bluuebunny/crossref_metadata_2025_split huggingface dataset:
Further remarks on asymptotic normality of likelihood and conditional analyses
Authors: Fraser D. A. S. , Mcdunnough P. 
Published: June 2006

AbstractUnder weak conditions the normalized likelihood with or without weight function almost surely converges to a normal density function: for a real parameter or a vector parameter; with or without the assumption of independent identical distributions. Applications arise for confidence intervals, confidence distributions, structural distributions. and conditional analyses with transformation and structural models.
Some observations on semi‐markov models for partially censored data
Authors: Matthews David E. 
Published: June 2006

AbstractCause‐specific hazard functions are employed to analyze a semi‐Markov model which could be used to describe data arising from clinical trials or certain types of observational studies. The use of these hazard functions to fit a set of data arising from N possibly incomplete case histories is shown to have several notable advantages over the approach adopted by Lagakos, Sommer, and Zelen (1978).
Asymptotic normality of the lengths of a class of nonparametric confidence intervals for a regression parameter
Authors: Puri Madan L. , Wu Tiee‐Jian 
Published: June 2006

AbstractIn the linear regression model, the asymptotic distributions of certain functions of confidence bounds of a class of confidence intervals for the regression parameter arc investigated. The class of confidence intervals we consider in this paper are based on the usual linear rank statistics (signed as well as unsigned). Under suitable assumptions, if the confidence intervals are based on the signed linear rank statistics, it is established that the lengths, properly normalized, of the confidence intervals converge in law to the standard normal distributions; if the confidence intervals arc based on the unsigned linear rank statistics, it is then proved that a linear function of the confidence bounds converges in law to a normal distribution.
Certain nonparametric classification rules and their asymptotic efficiencies
Authors: Govindarajulu Z. , Gupta A. K. 
Published: June 2006

AbstractTwo nonparametric classification rules for e‐univariace populations are proposed, one in which the probability of correct classification is a specified number and the other in which one has to evaluate the probability of correct classification. In each case the classification is with respect to the Chernoff and Savage (1958) class of statistics, with possible specialization to populations having different location shifts and different changes of scale. An optimum property, namely the consistency of the classification procedure, is established for the second rule, when the distributions are either fixed or “near” in the Pitman sense and are tending to a common distribution at a specified rate. A measure of asymptotic efficiency is defined for the second rule and its asymptotic efficiency based on the Chernoff‐Savage class of statistics relative to the parametric competitors ie the case of location shifts and scale changes is shown to be equal to the analogous Pitman efficiency.
Optimum spacings of elementary treatment contrasts in symmetrical 2‐factor pa block designs
Authors: Sia L. L. 
Published: June 2006

AbstractThe concept of optimum spacing of an arbitrary group of treatments was introduced by Sinha and Sinha (1969) in a study of the relative efficiencies of a group of block designs. In this paper, the optimum spacings of elementary treatment contrasts in a 2‐factor symmetrical block design with Property A are studied using the A‐optimality criterion. Conditions for optimum spacings are expressed in terms of the relative magnitudes of the efficiency factors.
The strong uniform convergence of multivariate variable kernel estimates
Authors: And Luc Devroye , Penrod Clark S. 
Published: June 2006

AbstractWe show that sup, completely as, where f is a uniformly continuous density on are independent random vectors with common density f, and fn is the variable kernel estimateHere Hni is the distance between Xi and its kth nearest neighbour, K is a given density satisfying some regularity conditions, and k is a sequence of integers with the property that log asn
A concise proof of a theorem on products of power sums
Authors: Dwyer P. S. , Mikhail N. N. , Tracy D. S. 
Published: June 2006

AbstractThe heart of a direct solution of the problem of moments of moments is a formula for the expected value of a product of sample power sums in terms of a linear function of products of population power sums. Such a result was given by Skellam (1949) and, earlier and more generally, by Dwyer (1938). The approach here leads to a result for the easily handled case which features the product of unit power sums of each multivariate variable from which a general case comes by easy extension without the need of technical material required by the earlier approaches. A corollary provides a new solution for the problem of obtaining the unbiased estimate of any linear function of products of power sums.
Interval estimates for variance components
Authors: Venables W. , James A. T. 
Published: June 2006

AbstractA new approach to inference on variance components is propounded. This approach not only gives a new justification for Fisher's fiducial, distribution for the “between classes” component, but also leads to a new distribution for the “within classes” component. This latter distribution is studied, and has some intuitively very reasonable properties. Numerical results are given.
A mixed poisson–inverse‐gaussian regression model
Authors: Dean C. , Lawless J. F. , Willmot G. E. 
Published: June 2006

AbstractThe mixed Poisson–inverse‐Gaussian distribution has been used by Holla, Sankaran, Sichel, and others in univariate problems involving counts. We propose a Poisson–inverse‐Gaussian regression model which can be used for regression analysis of counts. The model provides an attractive framework for incorporating random effects in Poisson regression models and in handling extra‐Poisson variation. Maximum‐likelihood and quasilikelihood‐moment estimation is investigated and illustrated with an example involving motor‐insurance claims.
Second‐order inference for generalized least squares
Authors: Fraser D. A. S. , Massam H. 
Published: June 2006

AbstractConfidence regions for generalized least squares are commonly derived from a measure of departure calculated on the tangent plane at the MLE or on the tangent plane at the true value; the first gives approximate confidence regions, the second exact. For surfaces with curvature, indeed with varying curvature, the exact regions typically are not likelihood regions and can include parameter values of highest and of lowest likelihood. This paper develops an alternative approach to deriving exact confidence regions and uses both surface curvature and distance from the surface as supporting ingredients. For this, conditionality is invoked in two ways beyond that supported by the usual conditionality principle. For the case of normal error the ordinary chi‐squared departure is replaced by a Von Mises‐type angular (or cosine) departure which is assessed using curvature properties in the data direction and radial distance of the data from the regression surface. For the usual linear model (constant curvature equal to zero) the method coincides with the ordinary tests and confidence regions; for the case of constant nonzero curvature, the method generalizes to spheres and sphere‐cylinders the Fisher (Statistical Methods and Scientific Inference, 1956) analysis of a rotationally symmetric normal on ℝ2with mean constrained to a circle. The effects of conditioning are indicated by a computer plot for obtaining 95% confidence.
Asymptotic properties of Bayes risk for one‐sided tests
Authors: Johnson Bruce R. , Truax Donald R. 
Published: June 2006

AbstractConsider a given sequence {Tn} of estimators for a real‐valued parameter θ. This paper studies asymptotic properties of restricted Bayes tests of the following form: reject H0:θ ≤ θ0 in favour of the alternative θ > θ0 if Tn ≤ Cn, where the critical point Cn is determined to minimize among all tests of this form the expected probability of error with respect to the prior distribution. Such tests may or may not be fully Bayes tests, and so are called Tn‐Bayes. Under fairly broad conditions it is shown that

and the Tn‐Bayes risk

where an is the order of the standard error of Tn, ‐ is the prior density, and μ is the median of F, the limit distribution of (Tn – θ)/anb(θ). Several examples are given.
Equi‐information robust designs: Which designs are possible?
Authors: Herzberg Agnes M. , Prescott P. , Akhtar M. 
Published: June 2006

AbstractThe effects of missing observations in a designed experiment are reviewed. Conditions are determined for a design to retain equal information, i.e. the same generalized variance of unknown parameters, when either any single or any pair of observations is lost. Some examples of designs with this property are given. Although there are many designs which retain equal information for the loss of exactlytobservations, wheret= 1,2,3,…, it is shown that it is not possible to obtain any design which retains equal information when any one and any two and also any three observations are missing.
Transient analysis of birth‐death processes with two boundaries
Authors: Campbell L. Lome 
Published: June 2006

AbstractThis paper considers a birth‐death process with constant birth rate, constant death rate, and a finite set of states {0,1, …, m – 1}. If the process is in state 0 and a death occurs, it goes instantaneously to state k with a given probability, and if it is in state m – 1 and a birth occurs, it goes to state k with another given probability. The Laplace transform of the generating function for the probabilities is obtained. The steady‐state probabilities and a polynomial equation for the poles of the transform are then obtained. The particular example where the process moves a units into the interior whenever it reaches a boundary is examined. This example includes, for a = 0, the well‐known M/M/1 queue with a finite waiting room.Considérons un processus de naissance et de mort possédant un ensemble fini ďétats {0,1, …, m – 1} et dont les taux de naissance et de mort sont tenus constants. Lorsque le processus est dans l'état 0 et qu'un décès survient, on convient de renvoyer le processus à l'état k avec une certaine probabilité fixée a l'avance; de měme, le processus revient à l'état k si une naissance survient au moment il se trouve dans l'état m – 1. Sous de telles hypothèses, nous calculons la transformée de Laplace de la fonction génératrice des probabilités de transition. Les pǒles de cette transformée doivent satisfaire une équation polynomiale que nous déduisons. Nous déduisons aussi les probabilités stationnaires du processus. Nous examinons de façon particulière le cas où le processus se déplace de a unités vers l'intérieur à chaque fois qu'il atteint l'une des extrémités de son domaine. Lorsque a = 0, cet exemple se réduit au cas classique ďun phénomène ďattente de type M/M/1 avec salle ďattente à capacite finie.
Uniform asymptotic linearity in a regression parameter of a process based on a rank statistic
Authors: Boulanger Alain 
Published: June 2006

AbstractFor X1, …, XNa random sample from a distribution F, let the process SδN(t) be defined aswhere K2N= σNi=1(ci− c̄)2and R xi, + Δd, is the rank of Xi+ Δdi, among X1+ Δd1, …, XN+ ΔdN. The purpose of this note is to prove that, under certain regularity conditions onFand on the constantscianddi, SΔN(t) is asymptotically approximately a linear function of Δ, uniformly intand in Δ, |Δ| ≤C. The special case of two samples is considered.
A characterization of invariant power‐series abundance distributions
Authors: Wani Jagannath K. , Lo Hing Po 
Published: June 2006

AbstractConsider a population the individuals in which can be classified into groups. Let y, the number of individuals in a group, be distributed according to a probability function f(y;øo) where the functional form f is known. The random variable y cannot be observed directly, and hence a random sample of groups cannot be obtained. Consider a random sample of N individuals from the population. Suppose the N individuals are distributed into S groups with x1, x2, …, xS representatives respectively. The random variable x, the number of individuals in a group in the sample, will be a fraction of its population counterpart y, and the distributions of x and y need not have the same functional form. If the two random variables x and y have the same functional form for their distributions, then the particular common distribution is called an invariant abundance distribution. The paper provides a characterization of invariant abundance distributions in the class of power‐series distributions.
Minimum‐distance methods based on quadratic distances for transforms
Authors: Luong A. , Thompson M. E. 
Published: June 2006

AbstractA class of minimum‐distance methods based on empirical transforms is considered. This class includes the minimum‐chi‐squared method, the K‐L method for empirical characteristic functions, and the analogous method for empirical moment generating functions. Asymptotic properties of the minimum‐distance estimators and goodness‐of‐fit test statistics are derived. A general analogue of the Rao‐Robson statistic is formulated.
Invariance principles in probability for stable processes generated by a class of dependent sequences
Authors: Dabrowski André Robert 
Published: June 2006

AbstractWe prove an invariance principle in probability for φ‐mixing sequences of random variables taking values in a separable Banach space. The conditions on the dependence structure required for this approximation result are known to be necessary and sufficient for weak convergence of the partial‐sum process to the appropriate limiting process.
An inequality for random replacement sampling plans
Authors: O'Brien George L. , Wong Augustine 
Published: June 2006

AbstractA sample (X1 …, Xn) is drawn from a population of size N. Karlin (1974) conjectured that for any function ϕ in a certain class of real‐valued functions on the sample space, ϕ is at least as large for sampling with replacement as for any other random replacement sampling plan. This conjecture is proved under the assumption that ≫
On distinguishability of sets of distribution functions and non‐parametric median problem
Authors: Basu A.K. 
Published: June 2006

AbstractHoeffding and Wolfowitz's concept of “distinguishability of sets of distributions” has been extended to two‐sample problems. We have shown that the two‐sample problem about equality of two medians is not “finitely distinguishable” but “sequentially distinguishable”. Then we have constructed a practical non‐parametric sequential test for equality of two medians. This sequential procedure converges with probability one. Upper bounds of two types of error probabilities are also calculated.
Exact distribution of product of generalized F‐variates
Authors: Shah M.C. , Rathie P.N. 
Published: June 2006

AbstractIn this paper the exact distributions of products of independent generalized Snedecor's F‐variables have been established in H‐function, G‐function, and in computable form. The exact distributions of products of independent F‐variables, folded Student‐t variables, beta second kind and folded Cauchy variables have also been obtained as particular cases. One particular case is verified with the result available in the literature. Calculus of residues, properties of Meijer's G‐function, Psi function, H‐function and Zeta function are used in deriving the results. Percentage points can be computed directly from the representation given in this article.
The inverse gaussian distribution: Some properties and characterizations
Authors: Seshadri V. 
Published: June 2006

AbstractThis article presents some structural properties of the inverse Gaussian distribution, together with several new characterizations based on constancy of regression of suitable functions on the sum ofnindependent identically distributed random variables. A decomposition of the statistic λσ(X−1i−X−1) inton‐ 1 independent chi‐squared random variables, each with one degree of freedom, is given whennis of the form 2r.
Some Bayesian lower bounds on reliability in the lognormal distribution
Authors: Padgett W. J. , Johnson M. P. 
Published: June 2006

AbstractThe two‐parameter lognormal distribution with density function f(y: γ, σ2) = [(2πσ2)1/2y] 1exp[−(ln y − γ)2/2σ2], y > 0, is important as a failure‐time model in life testing. In this paper, Bayesian lower bounds for the reliability function R(t: γ, σ2) = ϕ[(γ − ln t)/σ] are obtained for two cases. First, it is assumed that γ is known and σ2 has either an inverted gamma or “general uniform” prior distribution. Then, for the case that both γ and σ2 are unknown, the normal‐gamma prior and Jeffreys' vague prior are considered. Some Monte Carlo simulations are given to indicate some of the properties of the Bayesian lower bounds.
Multivariate studentization and its applications
Authors: Tan W. Y. 
Published: June 2006

AbstractIn this paper we study the distribution ofT= XS, whereXwith orderp × qis normally distributed with zero expectations and covariance matrix Σ⊗V, (that is,Cov(,) = σij,being thej‐th column ofX, Σ=(σij)) and whereS1′S1=Sis distris uted as Wishart independently ofX, withd.f.=fand parameter matrix Σ=(σij) This is then a multivariate extension of the stu‐dentization process. As we shall see, however, the distribution ofTdepends on howSis partitioned. In this paper we shall consider the cases whereS1is lower triangular with positive diagonal elements and where S, is upper triangular with positive diagonal elements. The distributions ofTcorresponding to these two decompositions ofSare called respectively the upper and lower disguised matrix‐tdistributions. Properties of these distributions are derived. Some applications of these distributions to multivariate regression problems are also pointed out.
Bayesian nonparametric smoothers for regular processes
Authors: Weerahandi S. , Zidek J. V. 
Published: June 2006

AbstractThis report is about the analysis of stochastic processes of the formR = S + N, whereSis a “smooth” functional andNis noise. The proposed methods derive from the assumption that the observedR‐values and unobserved values ofR, the assumed inferential objectives of the analysis, are linearly related through Taylor series expansions of observed about unobserved values. The expansion errors and all otherprioriunspecified quantities have a joint multivariate normal distribution which expresses the prior uncertainty about their values. The results include interpolators, predictors, and derivative estimates, with credibility‐interval estimates automatically generated in each case. An analysis of an acid‐rain wet‐deposition time series is included to indicate the efficacy of the proposed method. It was this problem which led to the methodological developments reported in this paper.
The one‐way analysis of variance with ordered alternatives: A modification of bartholomew's Ē2Test
Authors: Wright F. T. 
Published: June 2006

AbstractTests of homogeneity of normal means with the alternative restricted by an ordering on the means are considered. The simply ordered case, μ1≤ μ2≤ ··· ≤ μk, and the simple tree ordering, μ1≤ μj, for;j= 2, 3,…,k, are emphasized. A modification of the likelihood‐ratio test is proposed which is asymptotically equivalent to it but is more robust to violations of the hypothesized orderings. The new test has power at the points satisfying the hypothesized ordering which is similar to that of the likelihood‐ratio test provided the degrees of freedom are not too small. The modified test is shown to be unbiased and consistent.
Mixed‐scale models for survival/sacrifice experiments
Authors: Rai S. N. , Matthews D. E. , Krewski D. R. 
Published: June 2006

AbstractInformation derived from interim sacrifices or on cause of death is routinely used in the statistical analyses of carcinogenicity experiments involving occult tumours. The authors describe a simple semiparametric model which does not require this information. Natural deaths during the experiment and the usual terminal sacrifice provide sufficient information to ensure that the tumour incidence rates, which are of primary interest in occult‐tumour studies, can be estimated nonparametrically. The advantages of this semiparametric approach to the analysis of survival/sacrifice experiments are illustrated using data from a study on benzyl acetate conducted under the U. S. National Toxicology Program. The results derived compare favourably with those obtained using a previously published approach to the analysis of tumorigenicity data.
Locally best invariant and locally minimax test of independence
Authors: Basu Sujit Kumar , Sinha Bimal Kumar 
Published: June 2006

AbstractLet X1 X2 … XN be independent normal p‐vectors with common mean vector $$ = ($$) and common nonsingular covariance matrix $$ = Diag ($sGi) [(1–p) I + pE] Diag ($sGi), $sGi> 0, i = 1… p, 1>p>=1/p–1. Write rij = sample correlation between the i th and the j th variable i j = 1,… p. It has been proved that for testing the hypothesis H0 : p = 0 against the alternative H1 : p>0 where $$ and $sG1,…, $sGp are unknown, the test which rejects H0 for large value of $$ rij is locally best invariant for every $aL: 0 > $aL > 1 and locally minimax as p $$ 0 in the sense of Giri and Kiefer, 1964, for every $aL: 0 > $aL $$ $aL0 > 1 where$aL0 = Pp=0 $$.
A comparison of alternative rate estimators in some frequently used growth models
Authors: Ramasubban T. A. 
Published: June 2006

AbstractThis paper deals with the linear, exponential and Gompertz models and compares the bias and variance of a number of estimators of the growth‐rate parameters of these models. Some of these estimators have been commonly recommended in the literature and others are most frequently used in empirical practice. The present analysis points to the strengths and weaknesses of the estimators in their usage.
Stochastic models of failure in random environments
Authors: Desmond Anthony 
Published: June 2006

AbstractStochastic models of failure modes of frequent occurrence in the engineering sciences are considered. The failure‐producing stress environment is modelled as a stationary stochastic process. Using theoretical properties of the sample paths of these processes, failure‐time distributions which belong to the Birnbaum‐Saunders family are obtained. Several examples of particular engineering relevance are treated.
Regression analysis and ratio analysis for domains: A randomization‐theory approach
Authors: Elvers Eva , SÄRNDAL Carl Erik , Wretman Jan H. , ÖRNBERG Göran 
Published: June 2006

AbstractIn most surveys, inference for domains poses a difficult problem because of data shortage. This paper presents a probability sampling theory approach to some common types of statistical analysis for domains of a surveyed population. Simple and multiple regression analysis, and analysis of ratios are considered. Two new methods are constructed and explored which can improve substantially over the common method based on sample‐weighted sums of squares and products. These new methods use auxiliary variables whose importance depends on the extent to which they succeed in explaining certain patterns in the regression residuals. The theoretical conclusions are supported by empirical results from Monte Carlo experiments.
Approach to normality of mean and M‐estimators of location
Authors: Field Christopher 
Published: June 2006

AbstractThe approach to normality of an estimate is displayed graphically by the nonlinearity in the derivative of the log density, and this nonlinearity is related to the accuracy of the normal approximation for the tail area. Using techniques from small‐sample asymptotics, an alternate proof of the central limit theorem is given and same indices of tail behavior are examined.