bluuebunny/crossref_metadata_2025_split huggingface dataset:
ON THE CHOICE OF ESTIMATOR IN SURVERY SAMPLING*
Authors: Rao J. N. K. , Singh M. P. 
Published: February 2008

SummaryWe 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.
AN ASYMPTOTIC EXPANSION OF THE EXPECTATION OF THE ESTIMATED ERROR RATE IN DISCRIMINANT ANALYSIS1
Authors: Mclachlan G. J. 
Published: February 2008

SummaryWhen 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

ABSTRCTSMany 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

SummaryGeneralized 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

SummaryFrom 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.
EMPIRICAL BAYES ESTIMATION WITH NON‐IDENTICAL COMPONENTS. CONTINUOUS CASE.
Authors: O'Bryan Thomas E. , Susarla V. 
Published: February 2008

AbstractIn 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)≤&#x006d;̄ < ∞ 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

AbstractIn 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 SummaryThe 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

AbstractSome 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.
POWER ASPECTS OF ANALYSIS OF VARIANCE IN FIXED EFFECT MODEL ONE‐WAY CLASSIFICATION
Authors: Kanji G. K. 
Published: February 2008

SummaryThe 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

SummaryEstimation 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

SummaryIf 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.
THE DESIGN OF CLINICAL TRIALS
Authors: Armitage P. 
Published: February 2008

SummaryClinical 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

AbstractThe 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

SummaryTo 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

SummaryWe 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

SummaryA 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

SummaryAn 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

SummaryA 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

SummaryWhen 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

SummaryUnder 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

SummaryIn 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

SummaryThe 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

SummaryLet 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

SummaryLet(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

SummaryA 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.