bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some results on commutation matrices, with statistical applications
Authors: Neudecker H. , Wansbeek Tom 
Published: June 2006

AbstractThe commutation matrix Pmn changes the order of multiplication of a Kronecker matrix product. The vec operator stacks columns of a matrix one under another in a single column. It is possible to express the vec of a Kronecker matrix product in terms of a Kronecker product of vecs of matrices. The commutation matrix plays an important role here. “Super‐vec‐operators” like vec A ⊗ vec A vec (A ⊗ A), and vec{(A ⊗ A)Pnn} are very convenient. Several of their properties are being studied. Both the traditional commutation matrix and vec operator and the newer concepts developed from these are applied to multivariate statistical and related problems.
Estimation of Pr{yp> max(y1, …, yp‐1)}: Predictive approach in exponential case
Authors: Rinco Stefan 
Published: June 2006

AbstractThe structural‐inference approach to predictive distributions is used to derive the estimator ofP= Pr{Yp> max(Y1, …,Yp‐1)} when the independent random variablesY1, …, Ypfollow exponential distributions with unequal location parameters and equal scale parameters. The result is Equation (4.6).
A combinatorial method for products of generalized h‐statistics
Authors: Tracy D. S. , Gupta B. C. 
Published: June 2006

AbstractThe h‐statistic h (Dwyer [1]) is extended to the generalized h‐statistic hP1…Ps such that E(hP1…Ps) with properties similar to polykays. In order to obtain their sampling moments, formulas expressing their products as linear combinations of the same are required. The paper presents a combinatorial method to achieve this. Certain rules are developed and applied to obtain products through weight 5.
An econometric model of the demand for energy in canada part one: The industrial demand for gas
Authors: Khazzoom J. Daniel 
Published: June 2006

AbstractThis is part one of a study of the demand for energy in Canada in the industrial, residential and residential‐commercial markets. The study focuses on the four major sources of energy: gas, oil, coal and electricity. The contents of this paper are as follows:1. The economic background. The main ideas; a diagrammatic derivation of the free and captive demand; the model.2. Estimation.The interdependence of demand and price: Natural gas, oil, electricity and coal; the price variables that enter the relationships; data and operational definitions of the variables.3. Estimation and simulation results for the industrial demand for natural gas. The price‐additive model, the problem of multicollinearity, the alternative.
A note on the expected values of powers of a matrix
Authors: Rahman M. , Ahsanullah M. 
Published: June 2006

AbstractIt is known [Z] that if X is any positive random variable, then E (Xn)>[E (X)]n for any integer n, provided the expectations exist. A matrix generalization of this result for n = ‐1 was given in [1]. We will show that a simple exercise in matrix analysis yields the matrix generalization for any integer n, positive or negative.
Confidence bands from censored samples
Authors: Csőrgő Sándor , Horváth Lajos 
Published: June 2006

AbstractSeveral types of asymptotic confidence bands have been proposed in the literature when the data are randomly censored on the right. Introducing new classes of bands, we place the old bands and their relationship to one another within a comprehensive theory of bands. A thorough analysis yields narrower bands and two kinds of modifications which are asymptotically distribution‐ and censor‐free. One of these is useful when the interval on which the bands are constructed is predetermined and the width of the bands is random; the other, when there is a predetermined bound on the width and the interval is random. We illustrate our bands on the Szeged pacemaker data. These methods also provide a general modification of the Kolmogorov band in the uncensored case.
Copules archimédiennes et families de lois bidimensionnelles dont les marges sont données
Authors: Genest Christian , Mackay R. Jock 
Published: June 2006

AbstractToute fonction de répartition bidimensionnelle dont les marges sont continues peut être représentée de fçon unique par une copule, c'est‐à‐dire par une fonction de répartition concentrée sur le carré unité et dont les marges sont uniformes. Dans cet article, nous nous intéressons à une classe de copules, dites archimédiennes, qui permet de représenter bon nombre de lois bidimensionnelles connues. Nous donnons des conditions sous lesquelles deux copules de cette classe sont ordonnées stochastiquement et nous examinons les propriétés limites de suites de copules archimédiennes. Nous fournissons également deux nouveaux exemples de families paramétriques de lois bidimensionnelles comprenant comme cas limites les bornes de Frechet et la loi d'indépendance.
Multivariate regression analysis and canonical variates
Authors: Van Der Merwe A. , Zidek J. V. 
Published: June 2006

AbstractA method called FICYREG of estimating regression coefficients is introduced. This is a generalization to the multivariate regression problem of the James‐Stein estimator. When suitably représentés FICYREG emerges as a rule in which the canonical variates and canonical correlations have an intrinsic role to play. By exploiting these objects FICYREG is able to achieve stability against the influence of the “noise” present in problems where the responses are correlated so that some of the response vector's canonical variates will be essentially independent of all others including the predictors. The least squares (LS) estimator is, by contrast, highly sensitive to this noise. The use of FICYREG is illustrated in terms of an example, and its peformance is compared to the LS estimator when a quadratic loss function is assumed. The cases of both fixed and random predictors are considered. Overall, FICYREG outperforms the LS estimator.
Asymptotic distribution of the latent roots of the noncentral wishart distribution and the power of the likelihood ratio test for nonadditivity
Authors: Carter E. M. , Srivastava M. S. 
Published: June 2006

AbstractIn this paper the asymptotic distribution of the roots of the noncentral Wishart distribution is derived with a remainder term of O(n−2). This distribution is used to derive the asymptotic distribution of the likelihood ratio test for nonadditivity. Some calculated values of the asymptotic power of this test is given. Also, an estimate of σ2 with a bias term of the order O(n−3/2) is given.
Probabilities of moderate deviations under m‐dependence
Authors: Ghosh Malay 
Published: June 2006

AbstractConsider a stationary sequence {X1, X2,… } of m‐dependent random variables. It is proved that for any constant c > 0, if E|X1|p < ∞ for some p > c2 + 2, then

and

as n → ∞, where μ = E(X1) and

The above results on probabilities of moderate deviations for sample means are then used to obtain similar results for U‐statistics and Von Mises' differentiable statistical functions when the underlying variables form a stationary m‐dependent sequence.
A power study of a rank transform for the two‐way classification model when interaction may be present
Authors: Iman Ronald L. 
Published: June 2006

AbstractThe power of the usual parametric analysis of variance for the two‐way model when interaction may be present is compared with the power of a test based on performing the usual parametric analysis on ranks, i.e., a rank transform is used. While the mathematical theory has not yet been developed for such an approach, this study shows the value of developing the theory for such an approach to the analysis of experimental designs, and indicates that this approach is probably a valid procedure. Simulation results are présentés for three underlying populations: normal, contaminated normal, and exponential. These results show the rank transform approach has a null distribution similar to that of the F‐statistic computed on the raw data in all the cases considered. Though little, if any, loss of power occurs from using the rank transform approach, a significant increase in power is apparent when the underlying population is contaminated normal.
Statistical problems in environmental research
Authors: Ware James H. , Louis Thomas A. 
Published: June 2006

AbstractGrowing concern about the health effects of exposure to pollutants and other chemicals in the environment has stimulated new research to detect and quantify environmental hazards. This research has generated many interesting and challenging methodological problems for statisticians. One type of statistical research develops new methods for the design and analysis of individual studies. Because current research of this type is too diverse to summarize in a single article, we discuss current work in two areas of application: the carcinogen bioassay in small rodents and epidemiologic studies of air pollution. To assess the risk of a potentially harmful agent, one must frequently combine evidence from different and often quite dissimilar studies. Hence, this paper also discusses the central role of data synthesis in risk assessment, reviews some of the relevant statistical literature, and considers the role of statisticians in evaluating and combining evidence from diverse sources.
The interpretation of maximum‐likelihood estimation
Authors: Sprott David A. , Viveros‐Aguilera Román 
Published: June 2006

AbstractMaximum‐likelihood estimation is interpreted as a procedure for generating approximate pivotal quantities, that is, functions u(X;θ) of the data X and parameter θ that have distributions not involving θ. Further, these pivotals should be efficient in the sense of reproducing approximately the likelihood function of θ based on X, and they should be approximately linear in θ. To this end the effect of replacing θ by a parameter ϕ = ϕ(θ) is examined. The relationship of maximum‐likelihood estimation interpreted in this way to conditional inference is discussed. Examples illustrating this use of maximum‐likelihood estimation on small samples are given.
Recent developments in nonlinear stochastic modelling of social processes
Authors: Bartholomew D. J. 
Published: June 2006

AbstractAfter a brief review of social applications of Markov chains, the paper discusses nonlinear (“interactive”) Markov models in discrete and continuous time. The rather subtle relationship between the deterministic and stochastic versions of such models is explored by means of examples. It is shown that the behaviour of nonlinear systems over time periods of practical interest depends critically on the total size as well as on the system parameters. Particular attention is paid to strong and weak forms of quasi‐stationarity exhibited by stochastic systems.
Sampling properties of estimators of the log‐logistic distribution with application to Canadian precipitation data
Authors: Shoukri M. M. , Mian I. U. H. , Tracy D. S. 
Published: June 2006

AbstractWe consider the probability‐weighted moment and the maximum‐likelihood estimators of two parameters in the log‐logistic distribution. Quantile estimators are obtained using both methods. The distributional properties of these estimators are studied in large samples, via asymptotic theory, and in small and moderate samples, via Monte Carlo simulation. The distribution is shown to be appropriate for a wide variety of meteorological data.
Small sample properties of isotonic estimators — bias and mean squared error of linear combinations under normality
Authors: Parsons Van L. , Hoang Thu M. 
Published: June 2006

AbstractBias and mean squared error for linear combinations of the isotonic regression estimators are computed. The case of sampling three distinct populations and the case of sampling seven or fewer populations having common mean are studied in detail. Numerical results are given, and comparisons between isotonic and unbiased estimation procedures are made.
A neighbourhood‐based classifier for landsat data
Authors: Owen Art 
Published: June 2006

AbstractA classifier is developed which uses information from all pixels in a neighbourhood to classify the pixel at the center of the neighbourhood. It is not a smoother in that it tries to recognize boundaries. and it makes explieite use of the relative positions of pixels in the neighbourhood. It is based on a geometric probability model for the distribution of the classes in the plane. The neighbourhood‐based classifier is shown to outperform linear discriminant analysis on some LANDSAT data.
The asymptotic behavior of monotone percentile regression estimates
Authors: Wright F. T. 
Published: June 2006

AbstractThe least‐absolute‐deviation estimate of a monotone regression function on an interval has been studied in the literature. If the observation points become dense in the interval, the almost sure rate of convergence has been shown to be O(n1/4). Applying the techniques used by Brunk (1970, Nonparametric, Techniques in Statistical Inference. Cambridge Univ. Press), the asymptotic distribution of the l1 estimator at a point is obtained. If the underlying regression function has positive slope at the point, the rate of convergence is seen to be O(n1/3). Monotone percentile regression estimates are also considered.
On the power of the t‐test and some rank tests when outliers may be present
Authors: Iman Ronald L. , Conover W. J. 
Published: June 2006

AbstractThe power of some rank tests, used for testing the hypothesis of shift, is found when the underlying distributions contain outliers. The outliers are assumed to occur as the result of mixing two normal distributions with common variance. A small sample case shows how the scores for the rank tests are found and the exact power is computed for each of these rank tests. A Monte Carlo study provides an estimate of the power of the usual two sample t‐test.
On a random series in a hilbert space
Authors: Deo Chandrakant M. 
Published: June 2006

AbstractLet (Sn) be partial sums of a non‐degenerate sequence of Identically and independently distributed random variables taking values in a separable Hilbert space. Then for 0 ≤ β ≤ 3/2, the series

converges almost nowhere. For β > 3/2 this may not be true.
An improved ranked set two‐sample mann‐whitney‐wilcoxon test
Authors: Öztürk Ömer , Wolfe Douglas A. 
Published: June 2006

AbstractThe authors present an improved ranked set two‐sample Mann‐Whitney‐Wilcoxon test for a location shift between samples from two distributions F and G. They define a function that measures the amount of information provided by each observation from the two samples, given the actual joint ranking of all the units in a set. This information function is used as a guide for improving the Pitman efficacy of the Mann‐Whitney‐Wilcoxon test. When the underlying distributions are symmetric, observations at their mode(s) must be quantified in order to gain efficiency. Analogous results are provided for asymmetric distributions.
On the stability of maximum‐likelihood estimators of orthogonal parameters
Authors: Cox D. R. , Reid N. 
Published: June 2006

AbstractIf two parameters ψ and λ, are orthogonal, λψ, the maximum‐likelihood estimate of λ for given ψ, varies only slowly with ψ in the neighbourhood of the overall maximum‐likelihood point. The same is true if ψλ is replaced by a nonlinear functionh(ψλ). The detailed form of the variation of ψλ with ψ is studied, and a basis suggested for choosing a particular functionh(ψλ) that shows the dependence in the least informative fashion.
Measures of centrality for multivariate and directional distributions
Authors: Small Christopher G. 
Published: June 2006

AbstractMeasures of centrality that generalize the univariate median are studied and applied to multivariate and directional distributions. A standard example is developed for general multivariate settings, and the uniqueness of the median proved for distributions satisfying certain regularity conditions. In the presence of weaker regularity, this median is shown to be of codimension 2. Conditions are also provided for these measures of centrality to be equivariant under transformations on the sample space. The equivariance of the usual univariate median under monotone transformations is seen as a special case.
Estimators of shift based on statistics of the Kolmogorov‐Smirnov type
Authors: Boulanger Alain 
Published: June 2006

AbstractThis paper is concerned with the estimation of a shift parameter δo, based on some nonnegative functionalHg1of the pair (DδN(x), f̄δN(x)), whereDδN(x) = KN/b {F2,n(x)—F1,m(x + δ)}, +δN(x) = {mF1,m(x + δ) +nF2,n(x)}/N, whereF1,mandF2,nare the empirical distribution functions of two independent random samples (N = m + n), and whereK2N=mn/N.First an estimator δN, is defined as a value of δ minimizing a functionalHof the type ofH1. A second estimator δ1Nis also defined which is a linearized version of the first. Finite and asymptotic properties of these estimators are considered. It is also shown that most well‐known test statistics of the Kolmogorov‐Smirnov type are particular cases of such functionalsH1. The asymptotic distribution and the asymptotic efficiency of some estimators are given.
Uniform asymptotic linearity of a process based on a signed rank statistic
Authors: Boulanger Alain , Eeden Constance Van 
Published: June 2006

AbstractConsider the processwith, cf. (1.2) on page 265 in B1,X1, …, XNa sample from a distributionFand, fori= 1, …, N, R, the rank of |X1‐ q1ø| among |X1‐ q1ø|, …, |XN‐ qNø|. It is shown that, under certain regularity conditions onFand on the constantspiand qi, TøN(t) is asymptotically approximately a linear function of ø uniformly intand in ø for |ø| ≤ C. The special case where thepiand theqi, are independent ofiis considered.
On a Berry‐Esséen theorem for a Studentized jackknife L‐estimate
Authors: Cheng Kuang‐Fu 
Published: June 2006

AbstractConsider a linear function of order statistics (“L‐estimate”) which can be expressed as a statistical function T(Fn) based on the sample cumulative distribution function Fn. Let T*(Fn) be the corresponding jackknifed version of T(Fn), and let V2n be the jackknife estimate of the asymptotic variance of n 1/2T(Fn) or n 1/2T*(Fn). In this paper, we provide a Berry‐Esséen rate of the normal approximation for a Studentized jackknife L‐estimate n1/2[T*(Fn) ‐ T(F)]/Vn, where T(F) is the basic functional associated with the L‐estimate.
Estimation in the presence of incidental parameters
Authors: Mak Tak K. 
Published: June 2006

AbstractThis paper considers the estimation of “structural” parameters when the number of unknown parameters increases with the sample size. Neyman and Scott (1948) had demonstrated that maximum likelihood estimators (MLE) of structural parameters may be inconsistent in this case. Patefield (1977) further observed that the asymptotic covariance matrix of the MLE is not equal to the inverse of the information matrix. In this paper we establish asymptotic properties of estimators (which include in particular the MLE) obtained via the usual likelihood approach when the incidental parameters are first replaced by their estimates (which are allowed to depend on the structural parameters). Conditions for consistency and asymptotic normality together with a proper formula for the asymptotic covariance matrix are given. The results are illustrated and applied to the problem of estimating linear functional relationships, and mild conditions on the incidental parameters for the MLE (or an adjusted MLE) to be consistent and asymptotically normal are obtained. These conditions are weaker than those imposed by previous authors.
Bayesian estimation of the difference between two proportions
Authors: Alvo Mayer , Cabilio Paul 
Published: June 2006

AbstractThis paper is concerned with the problem of allocating a fixed number of trials between two independent binomial populations with unknown success probabilities θ1 and θ2, in order to estimate θ1 ‐ θ2 with squared error loss. Introducing independent beta priors on θ1 and θ2, a heuristic allocation procedure is introduced and compared both with the optimal and with the best fixed allocation procedure. Numerical and asymptotic results of these comparisons are given and seem to indicate that there are situations when the best fixed allocation procedure performs almost as well as the optimal procedure.
Inférence statistique dans les processus stochastiques: Aperçu historique
Authors: Moore Marc 
Published: June 2006

AbstractL'étude de I'inférence statistique relative aux processus stochastiques s'est poursuivie suivant deux voies. On a d'une part considéré des problèmes liés à des processus particuliers et, d'autre part, on a aussi considéré l'extension de résultats généraux obtenus pour des variables aléatoires indépendantes. On retrace ici les premières contributions marquantes, on apprécie leur influence, et on donne une idée de l'évolution des activités dans le domaine de l'inférence statistique faite à partir de l'observation d'un processus stochastique.
Bootstrap variance and bias estimation in linear models
Authors: Shao Jun 
Published: June 2006

AbstractLet θ be a nonlinear function of the regression parameters and θ be its estimator based on the least‐squares method. This paper studies the bootstrap estimators of the variance and bias of θ. The bootstrap estimators are shown to be consistent and asymptotically unbiased under some conditions. Asymptotic orders of the mean squared errors of the bootstrap estimators are also obtained. The bootstrap and the classical linearization method are compared in a simulation study. Discussions about when to use the bootstrap are given.
L1‐Tightness and the law of large numbers in D(IR)
Authors: Daffer Pete , Schiopu‐Kratina Loana 
Published: June 2006

AbstractThis article presents laws of large numbers for random elements of D(IR). The proofs bring forth the similarities between processes restricted to compact sets of D (IR) and processes with increasing trajectories. The results appear to generalize existing results and cover the independent identically distributed case studied by Ranga Rao.
Patterned matrix derivatives
Authors: Tracy D. S. , Jinadasa K. G. 
Published: June 2006

AbstractA general procedure for obtaining matrix derivatives of functions of nonlinear patterned matrices is proposed. The method is extended to obtain the Jacobians of patterned matrix transformations. Nel (1980) and Wiens (1985) consider the linear patterned cases. The procedure proposed here takes care of these cases as well.
Some robust tests of independence in symmetrical multivariate distributions
Authors: Giri Narayan C. 
Published: June 2006

AbstractLet X =(x)ij=(111, …, X,)T, i = l, …n, be an n X random matrix having multivariate symmetrical distributions with parameters μ, Σ. The p‐variate normal with mean μ and covariance matrix is a member of this family. Let be the squared multiple correlation coefficient between the first and the succeeding p1 components, and let p2 = + be the squared multiple correlation coefficient between the first and the remaining p1 + p2 =p – 1 components of the p‐variate normal vector. We shall consider here three testing problems for multivariate symmetrical distributions. They are (A) to test p2 =0 against; (B) to test against =0, 0; (C) to test against p2 =0, We have shown here that for problem (A) the uniformly most powerful invariant (UMPI) and locally minimax test for the multivariate normal is UMPI and is locally minimax as p2 0 for multivariate symmetrical distributions. For problem (B) the UMPI and locally minimax test is UMPI and locally minimax as for multivariate symmetrical distributions. For problem (C) the locally best invariant (LBI) and locally minimax test for the multivariate normal is also LBI and is locally minimax as for multivariate symmetrical distributions.