bluuebunny/crossref_metadata_2025_split huggingface dataset:
TWO MODEL‐BASED INFERENCE ARGUMENTS IN SURVEY SAMPLING
Authors: Särndal C. E. 
Published: February 2008

SummaryWhich 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

SummaryWe 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.
The Exact Null Distribution of Bartlett's Criterion
Authors: Nandi S. B. 
Published: February 2008

SummaryIn 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

SummaryA 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

SummaryThe 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

SummaryBrook (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.
Extending Product Method of Estimation to Positive Correlation Case in Surveys
Authors: Srivenkataramana T. , Tracy D. S. 
Published: February 2008

SummaryThe 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.
Estimating Marihuana Usage Using Randomized Response—Some Paradoxical Findings
Authors: Brewer K. R. W. 
Published: February 2008

SummaryA 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

SummaryA 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

SummaryLimited 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

SummaryConsider 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

SummaryFor 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.
Closeness of Grassia's Transformed Gammas and the Beta Distribution
Authors: Griffiths David , CSIRO Christine Schafer 
Published: February 2008

SummaryThe 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

SummaryIn 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

SummaryIn 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.
A Descriptive Interpretation of Standard Error
Authors: Finch Peter D. 
Published: February 2008

SummaryWhen 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

SummaryARIMA 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

SummaryIn 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

SummaryLet 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

SummaryIn 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

SummaryIn 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

SummaryThis 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

SummaryA 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

SummaryIn 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

SummaryA 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

SummaryA 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.
Covariate Classification Using Dependent Samples
Authors: Bandyopadhyay Shibdas 
Published: February 2008

SummaryThe 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.
EXAMPLES OF MINIMUM VARIANCE ESTIMATION1
Authors: Bartlett M. S. 
Published: February 2008

AbstractIn this sequel to a previous discussion of minimum variance estimation (Bartlett, 1982), the gain with conditional estimation procedures is illustrated for the location parameter for (i) the rectangular distribution; (ii) a triangular distribution (typifying an asymmetric case). This note concludes with further remarks on the multi‐sample and multi‐parameter cases.
MINIMUM SIGNIFICANCE AND DISTRIBUTION FREE TESTS1
Authors: Brown B. M. 
Published: February 2008

SummaryA general way of testing in the presence of nuisance parameters is to choose from a family of tests the one to maximize evidence against null hypothesis; that is, to minimize the significance level. This method yields exact tests when applied to distribution‐free testing in various statistical designs; arbitrary choice of score functions is eliminated. However, the exact null distributions are highly non‐normal, and there are problems with both computation and asymptotic theory.
THE CONVERGENCE OF AUTOCORRELATIONS AND AUTOREGRESSIONS1
Authors: Hannan E. J. , Kavalieris L. 
Published: February 2008

SummaryFor a general class of scalar stationary processes, essentially those for which the best linear predictor is the best predictor (in the mean square sense), it is shown that, under fairly minor additional conditions, the sample autocorrelations converge to the true values almost surely and hniformly in the lag, t, at a rate (T‐1log T)1/2, where T is the sample size. For ARMA processes, if |t|(log T)a, a < ∞, the rate is the best possible, namely (T‐1log log T)1/2. In particular the somewhat implausible condition, on the innovations, that E{ε(t)2| Ft‐l} is constant is avoided in these results. The theorems are used to discuss autoregressive approximation. When the stationary process is a vector process the condition on the innovation sequence, ε(t), that E{ε(t)ε(t)| Ft‐l} be constant, cannot be entirely avoided in relation to autoregressive approximation. This is also discussed.
SOME PROPERTIES OF A RANDOM LINEAR DIFFERENCE EQUATION1
Authors: Pakes Anthony G. 
Published: February 2008

SummarySome simple conditions are given for the absolute continuity of the limiting distribution of a random linear difference equation. These results are applied to the super‐critical Bellman‐Harris branching process with immigration. When the coefficients of the difference equation are non‐negative and there is no limiting distribution, it is shown that the asymptotic behaviour of the solutions is the same as that of the partial sums of a divergent random power series. A number of limit theorems are given for the latter situation.
ASYMPTOTIC TESTS FOR THE CONTINUOUS TIME MARKOV BRANCHING PROCESS WITH IMMIGRATION
Authors: Hudson Irene L. 
Published: February 2008

SummaryThis paper presents limit distributions for the modified score and the likelihood‐ratio (LR) statistic for testing a composite hypothesis involving the split intensity and mean of the offspring distribution of the supercritical continuous time Markov branching process allowing immigration (CBPI). The immigration intensity and mean are treated as nuisance parameters.
ON THE NONCENTRAL DISTRIBUTION OF A RANDOM MATRIX USEFUL IN CLASSIFICATION THEORY
Authors: Rogers G. S. , Kabe D. G. 
Published: February 2008

SummaryTo prove the optimality properties of the maximum likelihood (and also minimum distance) discriminant rule Rogers (1980, p. 98) embeds the maximum likelihood discriminant function in a Cauchy‐Schwartz inequality. This embedding procedure of Rogers (1980) may be used to derive a new distribution for Anderson's (1958) classification statistic.
A NORMAL APPROXIMATION TO THE FISHER DISTRIBUTION
Authors: Clark R. M. , Morrison B. J. 
Published: February 2008

SummaryA simple normal approximation is given for the joint probability density function of the polar co‐ordinates (θ, ψ) of a random vector following the Fisher distribution with arbitrary mean direction (θ0, ψ0). The approximation leads to simple inference procedures which are particularly useful in regression models. Conditions for the adequacy of the approximation are investigated and summarized in tabular form.
AN ANALYTIC FORM FOR THE CUMULATIVE DISTRIBUTION FUNCTION OF THE BELL‐DOKSUM STATISTIC
Authors: Clarke A. P. , Marwood W. 
Published: February 2008

SummaryA closed form analytic expression for the Bell‐Doksum Statistic is developed. The use of the generalized hypergeometric function to evaluate the expression is demonstrated, and a table of critical values for 2 n 25 is presented.
ASYMPTOTIC DEFICIENCY OF THE JACKKNIFE ESTIMATOR
Authors: Akahira Masafumi 
Published: February 2008

SummaryIn this paper it is shown that the bias‐adjusted maximum likelihood estimator (MLE) is asymptotically equivalent to the jackknife estimator in the variance up to the order n‐1 and the asymptotic deficiency of the jackknife estimator relative to the bias‐adjusted MLE is equal to zero.
ON CHARACTERIZING SOME BIVARIATE DISCRETE DISTRIBUTIONS
Authors: Papageorgiou H. 
Published: February 2008

SummaryThe bivariate (correlated) Poisson, binomial, negative binomial and logarithmic distributions are characterized by the conditional distribution of one random vector on the other and a regression function of the second random vector on the first. Characterizations of the above distributions when their component random variables are independent are also included.
ON A TEST OF FIT IN TIME SERIES MODELS
Authors: Beveridge Stephen 
Published: February 2008

SummaryIt is shown that a test for adequacy of a fitted Arma (p, 4) model based on forecast errors, has the same asymptotic expected value whether the null hypothesis is true or false. A sampling study supports the conclusion in small to moderately large samples and indicates that for sample sizes commonly used by practitioners, the power of the test is very low.
IMPROVING UPON THE BEST INVARIANT ESTIMATOR IN MULTIVARIATE LOCATION PROBLEMS
Authors: Puri Madan L. , Ralescu Dan A. 
Published: February 2008

SummaryWe are concerned with estimators which improve upon the best invariant estimator, in estimating a location parameter θ. If the loss function is L(θ ‐ a) with L convex, we give sufficient conditions for the inadmissibility of δ0(X) = X. If the loss is a weighted sum of squared errors, we find various classes of estimators δ which are better than δ0. In general, δ is the convolution of δ1 (an estimator which improves upon δ0 outside of a compact set) with a suitable probability density in Rp. The critical dimension of inadmissibility depends on the estimator δ1 We also give several examples of estimators δ obtained in this way and state some open problems.