bluuebunny/crossref_metadata_2025_split huggingface dataset:
FIXED VERSUS RANDOM SAMPLING OF CERTAIN CONTINUOUS PARAMETER PROCESSES
Authors: McDunnough Philip , Wolfson David B. 
Published: February 2008

SummaryLet {Z(t)} be a stochastic point process. When {Z(t)} is Poisson and it is desired to estimate the intensity A, it is shown that the optimal (in terms of Fisher information) discrete sampling scheme is to sample {Z(t)} at predetermined fixed time points. On the other hand, when {Z(t)} is a pure birth process and a maximum likelihood estimator of the birth rate is desired, it is sometimes better to sample at random time points, according to a renewal process. An application of these ideas is given in the estimation of bacterial density in a liquid, by the method of dilutions.
DETECTING NATURAL SELECTION: THE STEPWISE MUTATION MODEL WITH HETEROSIS
Authors: Watterson G. A. , Anderson R. 
Published: February 2008

SummaryThe problem of testing whether heterozygotes have a selective advantage is considered, assuming the stepwise mutation model for electrophoretic alleles. The population is observed for a number of generations, and the likelihoods of the changes in allele frequencies under the heterozygote advantage model and under the strict neutrality model are compared. It is shown by simulation that statistical tests based on the likelihoods have little power to detect selection if only a few generations of data are available.Many population genetic models, including the stepwise mutation model, have been formulated as diffusion processes in continuous time. The paper gives expressions for the likelihoods of multivariate diffusions observed over a time interval.
RELAXING ASSUMPTIONS IN THE ONE SAMPLE t‐TEST
Authors: Cressie Noel 
Published: February 2008

SummaryThis paper reviews what is currently known about the behaviour of the t‐statistic when one is no longer sampling from a normal distribution. Suppose Y is a batch of data on which the t‐test is performed. Briefly then, heavy‐tailed components of Y give a light‐tailed t, positive correlation among Y gives a heavy‐tailed t, and positively skewed components of Y give a negatively skewed t. The emphasis is on understanding why one gets this type of behaviour, although some numerical tables are presented to illustrate the conclusions.
THE EXACT DISTRIBUTION OF THE BELL‐DOKSUM TEST OF INDEPENDENCE
Authors: Spurr Barrie D. 
Published: February 2008

SummaryAn expression for the exact distribution of the Bell‐Doksum test of independence based upon the use of order statistics from normally distributed random samples is derived and a table of critical values is provided. Two extensions of the theory are considered and possible applications to Poisson processes and queueing theory are noted.
TWO‐STAGE PROCEDURES FOR TESTING HOMOGENEITY OF MEANS AGAINST ORDERED ALTERNATIVES IN ONE‐WAY ANOVA WITH COMMON UNKNOWN VARIANCE
Authors: Marcus Ruth 
Published: February 2008

SummaryIn this paper we present two‐stage procedures for testing the equality of normal means against ordered alternatives in one‐way ANOVA with common and unknown variance. The procedures proposed are analogous to Williams's and Bartholomew's single‐stage methods. A table of percentiles needed for implementation is provided. Some Monte Carlo results for estimating the power of both procedures are given.
GOODNESS OF FIT STATISTICS BASED ON THE SPACINGS OF COMPLETE OR CENSORED SAMPLES
Authors: Tiku M. L. 
Published: February 2008

SummaryA goodness‐of‐fit statistic Z is defined in terms of the spacings generated by the order statistics of a complete or a censored sample from a distribution of the type (l/s̀)f((x‐μ)/s̀), μ and s̀ unknown. The distribution of Z is studied, mostly through Monte Carlo methods. The power properties of Z for testing Exponential, Uniform, Normal, Gamma and Logistic distributions are discussed; Z is shown to be more powerful than the Smith & Bain (1976) correlation statistic, except for testing Uniform, Normal and Logistic (symmetric distributions) against symmetric alternatives. The statistic Z is generalized to test the goodness‐of‐fit from κ 2 independent complete or censored samples.
TESTING THE LARGEST OF A SET OF CORRELATION COEFFICIENTS
Authors: Moran P. A. P. 
Published: February 2008

SummaryA previous paper which studied the distribution of the smallest distance between N independent random points on the surface of a sphere is generalised to higher dimensions in order to study the distribution of the largest sample correlation coefficient between a set of independent normally distributed variables. Inclusion‐exclusion arguments provide accurate bounds for the tail of this distribution, and by another argument more exact bounds are also found, one of which is an improvement on the result in the previous paper. Bounds are also found for the power of the test against the alternative hypothesis that one only of the population correlation coefficients is non‐zero. The test is also shown to be the likelihood ratio test against the latter alternative.
An Application of Discrimination When Covariance Matrices are Proportional
Authors: Dargahi‐Noubary G. R. 
Published: February 2008

SummaryIn the context of time series, a situation is considered which leads to the discrimination between two normal populations having unequal means and proportional covariance matrices. It is then shown that this has an application to the important problem of earthquake‐explosion differentiation. The latter is done by introducing a non‐stationary model for seismic records of P‐waves from these two kinds of events.
A Note on the Canonical Correlations From Contingency Tables
Authors: O'Neill M. E. 
Published: February 2008

SummaryExplicit formulae are obtained for the asymptotic variances and covariances of canonical correlations which correspond to non‐zero theoretical correlations in (p+ 1) x (q+1) contingency tables, withp≤q. The moments of the roots of a central Wishart matrix distributed as Wp(q;I) are also given in general, with means, variances and covariances tabulated forp= 2, 3, 4: these may apply to canonical correlations corresponding to zeros.
Asymptotic Properties of an Estimate of the Prediction Error Variance
Authors: Hong‐Zhi An 
Published: February 2008

SummaryAn estimate of the variance of the prediction error for a linear stationary time series is constructed by using only a part, ŷ0, ŷ1,…, ŷM, of the sample autocovariance sequence, whereMincreases withT, the length of the time series observed.Mincreases asTα(α <14). Under a higher moment condition, but not assuming Gaussianity, the estimate obtained is shown to be strongly consistent and asymptotically normal. The asymptotic variance of the estimation error is also obtained.
A Theorem on Products of Random Variables, With Application to Regression
Authors: Maller R. A. 
Published: February 2008

SummaryIt is shown that the product of two independent random variables in the domain of attraction of the normal distribution is also in the domain of attraction of the normal distribution, while if the product is in the domain of attraction of the normal distribution and one of the variables has finite variance, the other is in the domain of attraction of the normal distribution. This result is applied to prove the asymptotic normality of the regression coefficient in a linear regression when the error variance is not necessarily finite.
Sequential Estimation of Expectations in the Presence of Trend2
Authors: Theodorescu Radu , Wolff Hans 
Published: February 2008

SummaryA sequence of independent random variables {Zn:n≥ 1} with unknown probability distributions is considered and the problem of estimating their expectations {Mn+1: n≥ 1} is examined. The estimation of Mn+1 is based on a finite set {zk:1≤k≤n}, each zk being an observed value of Zk, 1 ≤k≤n, and also based on the assumption that {Mn:n≥ 1} follows an unknown trend of a specified form.
Simultaneous Confidence Intervals for Monotone Contrasts of Normal Means
Authors: Marcus Ruth 
Published: February 2008

SummaryThe one‐way ANOVA model is considered. The variances are assumed to be either equal but unknown or unequal and unknown. Two‐stage procedures for generating simultaneous confidence intervals (SCI) for the class of monotone contrasts of the means are presented. The intervals are of fixed length and independent of the unknown variances.
A Characterization of a Matric‐Variate Exponential Distribution
Authors: Richards Donald St. P. 
Published: February 2008

SummarySuppose S is a positive definite m x m random matrix and S> Ω denotes the event that S—Ω is positive definite, Ω being a constant positive definite matrix. Under very mild regularity conditions, we show that the constraint Pr(S>Ω1+Ω2 | S>Ω2) = Pr(S>Ω1) implies that S has a Wishart distribution on m+ 1 degrees of freedom.
A Note on the Effect of Autocorrelation on Multiple Regression Statistics
Authors: Praetz Peter 
Published: February 2008

SummaryThis note discusses the effect of autocorrelated distrubances when they are not modelled on the statistics used in drawing inferences in the multiple linear regression model. It derives biases for the F and R2 statistics and evaluates them numerically for an example. The note concludes with a few brief reflections for empirical research on the causes, detection and treatment of autocorrelation.
On Level Crossing Analysis of Queues
Authors: Shanthikumar J. G. 
Published: February 2008

SummaryIn this note we introduce a new level crossing analysis and using it derive an integral equation for the steady state waiting time in the GI/G/1 Queue. For the GI/M/1 queue we derive the rates of up‐ and down‐crossings of the virtual delay process and two integral equations, one for the steady state time spent in the system and the other for the steady state waiting time in the queue. Also, the steady state probability distributions of the time spent in the system and the waiting time in the queue are obtained by solving these integral equations.
Sampling on Two Occasions With Varying Probabilities
Authors: Arnab R. 
Published: February 2008

SummaryIn estimating the current value of a finite population total from two consecutive surveys with samples chosen with varying probabilities, we demonstrate through examples the intuitively expected superiority of strategies when current unmatched samples are chosen from the complements of the current matched sub‐samples, over the usual ones where these are chosen from the entire population.
Variations in Household Telephone Access: Implications for Telephone Surveys
Authors: Jones Roger 
Published: February 2008

SummaryThe growing proportion of households that have telephones and the increasing cost of face‐to‐face interviewing have led to greater interest in the use of telephone surveys in Australia over recent years. However about 20 per cent of private households do not have a telephone service, which could give rise to significant biases in population estimates derived from telephone surveys if no adjustment is made to take account of the differences between those with and without telephone access. This paper examines these differences and suggests ways in which their possible effects might be overcome.
Nonparametric Tests for Intercept in Linear Regression Problems
Authors: Rao K. S. Madhava , Gore A. P. 
Published: February 2008

SummaryIn this paper we demonstrate how various hypotheses of interest about the intercept parameter in one‐sample, two‐sample and several‐sample linear regressions could be tested by simple adaptations of familiar nonparametric procedures, when an experimenter has the liberty to choose the values of the independent variable. Asymptotic Relative Efficiencies of the proposed procedures are discussed.
Jackknifing in Categorical Data Analysis
Authors: Parr William C. , Tolley H. Dennis 
Published: February 2008

SummaryEstimation of nonlinear functions of a multinomial parameter vector is necessary in many categorical data problems. The first and second order jackknife are explored for the purpose of reduction of bias. The second order jackknife of a function g(.) of a multinomial parameter is shown to be asymptotically normal if all second order partials ∂2g(p)∂dpi∂pj obey a Hölder condition with exponent α>1/2. Numerical results for the estimation of the log odds ratio in a 2times2 table demonstrate the efficiency of the jackknife method for reduction of mean‐square‐error and the construction of approximate confidence intervals.
Contiguity of Probability Measures
Authors: Scott David J. 
Published: February 2008

SummaryThe notion of contiguity of probability measures is a very useful one, providing a generally applicable method of calculating the asymptotic power of a sequence of tests and thus a means of comparing competing tests. This paper attempts to give an account of the basic results of contiguity theory which is self‐contained and accessible to statisticians to whom the theory is of use. In addition, the relationship between contiguity and mutual contiguity is explored.
Some Remarks on The Paper by Theodorescu and Wolff: “Sequential Estimation of Expectations in the Presence of Trend”
Authors: Pakes Anthony G. 
Published: February 2008

SummaryRecently Theodoresu and Wolff have proposed a sequence of random variables for estimating a sequence of constants satisfying a certain recurrence equation. Their problem, which is similar to some arising in stochastic approximation theory, was solved by using techniques from this theory. The present paper shows that the theory of sums of independent random variables is a more natural tool for tackling this problem.
On the Extinction Time of a Continuous time Markov Branching Process
Authors: Narayan Prakash 
Published: February 2008

SummarySeveral authors have studied and derived bounds for the mean extinction time of a discrete branching process. In this note, we obtain the mean and variance of the extinction time, given extinction of a continuous time Markov branching process. We also obtain bounds for the mean extinction time in terms of moments of the offspring distribution.
Stochastic Multigrade Population Models in Continuous Time
Authors: Agrafiotis G. K. 
Published: February 2008

SummaryA continuous time stochastic model for the analysis of wastage in a hierarchically structured multigrade population system, with non‐homogeneous Poisson input, is developed in this paper. Special cases of the model are discussed and the distribution of the grade sizes at any time is obtained through the use of straightforward probabilistic arguments.
Series Expansion for a Hypergeometric Function of Matrix Argument with Applications
Authors: Gupta Rameshwar D. , Richards Donald St P. 
Published: February 2008

SummaryA series expansion is obtained for the confluent hypergeometric function of the second kind when the argument is a 2 times 2 positive definite matrix. Applications are made to the distributions of Hotelling's generalized T02 statistic, and the smallest latent root of the covariance matrix.
The Joint Treatment of Exact and Stochastic Restrictions
Authors: Shonkwiler J. S. 
Published: February 2008

SummaryIn regression analysis both exact and stochastic extraneous information may be represented via restrictions on the parameters of a linear model which then may be estimated by applying constrained generalized least squares. It is shown that this estimator can be recast as a computationally simpler estimator that is a combination of the ordinary least squares estimator and the discrepancy between the OLS estimator and both types of restrictions. The variance of the restricted parameters is explicitly shown to depend on the variance of the extraneous information.
Robustness Against Inequality of Variances
Authors: Brown B. M. 
Published: February 2008

SummaryVarious asymptotic‐based criteria are used to assess the robustness against inhomogeneity of variance of various standard and/or distribution‐free tests in the two sample problem. The extent of robustness is influenced greatly by the equality or not of the two sample sizes, conforming to an earlier principle of G. E. P. Box. With equal sample sizes, t‐tests and related trimmed‐mean‐like tests are robust, but otherwise, the sign test emerges clearly as the most robust test to variance inequality.
Estimable Versions of Griffiths' Measure of Association
Authors: Bolyai Sándor Csörgö , Hall Peter 
Published: February 2008

SummaryMany techniques have been proposed for measuring the degree of association between a pair of random variables X and Y. However, the measures often suffer from two drawbacks: they are difficult to calculate when the joint distribution of (X, Y) is known, and difficult to estimate when the joint distribution is unknown. In the present paper we present two modifications of a measure proposed by Griffiths (1972), and show that they exhibit neither of these deficiencies.
Distribution‐Free Methods in Regression1
Authors: Brown B. M. , Maritz J. S. 
Published: February 2008

SummaryA modification to the least‐squares estimating equations in simple linear regression, leading to exact distribution‐free inference about slope, is outlined. The modification involves a general residual‐transformation iψ and the cases of ψ— sign, rank, and the identity are discussed in some detail.It is also shown how exact inference about individual parameters in regressions with more than one design variable can be carried out by a restricted permutation argument coupled with a suitable design.
Difficulties of Interpretation With Markov Chain Models
Authors: Finch Peter D. 
Published: February 2008

SummaryQuestions such as “how useful is a Markov chain model!” and “what does it tell us about a real process?” are discussed. The relevance of context is stressed and it is argued that good data fits are not enough by themselves. It is suggested that a descriptive data analytic interpretation of the modelling process might sometimes be more appropriate than the usual probabilistic interpretation.
RECENT TRENDS IN ASYMPTOTIC OPTIMAL INFERENCE FOR DEPENDENT OBSERVATIONS1
Authors: Basawa I. V. 
Published: February 2008

SummaryAn overview of some recent developments in the area of asymptotic inference for non‐ergodic type stochastic processes is presented. Both local and global formulations of the asymptotic model are given, and non‐local optimality results are reviewed. Recent results on conditional inference are briefly discussed. Some open problems and possibilities for new developments are also mentioned.
CATASTROPHE PROCESSES WITH CONTINUOUS STATE‐SPACE1
Authors: Brockwell P. J. , Gani J. M. , Resnick S. I. 
Published: February 2008

SummarySome continuous state‐space models for the size of a population subject to catastrophes are examined. Inputs to the population constitute a compound Poisson process, and catastrophes, which are of random magnitudes, occur at a rate which is dependent on the population size. Necessary and sufficient conditions for the existence of stationary distributions are investigated and in special cases the stationary distributions are found explicitly. The time‐dependent behaviour of a process with linear catastrophe rate and truncated exponential catastrophe sizes is also studied.
ESTIMATION OF PARAMETERS IN THE MARGINAL FISHER DISTRIBUTION1
Authors: Clark R. M. 
Published: February 2008

SummaryThe Fisher distribution is frequently used as a model for the probability distribution of directional data, which may be specified either in terms of unit vectors or angular co‐ordinates (co‐latitude and azimuth). If, in practical situations, only the co‐latitudes can be observed, the available data must be regarded as a sample from the corresponding marginal distribution. This paper discusses the estimation by Maximum Likelihood (ML) and the Method of Moments of the two parameters of this marginal Fisher distribution. The moment estimators are generally simpler to compute than the ML estimators, and have high asymptotic efficiency.
AN ESTIMATION PARADOX ARISING IN POPULATION GENETICS THEORY1
Authors: Ewens W. J. 
Published: February 2008

SummaryWe consider a stochastic process describing the evolution of a certain population. A sample is taken from this population in some given generation and is to be used for estimation purposes. It is shown that if one wishes to estimate, from the sample, the actual value of a certain population quantity F in the current generation, estimation using a statistic f is preferred to estimation using a different statistic k, whereas, if one wishes to estimate the mean value of F relative to the stochastic process describing the population evolution, estimation using k is preferred to estimation using f.
A GALTON‐WATSON BRANCHING PROCESS IN VARYING ENVIRONMENTS WITH ESSENTIALLY CONSTANT OFFSPRING MEANS AND TWO RATES OF GROWTH1
Authors: MaCphee I. M. , Schuh H.‐J. 
Published: February 2008

SummaryA Galton‐Watson process in varying environments (Zn), with essentially constant offspring means, i.e. E(Zn)/mn→α∈(0, ∞), and exactly two rates of growth is constructed. The underlying sample space Ω can be decomposed into parts A and B such that (Zn)n grows like 2non A and like mnon B (m > 4).
THE WEIGHTED MEDIAN AND MULTIPLE REGRESSION1
Authors: Seneta E. 
Published: February 2008

SummaryThis paper reviews the iterative use of the weighted median to estimate the parameter vector in the classical linear model when the fitting criterion is (i) least absolute deviation sum (LAD); and (ii) the Cauchy criterion. The implications of the Cauchy criterion, little developed hitherto, are compared and contrasted with results for the better‐known LAD procedure. Since the weighted median is essentially an estimation technique for the simplest regression model, its use in these contexts illustrates the central role in statistical theory that is played by regression analysis, a focal area of the work of E. J. Williams (1959).
DISTRIBUTIONS IN R WITH ROTATIONAL SYMMETRIES1
Authors: Watson G. S. 
Published: February 2008

SummaryLet X ∈ R be a random vector with a distribution which is invariant under rotations within the subspaces Vj (dim Vj. = qj) whose direct sum is R. The large sample distributions of the eigenvalues and vectors of Mn= n‐1Σnl xixi are studied. In particular it is shown that several eigenvalue results of Anderson & Stephens (1972) for uniformly distributed unit vectors hold more generally.
REMARKS ON OPTIMAL INFERENCE FOR MARKOV BRANCHING PROCESSES: A SEQUENTIAL APPROACH
Authors: Basawa I. V. , Becker Niels 
Published: February 2008

SummaryUse of a suitable stopping rule yields exact uniformly most powerful tests and minimum variance unbiased estimators of various parameters of a Markov branching model with or without immigration. The population model discussed includes the pure birth, simple epidemic, immigration‐death, M/M/ 1 queue, linear birth‐death and a branching diffusion process, among others, as special cases.
REDUCED DISTANCE MEASURES AND TRANSFORMATIONS IN PROCESSING MULTIVARIATE OUTLIERS
Authors: Barnett Vic 
Published: February 2008

SummaryThe study of multivariate outliers raises many problems of definition, principle and manipulation. Well‐authenticated tests of discordancy exist only for the multivariate normal distribution. Detection of outliers in non‐normal distributions involves the adoption of appropriate criteria to represent ‘extremeness' of observations in a sample; corresponding tests of discordancy usually require tedious, or even intractable, distributional and computational manipulations. A class of transformations of the data is considered with a view of transferring some of the familiar and desirable features of discordancy tests for normal samples to non‐normal situations.
AN ESTIMATE OF THE ASYMPTOTIC STANDARD ERROR OF THE SAMPLE MEDIAN
Authors: Sheather S. J. , Maritz J. S. 
Published: February 2008

SummaryA method for estimating the asymptotic standard error of the sample median based on generalized least squares is outlined. The practical problems of implementing this new estimate along with those associated with two existing estimates are discussed. Finally a simulation study is presented to compare the three estimates.