2n is the appropriate normalization for a law of the iterated logarithm (LIL) for Z±n we show that Z‐n/(2 log2n)1/2 is the appropriate normalization for Z‐n. Csörgö & Révész (1975) posed the question: if we replace the sup over (0,1/2) above, by ‐the sup over [an, 1‐an] where an→0, how fast can an→0 and still have |Zn|/(2 log2n)1/2 maintain a finite lim sup a.s.? This question is answered herein. The techniques developed are then used in Section 4 to give an interesting new proof of the upper class half of a result of Chung (1949) for |Un(t)|. The proofs draw heavily on James (1975); two basic inequalities of that paper are strengthened to their potential, and are felt to be of independent interest.
A TEST OF INDEPENDENCE FOR BIVARIATE SYMMETRIC STABLE DISTRIBUTIONS
Authors: DeSilva B. M. , Griffiths R. C.
Published: February 2008

A test of independence in symmetric bivariate stable distributions is constructed using the empirical characteristic function as a test statistic. A particular class of distributions considered in detail is X = U + V, Y=V+W where U, V, and W are mutually independent symmetric stable distributions with the same index.
LOGISTIC REGRESSION COMPARED TO NORMAL DISCRIMINATION FOR NON‐NORMAL POPULATIONS‘
Authors: Byth K. , McLachlan G. J.
Published: February 2008

An investigation is undertaken of the logistic regression procedure for estimating the posterior probability of an object belonging to one of two populations. The asymptotic bias and mean square error associated with the procedure are derived for univariate populations whose distributions satisfy the general Day‐Kerridge model for which the logistic form is valid for the posterior probability. These properties are compared with those of the normal discrimination method based on the classical assumption of normal populations with common variances. The asymptotic relative efficiency of logistic regression is considered on the basis of asymptotic mean square error.
BILATERAL PROCESSES ON A RECTANGULAR LATTICE
Authors: Gleeson A. C. , McGilchrist C. A.
Published: February 2008

A new class of simultaneous bilateral models is introduced to describe spatial dependence on a rectangular lattice. These models, developed primarily for plant competition data, are suitable for small data arrays with sizeable border effects. A maximum likelihood procedure, conditional on fixed border effects, is developed to estimate parameters of such models. Examples are presented for simulated data and for data from a plant competition experiment.
QUANTILE ESTIMATION AND PROBABILITY COVERAGES
Authors: Breth M.
Published: February 2008

When estimating population quantiles via a random sample from an unknown continuous distribution function it is well known that a pair of order statistics may be used to set a confidence interval for any single desired, population quantile. In this paper the technique is generalized so that more than one pair of order statistics may be used to obtain simultaneous confidence intervals for the various quantiles that might be required. The generalization immediately extends to the problem of obtaining interval estimates for quantile intervals. Distributions of the ordered and unordered probability coverages of these confidence intervals are discussed as are the associated distributions of linear combinations of the coverages.
MODEL‐UNBIASEDNESS AND THE HORVITZ‐THOMPSON ESTIMATOR IN FINITE POPULATION SAMPLING
Authors: Ho E. W. H.
Published: February 2008

Under the, notion of superpopulation models, the concept of minimum expected variance is adopted as an optimality criterion for design‐unbiased estimators, i.e. unbiased under repeated sampling. In this article, it is shown that the Horvitz‐Thompson estimator is optimal among such estimators if and only if it is model‐unbiased, i.e. unbiased under the model. The family of linear models is considered and a sample design is suggested to preserve the model‐unbiasedness (and hence the optimality) of the Horvitz‐Thompson estimator. It is also shown that under these models the Horvitz‐Thompson estimator together with the suggested sample design is optimal among design‐unbiased estimators with any sample design (of fixed size n) having non‐zero probabilities of inclusion for all population units.
TESTING FOR INDEPEDENCE IN MULTIVARIATE EXPONENTIAL DISTRIBUTIONS2
Authors: Weer D. R. , Basu A. P.
Published: February 2008

In this paper the work of Weier & Basu (1980) is extended to a special case of the trivariate exponential distributions and to the general k‐variate case. In the trivariate case several statistics are derived including one based on the likelihood ratio approach and the locally most powerful rank statistic, and power studies are carried out. The general k‐variate model is derived, and testing for independence is shown to reduce to a solved problem.
A NOTE ON THE APPLICATION OF THE KALMAN FILTER TO REGRESSION MODELS WITH SOME PARAMETERS VARYING OVER TIME AND OTHERS UNVARYING
Authors: Hatanaka Michio
Published: February 2008

The Kalman filter has been applied to estimation of the time‐varying vector of regression parameters. I investigate the case where a portion of elements of the vector is invariant over time while others are varying as generated by the nonstationary, random walk model. Combined with the regression model it yields a state‐space model in which observability holds but controllability does not. Under Grenan‐der's condition on the exogenous variables I shall show that the estimate of the time‐invariant portion is consistent, despite the seemingly unfavorable circumstances mentioned above, with the order equal to the reciprocal of sample size.
A TWO STAGE PROCEDURE FOR ESTIMATING THE SIZE OF A TRUNCATED EXPONENTIAL SAMPLE
Authors: Watson Dan A. , Blumenthal Saul
Published: February 2008

Let X1, …, XN be i.i.d. exponential random variables with unknown scale parameter θ. If one can observe only those Xi in (0, T0), an estimate of N based on the J observations obtained has a variance which explodes as θ→θC. Using θC based on the observations in (0, T0) T is computed and all Xi in (0, T̂) are observed. An estimate of N based on all observations in (0, T̂) has a bounded variance where the bound can be adjusted by proper choice of T̂.
A NOTE ON PREDICTION SUFFICIENCY (ADEQUACY) AND SUFFICIENCY
Authors: Akahira Masafumi , Takeuchi Kei
Published: February 2008

Let(X, A) be a measurable space and P a family of probability measures on A. Let B and C be sub s̀‐algebras of A and B0 a sub s̀‐algebra of B. It is shown that if B0 is prediction sufficient (adequate) for B with respect to C and P, and Y is sufficient for B0vC with respect to P then Y is sufficient for BvC with respect to P; that if P is homogeneous and (B0; B, C) is Markov for P, and B0vC is sufficient for Bvc with respect to P, then B0 is sufficient for B with respect to P; and by example that the Markov property is necessary for the latter proposition to hold.
RANDOM SAMPLING IN PATTERN RECONSTRUCTION
Authors: Moore Marc
Published: February 2008

A random pattern is the realization of a random set process giving a partition of a set. We are interested by the situation where an unknown random pattern has to be estimated (reconstructed) from sample data. Two sampling strategies to do so are presented. One is of random character the other is not. The risk corresponding to each is obtained. Some numerical comparisons are made for a particular model.
TWO MODEL‐BASED INFERENCE ARGUMENTS IN SURVEY SAMPLING
Authors: Särndal C. E.
Published: February 2008

Which of the two model‐based inference arguments in survey sampling is the “correct” one? The answer seems simple once the goal of the estimation procedure has been clearly defined, but the literature to date on the topic is inconclusive and likely to mislead sampling practitioners. On the one hand we have the approach used by a classical exponent of sampling theory such as Cochran (1977) in those rare instances where he does invoke a model, on the other hand we have the prediction approach formalized by Brewer (1963) and Roy all (1970). (The latter is also available in Bayesian and fiducial versions.) Both approaches are valid, but it is necessary to make a distinction between them. The results they yield are not always identical. In this paper we describe the differences between the two approaches and point to the conditions under which they agree or disagree.
TWO‐STAGE SAMPLING OVER TWO OCCASIONS
Authors: Arnab Raghunath
Published: February 2008

We propose a general sampling strategy for estimating a finite population total for the current occasion based on a two‐stage sampling scheme adopted on the current and a previous occasion. This is in generalization of sampling schemes considered earlier by, among others, Singh (1968), Abraham, Khosla & Kathuria (1969), Singh & Kathuria (1969) and Kathuria (1975). Applications of the general strategy in specific situations are illustrated.
A NOTE ON SAMPLE QUANTILE PROCESSES OF FINITE POPULATIONS
Authors: Singh Kesar
Published: February 2008

A representation is established for sample quantile processes of simple random samples drawn without replacement from finite populations. The result is then used to obtain weak limits of properly normalized quantile processes and their linear functions.
The Exact Null Distribution of Bartlett's Criterion
Authors: Nandi S. B.
Published: February 2008

In this paper the exact null distribution of Bartlett's criterion for testing the homogeneity of variances in normal samples with unequal sizes is derived. The most general form of the density function is obtained by using contour integration. The expression for the cumulative distribution, being a series in simple algebraic functions, seems quite tractable for computation of the exact critical values. In the special case of equal sample sizes, some indication of the relation of the work of others to our series expansions has also been given.
A Simple Test For The Independence of Sets of Variables
Authors: Maritz A.
Published: February 2008

A test for the mutual independence of subvectors of the p‐dimensional random vector X, distributed as N(0, S̀), is described. The test is based on the maximum likelihood estimates (MLEs) of the off‐(block) diagonal elements of S̀. It is shown that the resulting test statistic is much easier to compute than the likelihood ratio (LR) test statistic while retaining the same asymptotic power properties in view of the general properties of tests based on the MLEs (ML test) and the likelihood ratio (LR test).
On Asymptotic Deficiency of Estimators
Authors: Akahira Masafumi
Published: February 2008

The notion of deficiency was introduced by Hodges and Lehmann. It is known that best asymptotically normal (BAN) estimators are second order asymptotically efficient in the class A2 of all second order asymptotically median unbiased estimators.

In this paper it is shown that the asymptotic deficiency of any two estimators in the restricted class D of the third order asymptotically median unbiased BAN estimators is given by the difference between the coefficients of order n‐1 of the variances of the estimators.
On Bounds for Probability Generating Functions
Authors: Narayan P.
Published: February 2008

Brook (1966) gave an upper bound for the moment generating function (m.g.f.) of a positive random variable (r.v.) in terms of its moments, and used this to obtain an upper bound for the probability generating function (p.g.f.) and hence the extinction probability of a simple branching process. Agresti (1974) rederived this bound of the p.g.f. and used it to obtain a lower bound of the expectation of extinction time of a branching process. In both of these applications the random variable is integer valued, and for this class we improve on Brook's bound by deriving the best upper bound of the p.g.f. Our method, which is a variant of Brook's (1966) is used later to obtain the lower bound of the p.g.f. when the third moment is also known.
Length‐Biassed Sampling from a Finite Population
Authors: Littlejohn R. P.
Published: February 2008

Expressions are derived for the interval moments of a length‐biassed sample from a renewal process of finite length.
Extending Product Method of Estimation to Positive Correlation Case in Surveys
Authors: Srivenkataramana T. , Tracy D. S.
Published: February 2008

The product method of estimation (Murthy, 1964) complements the ratio method when the study variate, y, and an auxiliary variate, x, have negative correlation. However, such cases are not frequent in survey practice. This paper suggests a simple transformation of x in the more common situation of positive correlation between y and x, to permit a product method of estimation rather than a ratio method. This leads to the advantage that the bias and mean square error have exact expressions. The technique developed by Quenouille (1956) and applied by Shukla (1976) is used for making the estimator unbiased. The minimum variance situation is investigated. Two numerical examples are included. The case of negative correlation is also examined.
Peak Points in a Symmetrically Correlated Random Walk
Authors: Sabharwal Y. P. , Gupta B. R.
Published: February 2008

This note reports explicit formulae for the probability distribution and mean and variance of the number of peak points in a symmetrically correlated random walk.
Estimating Marihuana Usage Using Randomized Response—Some Paradoxical Findings
Authors: Brewer K. R. W.
Published: February 2008

A randomized response technique was used in parallel with direct questioning on the (illegal) usage of marihuana in a population survey of Canberra. Estimates of usage from the randomized questions were much lower than those obtained directly. A number of possible explanations for these paradoxical findings are considered.
A Goodness of Fit Statistic Based on the Sample Spacings for Testing a Symmetric Distribution Against Symmetric Alternatives
Authors: Tiku M. L.
Published: February 2008

A goodness‐of‐fit statistic based on the spacings of a complete or a symmetrically censored sample is defined and its null distribution is studied and shown to be normal (approximately). This statistic is shown to have good power properties for testing an assumed symmetric distribution against symmetric alternatives, from complete or symmetrically censored samples.
A Test For Heteroscedasticity in a Limited Dependent Variable Model
Authors: Jarque Carlos M.
Published: February 2008

Limited Dependent Variable models arise, for example, when the dependent variable is necessarily non‐negative. When these models are estimated under the incorrect assumption of homoscedasticity, serious consequences have been found. It is therefore important to test for its existence. In this paper, we make use of the Lagrange multiplier procedure to derive a test for heteroscedasticity in the Tobit model.
Nonparametric Estimation of a Regression Function: Limiting Distribution2
Authors: Cheng Kuang‐Fu , Lin Pi‐Erh
Published: February 2008

Consider the regression modelYi= g(xi) + ei, i = 1,…, n, where g is an unknown function defined on [0, 1], 0 = x0< x1< … < xn≤ 1 are chosen so that max1≤i≤n(xi‐xi‐ 1) = 0(n‐1), and where {ei} are i.i.d. with Ee1= 0 and Var e1‐ s̀2. In a previous paper, Cheng & Lin (1979) study three estimators of g, namely, g1nof Cheng & Lin (1979), g2nof Clark (1977), and g3nof Priestley & Chao (1972). Consistency results are established and rates of strong uniform convergence are obtained. In the current investigation the limiting distribution of &in, i = 1, 2, 3, and that of the isotonic estimator g**nare considered.
An Estimation Problem with Poisson Processes
Authors: Gelfand Alan E.
Published: February 2008

For n independent Poisson processes such that the i th process has intensity function lMi(t) =δiρ(t; α) we consider estimation of p(t; α) =∫oρ:(u; α) du. Two procedures are developed, one using exact arrival times, the other using categorical arrival times. Two instances where p(t; α) =p(α t) are investigated further. An example applying the methodology to the active life of a judicial opinion is described.
On Conditional Correlation Coefficients of a Wold Markov Process of Gamma Intervals
Authors: Lai C. D.
Published: February 2008

In this paper we discuss the conditional correlations between two future intervals given the length of the current one in a Wold Markov process of Gamma intervals.
Closeness of Grassia's Transformed Gammas and the Beta Distribution
Authors: Griffiths David , CSIRO Christine Schafer
Published: February 2008

The flexibility and applicability of the Beta distribution are well known. In this note a comparison is made between the Beta and two other distributions on (0,1) which have been proposed by Grassia (1977) and which are derived through transformation of the Gamma distribution.

The extreme closeness of the distributions is demonstrated graphically and explored more formally through a measure of closeness (Kolmogorov‐Smirnov distance). Alternative measures of closeness are also briefly discussed.

It is concluded that for many applications the distributions are sufficiently similar (that is, virtually identical) for a choice among them to rest solely on mathematical convenience.
A Class of Multivariate Distributions
Authors: Sivazlian B. D.
Published: February 2008

In this paper we introduce a class of multivariate distributions, known as the generalized Liouville distribution and defined by the functional form (0 ≤xi < ∞, αi > 0, βi > 0, qi > 0). It is shown that such distributions can be used to derive both the Dirichlet distribution and the beta distribution of the second kind.
Checks on Yates's Algorithm for a 2™ Factorial Experiment2
Authors: Gupta B. C.
Published: February 2008

In this paper two general rules for checking Yates's algorithm are given. With these rules one can check any of the intermediate columns as well as the last column, using any of the preceding columns including the observation column. Rules of Good and Quenouille are special cases of these rules.
TRENDS IN THE STATISTICAL SCIENCES
Authors: Heyde C. C.
Published: February 2008

The literature in probability and statistics over the past fifteen to twenty years is reviewed in broad terms and trends are highlighted. The evolution of some subject areas is then discussed, in particular queueing and branching processes. The motivation of research is considered and the importance of meaningful applications stressed.
A Descriptive Interpretation of Standard Error
Authors: Finch Peter D.
Published: February 2008

When are a record and a perturbation of it better described as two signals instead of one? Investigation of this question leads to the concept of a perturbation interval for a mean within which one signal is the preferred description. When the one and two signal descriptions are equally preferable, the size of the permitted perturbation is approximately the standard error of the mean.
Asymptotic Robustness of Prediction Intervals of Arima Models to Deviations From Normality
Authors: Heuts R. M. J.
Published: February 2008

ARIMA processes are extremely important in applied statistics. However, most theory is based on Gaussian stochastic processes, while it was pointed out by Mandelbrot (1965), Fama (1965), Heuts (1978) and others, that for many financial data the distribution of the shocks in the ARIMA schemes appears leptokurtic.

In this paper we shall investigate the implications of some asymptotic results, not assuming normality, for the construction of prediction intervals of future observations in an ARIMA scheme.
Simultaneous Tolerance Limits and a Unified Approach to some Nonparametric Theory
Authors: Breth M.
Published: February 2008

In this paper nonparametric simultaneous tolerance limits are developed using rectangle probabilities for uniform order statistics. Consideration is given to the handling of censored data, and some comparisons are made with the parametric normal theory.

The nonparametric regional estimation techniques of (i) confidence bands for a distribution function, (ii) simultaneous confidence intervals for quantiles and (iii) simultaneous tolerance limits are unified. A Bayesian approach is also discussed.
Sequential Fixed‐Width Confidence Interval for a Function of the Parameters
Authors: Perng S. K. , Hasza David P. , Paik C.
Published: February 2008

Let X1…, Xm and Y1…, Yn be two independent sequences of i.i.d. random variables with distribution functions Fx(.|θ) and Fy(. | φ) respectively. Let g(θ, φ) be a real‐valued function of the unknown parameters θ and φ. The purpose of this paper is to suggest a sequential procedure which gives a fixed‐width confidence interval for g(θ, φ) so that the coverage probability is approximately α (preas‐signed). Certain asymptotic optimality properties of the sequential procedure are established. A Monte Carlo study is presented.
A Simple Test Procedure When Data are Given by n Indepenent Blocks
Authors: Shirahata Shingo
Published: February 2008

In this article we consider a test procedure which is useful in the situations where data are given by n independent blocks and the experimental conditions differ between blocks. The basic idea is very simple. The significance of the sample for each block is calculated and then standardized by its null mean and variance. The sum of standardized significances is proposed as a test statistic. The normal approximation for large n and the exact method for small n are applied in the continuous case. For the discrete case, some devices are also proposed. Several examples are given in order to explain how to apply the procedure.
A Class of Experimental Designs Balanced for First Residuals
Authors: Sharma V. K.
Published: February 2008

In this paper a new class of designs involving sequences of treatments balanced for first residual effects has been introduced. These designs require only t experimental units for 2t periods, t being the number of treatments to be tested. A unified method of constructing these designs for all values of t (≥2) along with an appropriate method of analysis is presented. Besides, their efficiency relative to some well known designs is investigated.
An Adventure in Publishing: Eighteen Years of the Applied Probability Trust1
Authors: Gani J.
Published: February 2008

This paper describes the foundation of the Applied Probability Trust and the launching of the Journal of Applied Probability in 1964. The Trust office was set up in Sheffield in 1965; the Trust has since published Mathematical Spectrum (1968) and Advances in Applied Probability (1969). Various other publishing ventures are described, and some statistics given for the Applied Probability journals. In conclusion, tentative plans for the future of the Trust are outlined.
The Role of Randomization in Model‐Based Inference
Authors: Thornett M. L.
Published: February 2008

A common justification for randomization in sampling and experimental design is that it creates certain desirable invariance properties, e.g., exchangeability, in the distribution of the sample responses, and this is so regardless of the distribution of the population responses. This paper argues that for model‐based inference randomization's role is much more limited, viz., to preserve invariance properties already embodied in the model for the population responses.
On The Role of a Certain Eigenvalue in Estimating the Growth Rate of a Branching Process
Authors: Asmussen Søren
Published: February 2008

In many situations, the data given on a p‐type Galton‐Watson process Zn eP Np will consist of the total generation sizes |Zn| only. In that case, the maximum likelihood estimator ρML of the growth rate ρ is not observable, and the asymptotic properties of the most obvious estimators of ρ based on the |Zn|, as studied by Asmussen & Keiding (1978), show a crucial dependence on |ρ1|,ρ1 being a certain other eigenvalue of the offspring mean matrix. In fact, if |ρ1|2≤ρ, then the speed of convergence compares badly with ρML. In the present note, it is pointed out that recent results of Heyde (1981) on so‐called Fibonacci branching processes provide further examples of this phenomenon, and an estimator with the same speed of convergence as ρML and based on the |Zn| alone is exhibited for the case p= 2, ρ12≥ρ.
A Simulation Study of the Powers of Three Multiple Comparison Statistics
Authors: Morley Clive L.
Published: February 2008

A normal‐theory and two distribution‐free statistics used for multiple comparisons of homogeneity of location are compared on simulated data generated from six distributions. The normal‐theory statistic is found to be fairly robust to departures from the assumption of normally distributed data of the types considered. The Steel‐Dwass statistic is generally more powerful than a Kruskal‐Wallis range statistic.
A Note on an Unbiased Test of Homogeneity of Variances
Authors: Samiuddin M.
Published: February 2008

A necessary and sufficient condition for unbiasedness of the test of homogeneity of variances in normal samples is derived in a convenient form. In the case of two samples, it is shown that Bartlett's test is the only unbiased test of homogeneity of variances. A simple alternative proof of the unbiasedness of Bartlett's test in the general case is also provided.
Meixner Classes and Meixner Hyper‐Geometric Distributions
Authors: Lai C. D.
Published: February 2008

The Meixner hypergeometric distribution is defined and its various properties are investigated. A survey of characterizations of Meixner classes is also presented.
Covariate Classification Using Dependent Samples
Authors: Bandyopadhyay Shibdas
Published: February 2008

The two‐population classification problem using dependent samples is extended when covariates are available for classification. Analysis is done using a conditional model, under a multivariate normal set‐up, given the covariates. The conditional model considered here includes the parameter structure relevant to growth models. Likelihood ratio or plug‐in likelihood ratio classification rules are derived depending on the knowledge of the parameters in the model. For exact distribution of the classification statistics, they are reduced to forms suitable for application of standard results.