bluuebunny/crossref_metadata_2025_split huggingface dataset:
A STOCHASTIC LOGISTIC MODEL WITH TIME DELAY
Authors: Prajneshu  
Published: February 2008

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

SummaryAn algorithm is described for the optimal rearrangement of the treatments within each block of a Balanced Incomplete Block Design when a specified “nearest neighbour” correlation structure exists among observations from plots in the same block. The procedure uses results obtained by Kiefer & Wynn (1981). Designs obtained using the algorithm are found to compare favourably with those produced by combinatorial methods given in Cheng (1983). The algorithm produces optimal designs for all BIBD parameter sets, including those not covered by the results of Kiefer & Wynn or Cheng.
Selection of the Transformation Variable in the Laplace Transform Method of Estimation
Authors: Laurence Alexa F. , Morgan Byron J. T. 
Published: February 2008

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

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

SummaryThe pros and cons of applying regression shrinkage prediction arguments and methods to autoregressive time series forecasting are discussed. Simulation evidence of the performance of a Stein regression prediction formula suggests that the overall dominance of the shrunken predictor over least squares in regression no longer holds in time series samples of a reasonable length. Rather, shrinkage appears the better of the two, with respect to prediction mean squared error, only for weaker relationships and seems to be inferior to the least squares predictor when the autoregressive relationship is strong.
Incorporating Previous Results Into the Analysis of General Balanced Designed Experiments
Authors: Knuiman M. W. , Speed T. P. 
Published: February 2008

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

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

summaryNumerical experimentation with data, which is quite noisy and on a highly non‐even grid, shows that cubic smoothing splines give a visually pleasing fit to the data, even when the interpolating spline oscillates wildly. In part, Silverman (1984) has explained this fact by showing that the cubic smoothing spline converges, to a certain kernel approximation as the number of data points is increased. In this paper, we examine the convergence of the kernel functions which generate the cubic smoothing spline fit to data, under weaker conditions on the non‐even grid than imposed by Silverman.