bluuebunny/crossref_metadata_2025 huggingface dataset:
The correlated random walk in continuous time with barriers
Authors: Kapadia Asha Seth
Published: June 2006

In this paper correlation has been introduced between two successive transitions in the model investigated by Moyal and Heathcote (1959). The transition rate has been taken to be constant and for simplicity of mathematical expressions the time scale has been so chosen that this rate is unity. For the unrestricted walk we find that the mean position of the particle at time t is that position for which the probability of the particle arriving at some earlier instant from the left is 1/2. With both the barriers either absorbing or reflecting, we have obtained the Laplace Transform of the distributions, but because of the complicated nature of the mathematical expressions involved we are able to find only the asymptotic distributions. For the reflecting barrier case, we find that the process tends to a stationary distribution and that the expected position is eventually the middle point between the barriers.
Contribution empirique au probleme d'agregation de fonctions autoregressives: Le cas de la politique de distribution de dividendes
Authors: Chateau Jean‐Pierre D.
Published: June 2006

This paper deals with the aggregation problem of autoregressive functions. The macrocoefficients of the simplified specification are separated into three components, namely, a true value, an aggregation bias, and an implicit sampling error. Relative importance of these components is studied by using empirical data on a sample of 40 Canadian firms. The notion of aggregation gain of Grunfeld and Griliches is also examined.
Statistical theory of the analysis of experimental designs
Authors: Ogawa J.
Published: June 2006

(Abstracts of papers presented at the Annual Meeting of the Statistical Science Association of Canada; May 29, 30, 31, 1975. / R$eAsum$eAs des articles pr$eAsent$eAs au congres annuel; 29, 30, 31 mai 1975; University of Alberta, Edmonton, Alberta.)
Recursive estimation of the mode of a multivariate density
Authors: Devroye Luc
Published: June 2006

Let f be an unknown possibly multimodal density on Rd and let X1, X2, … be a sequence of independent random vectors with density f. Several recursive estimates of the mode of f are proposed, and sufficient conditions ensuring their weak and strong consistency are established.
Statistical problems in multi‐variate (etiological) surveys
Authors: Sterling Theodor D.
Published: June 2006

A number of multi‐variate etiological surveys are analyzed for recurrent sources of bias in balanced and purposive sampling designs. Three nonsampling components emerge that may dominate the total error of a sample survey estimate. Outstanding among these appear to be administrative consideration of cost and convenience which may actually determine a sampling procedure, especially by reliance on voluntary participation, proxy responses and case‐finding methods that restrict the sample. Next is lack of comparability of population series that differ on some initial state (as to smoking). Finally, errors are caused by strong beliefs in what results should be. Extensive experience has now shown that it may not be possible to conduct a satisfactory etiological inquiry by use of surveys using nonrandom population samples.
On the validation of fiducial techniques
Authors: Plante André
Published: June 2006

A structured model is essentially a family of random vectorsXθdefined on a probability space with values in a sample space. If, for a given sample valuexand for each ω in the probability space, there is at most one parameter value θ for whichXθ(ω) is equal tox, then the model is called additive atx.When a certain conditional distribution exists, a frequency interpretation specific to additive structured models holds, and is summarized in a unique structured distribution for the parameter. Many of the techniques used by Fisher in deriving and handling his fiducial probability distribution are shown to be valid when dealing with a structured distribution.
A percentile regression model with an application to error frequency in group conversation tests
Authors: Liski Erkki P. , Puntanen Simo
Published: June 2006

In many applications, estimates of percentile curves interest investigators more than the mean regression line. We consider the situation where the dependent variable is a compound Poisson variable. Explicit parametric assumptions are made using a linear model for scale and heterogeneous variance. The model is applied to the data on group conversation tests in spoken English.
Pooling operators with the marginalization property
Authors: Genest Christian
Published: June 2006

In this paper, we consider the problem of combining a number of opinions which have been expressed as probability measures P1, …, Pn, over some space. It is shown that a pooling formula which has the marginalization property of McConway (1981) must be of the form T = Σni=1Wi Pi + (1 ‐ Σni =1Wi)Q, where Q is an arbitrary measure and W1, …, Wn ϵ [—1,1] are weights such that| ΣJ Σ j wj | ≤ 1 for every subset J of {1, …, n}. If, in addition, T is required to preserve the independence of arbitrary events A and B whenever these events are independent under each Pi, then either T = Pi for some 1 ≤ i ≤ n or T = Q, in which case Q takes values in {0, l}.
A comparison of two exact confidence regions for partially nonlinear regression models
Authors: Hamilton David
Published: June 2006

Exact confidence regions for all the parameters in nonlinear regression models can be obtained by comparing the lengths of projections of the error vector into orthogonal subspaces of the sample space. In certain partially nonlinear models an alternative exact region is obtained by replacing the linear parameters by their conditional estimates in the projection matrices. An ellipsoidal approximation to the alternative region is obtained in terms of the tangent‐plane coordinates, similar to one previously obtained for the more usual region. This ellipsoid can be converted to an approximate region for the original parameters and can be used to compare the two types of exact confidence regions.
Distribution of multivariate quadratic forms under certain covariance structures
Authors: Pavur Robert J.
Published: June 2006

Necessary and sufficient conditions are given for the covariance structure of all the observations in a multivariate factorial experiment under which certain multivariate quadratic forms are independent and distributed as a constant times a Wishart. It is also shown that exact multivariate test statistics can be formed for certain covariance structures of the observations when the assumption of equal covariance matrices for each normal population is relaxed. A characterization is given for the dependency structure between random vectors in which the sample mean and sample covariance matrix have certain properties.
An example of ridge regression difficulties
Authors: Smith Gary
Published: June 2006

A simple consumption function is used to illustrate two fundamental difficulties with ridge regression and similarly motivated procedures. The first is the ambiguity of multicollinearity measures for judging the data's “ill‐conditioning”. The second is the sensitivity of the estimates to the arbitrary normalization of the model. Neither of these poses a problem for least squares or Bayesian estimates. The logical restructuring of ridge procedures to avoid these difficulties leads to a more explicitly Bayesian approach.
Effect of equicorrelation in detecting a spurious observation
Authors: Srivastava M. S.
Published: June 2006

This note examines the effect of equicorrelation of the observations on Grubbs' (1950) procedure of detecting an outlier in a sample of n independent observations. It is shown that the procedure is robust, in fact the significance level remains unchanged.
Bounds for moments through a general orthogonal expansion in a pre‐hilbert space‐II
Authors: Mathai A. M.
Published: June 2006

In an earlier article [Canad. J. Statist., Vol, 3, No. 1, 1975, 13–34] bounds are obtained for the product moments of an arbitrary finite number of ordered random variables. These bounds are obtained with the help of a representation of an arbitrary function in terms of a complete orthonormal system in a pre‐Hilbert space of square integrable functions defined in a k‐dimensional unit cube. These results are extended to symmetric cases in this article.
On testing correlation between growth curves
Authors: Tan W. Y.
Published: June 2006

Fitting the growth curves by polynomials, this paper is intended to test whether or not there is any correlation between two characters. The likelihood ratio statistic is derived and is shown to be distributed under the null hypothesis as the product of three independent U statistics as defined in Anderson (1958). Box's procedure is then applied to approximate the critical region. A numerical example is given to illustrate the procedure.
Inverse moments of discrete distributions
Authors: Kabe D. G.
Published: June 2006

In this paper an expression for the inverse moment of order r is given for the truncated binomial and Poisson distributions. This enables one to obtain inverse moments in a finite series. Some applications and multivariate generalizations are also given. The method also enables one to obtain relations between inverse moments and factorial moments and distributions of sums of variables.
A lower bound for the transition density function of a stochastic differential equation
Authors: Boyarsky A.
Published: June 2006

Let Wt be a one‐dimensional Brownian motion on the probability space (Ω,F,P), and let dxt = a(xt)dt + b(xt)dwt, b2(x) > 0, be a one‐dimensional Ito stochastic differential equation. For a(x) = a0 + a1x + … + anxn on a bounded interval we obtain a lower bound for p(t,x,y), the transition density function of the homogeneous Markov process xt, depending directly on the coefficients a0,a1, …, an, and b(x).
An alternative proof of order statistics moment problem
Authors: Ali M. M.
Published: June 2006

A necessary and sufficient condition that two distributions having finite means are identical is that for any fixed integer r > 0, the expected values of their rth (n ≫ r) order statistics are equal [or the expected values of their (n‐r)th (n > r ≫ 0) order statistics are equal] for all n where n is the sample size.
Clustering of correlation matrices: A step‐wise procedure
Authors: Wadycki Walter J.
Published: June 2006

An alternative to the criteria proposed by King [9] for clustering correlation matrices is explored. Several simple examples examined by total enumeration employing our criterion indicate that the criterion yields clusters with high within group correlation. A step‐wise routine is suggested for problems of realistic size and is applied to the examples presented in King's article. Additional evidence in the form of several Monte Carlo experiments indicates that the routine performs satisfactorily in determining the optimal separation of variables into two groups.
Measurements of separation among probability densities or random variables
Authors: Glick Ned
Published: June 2006

Distance between two probability densities or two random variables is a well established concept in statistics. The present paper considers generalizations of distances to separation measurements for three or more elements in a function space. Geometric intuition and examples from hypothesis testing suggest lower and upper bounds for such measurements in terms of pairwise distances; but also in Lp spaces some useful non‐pairwise separation measurements always lie within these bounds. Examples of such separation measurements are the Bayes probability of correct classification among several arbitrary distributions, and the expected range among several random variables.
Structural probability bounds for the strong Pareto law
Authors: Dyer Danny
Published: June 2006

By using the structural density function (Fraser 1979, Ch. 7) of the parameters of a Pareto distribution, the structural distribution function of the strong Pareto law is derived. Its fractiles have been evaluated numerically for special cases, and the results are displayed through graphs from which structural one‐sided probability bounds may be found. It is shown that these graphs may also be used to find structural tolerance bounds for the Pareto distribution.
Testing the equality of the variances of two linear models
Authors: Chaubey Y. P.
Published: June 2006

Testing the equality of variances of two linear models with common β‐parameter is considered. A test based on least squares residuals (ASR test) is proposed, and it is shown that this test is invariant under the group of scale and translation changes. For some special cases, it is also proved that this test has a monotone power function. Finding the exact critical values of this test is not easy; an approximation is given to facilitate the computation of these. The powers of the BLUS test, the F‐test and the new test are computed for various alternatives and compared in a particular case. The proposed test seems to be locally more powerful than the alternative tests.
Fourier smoother and additive models
Authors: Bilodeau Martin
Published: June 2006

Suppose the observations (ti,yi), i = 1,… n, follow the model

where gj are unknown functions. The estimation of the additive components can be done by approximating gj, with a function made up of the sum of a linear fit and a truncated Fourier series of cosines and minimizing a penalized least‐squares loss function over the coefficients. This finite‐dimensional basis approximation, when fitting an additive model with r predictors, has the advantage of reducing the computations drastically, since it does not require the use of the backfitting algorithm. The cross‐validation (CV) [or generalized cross‐validation (GCV)] for the additive fit is calculated in a further 0(n) operations. A search path in the r‐dimensional space of degrees of freedom is proposed along which the CV (GCV) continuously decreases. The path ends when an increase in the degrees of freedom of any of the predictors yields an increase in CV (GCV). This procedure is illustrated on a meteorological data set.
Small‐sample intervals for regression
Authors: Tingley M. A.
Published: June 2006

For the general linear regression model Y = Xη + e, we construct small‐sample exponentially tilted empirical confidence intervals for a linear parameter 6 = aTη and for nonlinear functions of η. The coverage error for the intervals is Op(1/n), as shown in Tingley and Field (1990). The technique, though sample‐based, does not require bootstrap resampling. The first step is calculation of an estimate for η. We have used a Mallows estimate. The algorithm applies whenever η is estimated as the solution of a system of equations having expected value 0.

We include calculations of the relative efficiency of the estimator (compared with the classical least‐squares estimate). The intervals are compared with asymptotic intervals as found, for example, in Hampel et at. (1986). We demonstrate that the procedure gives sensible intervals for small samples.
On the curtailment of sampling
Authors: Geisser Seymour
Published: June 2006

We address the problem of the curtailment or continuation of an experiment or trial at some interim point where say N observations are in hand and at least S > N observations had originally been scheduled for a decision. A Bayesian predictive approach is used to determine the probability that if one continued the trial with a further sample of size M where N +M ≥S, one would come to a particular decision regarding a parameter or a future observable. This point of view can also be applied to significance tests if one is willing to admit the calculation as a subjective assessment.
Linear statistics in change‐point estimation and their asymptotic behaviour
Authors: Rukhin A. L.
Published: June 2006

ABSTRACT The limiting behaviour of Bayes procedures in the asymptotic setting of the change‐point estimation problem is studied. It is shown that the distribution of the difference between the Bayes estimator and the parameter converges to the distribution of a fairly complicated random variable. A class of linear statistics is introduced, and the form of the Bayes estimator within this class is deduced. The asymptotic properties of this linear estimator are investigated in two different settings for the prior distribution.
Statistics on statistics: Measuring research productivity by journal publications between 1985 and 1995
Authors: Genest Christian
Published: June 2006

Sixteen international journals publishing statistical theory were surveyed over the 11‐year period beginning in 1985. Paper, author and adjusted page counts yield cursory measures of productivity for institutions and countries that contributed to fundamental statistical research during that period. These data clearly identify Canada as one of the main contributors to the development of the discipline in the past decade. They also provide valuable information on the evolution of publication habits, in terms of the volume of research, the length of papers, coauthorship practices, etc.
Time‐discrete beta‐process model for interval‐censored survival data
Authors: Sinha Debajyoti
Published: June 2006

Grouped survival data with possible interval censoring arise in a variety of settings. This paper presents nonparametric Bayes methods for the analysis of such data. The random cumulative hazard, common to every subject, is assumed to be a realization of a Lévy process. A time‐discrete beta process, introduced by Hjort, is considered for modeling the prior process. A sampling‐based Monte Carlo algorithm is used to find posterior estimates of several quantities of interest. The methodology presented here is used to check further modeling assumptions. Also, the methodology developed in this paper is illustrated with data for the times to cosmetic deterioration of breast‐cancer patients. An extension of the methodology is presented to deal with two interval‐censored times in tandem data (as with some AIDS incubation data).
Alternative Bayes factors for model selection
Authors: De Santis Fulvio , Spezzaferri Fulvio
Published: June 2006

Several alternative Bayes factors have been recently proposed in order to solve the problem of the extreme sensitivity of the Bayes factor to the priors of models under comparison. Specifically, the impossibility of using the Bayes factor with standard noninformative priors for model comparison has led to the introduction of new automatic criteria, such as the posterior Bayes factor (Aitkin 1991), the intrinsic Bayes factors (Berger and Pericchi 1996b) and the fractional Bayes factor (O'Hagan 1995). We derive some interesting properties of the fractional Bayes factor that provide justifications for its use additional to the ones given by O'Hagan. We further argue that the use of the fractional Bayes factor, originally introduced to cope with improper priors, is also useful in a robust analysis. Finally, using usual classes of priors, we compare several alternative Bayes factors for the problem of testing the point null hypothesis in the univariate normal model.
Overdispersed poisson regression models for studies of air pollution and human health
Authors: McNeney Brad , Petkau John
Published: June 2006

This paper presents results from a simulation study motivated by a recent study of the relationships between ambient levels of air pollution and human health in the community of Prince George, British Columbia. The simulation study was designed to evaluate the performance of methods based on overdispersed Poisson regression models for the analysis of series of count data. Aspects addressed include estimation of the dispersion parameter, estimation of regression coefficients and their standard errors, and the performance of model selection tests. The effects of varying amounts of overdispersion and differing underlying variance structure on this performance were of particular interest. This study is related to work reported by Breslow (1990) although the context is quite different. Preliminary work led to the conclusion that estimation of the dispersion parameter should be based on Pearson's chi‐square statistic rather than the Poisson deviance. Regression coefficients are well estimated, even in the présence of substantial overdispersion and when the model for the variance function is incorrectly specified. Despite potential greater variability, the empirical estimator of the covariance matrix is preferred because the model‐based estimator is unreliable in general. When the model for the variance function is incorrect, model‐based test statistics may perform poorly, in sharp contrast to empirical test statistics, which performed very well in this study.
Multivariate spatial interpolation and exposure to air pollutants
Authors: Brown Philip J. , Le Nhu D. , Zidek James V.
Published: June 2006

We develop and apply an approach to the spatial interpolation of a vector‐valued random response field. The Bayesian approach we adopt enables uncertainty about the underlying models to be représentés in expressing the accuracy of the resulting interpolants. The methodology is particularly relevant in environmetrics, where vector‐valued responses are only observed at designated sites at successive time points. The theory allows space‐time modelling at the second level of the hierarchical prior model so that uncertainty about the model parameters has been fully expressed at the first level. In this way, we avoid unduly optimistic estimates of inferential accuracy. Moreover, the prior model can be upgraded with any available new data, while past data can be used in a systematic way to fit model parameters. The theory is based on the multivariate normal and related joint distributions. Our hierarchical prior models lead to posterior distributions which are robust with respect to the choice of the prior (hyperparameters). We illustrate our theory with an example involving monitoring stations in southern Ontario, where monthly average levels of ozone, sulphate, and nitrate are available and between‐station response triplets are interpolated. In this example we use a recently developed method for interpolating spatial correlation fields.
Small‐area estimation by combining time‐series and cross‐sectional data
Authors: Rao J. N. K. , Yu Mingyu
Published: June 2006

A model involving autocorrelated random effects and sampling errors is proposed for small‐area estimation, using both time‐series and cross‐sectional data. The sampling errors are assumed to have a known block‐diagonal covariance matrix. This model is an extension of a well‐known model, due to Fay and Herriot (1979), for cross‐sectional data. A two‐stage estimator of a small‐area mean for the current period is obtained under the proposed model with known autocorrelation, by first deriving the best linear unbiased prediction estimator assuming known variance components, and then replacing them with their consistent estimators. Extending the approach of Prasad and Rao (1986, 1990) for the Fay‐Herriot model, an estimator of mean squared error (MSE) of the two‐stage estimator, correct to a second‐order approximation for a small or moderate number of time points, T, and a large number of small areas, m, is obtained. The case of unknown autocorrelation is also considered. Limited simulation results on the efficiency of two‐stage estimators and the accuracy of the proposed estimator of MSE are présentés.
Testing for and against a set of linear inequality constraints in a multinomial setting
Authors: Barmi Hammou El , Dykstra Richard
Published: June 2006

There are numerous situations in categorical data analysis where one wishes to test hypotheses involving a set of linear inequality constraints placed upon the cell probabilities. For example, it may be of interest to test for symmetry in k × k contingency tables against one‐sided alternatives. In this case, the null hypothesis imposes a set of linear equalities on the cell probabilities (namely pij = Pji ×i > j), whereas the alternative specifies directional inequalities. Another important application (Robertson, Wright, and Dykstra 1988) is testing for or against stochastic ordering between the marginals of a k × k contingency table when the variables are ordinal and independence holds. Here we extend existing likelihood‐ratio results to cover more general situations. To be specific, we consider testing Ht,0 against H1 ‐ H0 and H1 against H2 ‐ H 1 when H0:k × i=1 pixji = 0, j = 1,…, s, H1:k × i=1 pixji × 0, j = 1,…, s, and does not impose any restrictions on p. The xji's are known constants, and s × k ‐ 1. We show that the asymptotic distributions of the likelihood‐ratio tests are of chi‐bar‐square type, and provide expressions for the weighting values.
Comparing three bootstrap methods for survey data
Authors: Sitter R. R.
Published: June 2006

Various bootstrap methods for variance estimation and confidence intervals in complex survey data, where sampling is done without replacement, have been proposed in the literature. The oldest, and perhaps the most intuitively appealing, is the without‐replacement bootstrap (BWO) method proposed by Gross (1980). Unfortunately, the BWO method is only applicable to very simple sampling situations. We first introduce extensions of the BWO method to more complex sampling designs. The performance of the BWO and two other bootstrap methods, the rescaling bootstrap (Rao and Wu 1988) and the mirror‐match bootstrap (Sitter 1992), are then compared through a simulation study. Together these three methods encompass the various bootstrap proposals.
On a problem of counting by weighing
Authors: Yu Kai Fun
Published: June 2006

Suppose it is desired to obtain a large number Ns of items for which individual counting is impractical, but one can demand a batch to weigh at least w units so that the number of items N in the batch may be close to the desired number Ns. If the items have mean weight ωTH, it is reasonable to have w equal to ωTHNs when ωTH is known. When ωTH is unknown, one can take a sample of size n, not bigger than Ns, estimate ωTH by a good estimator ωn, and set w equal to ωnNs. Let Rn = Kp2N2s/n + Ksn be a measure of loss, where Ke and Ks are the coefficients representing the cost of the error in estimation and the cost of the sampling respectively, and p is the coefficient of variation for the weight of the items. If one determines the sample size to be the integer closest to pCNs when p is known, where C is (Ke/Ks)1/2, then Rn will be minimized. If p is unknown, a simple sequential procedure is proposed for which the average sample number is shown to be asymptotically equal to the optimal fixed sample size. When the weights are assumed to have a gamma distribution given ω and ω has a prior inverted gamma distribution, the optimal sample size can be found to be the nonnegative integer closest to pCNs + p2A(pC – 1), where A is a known constant given in the prior distribution.
Sequential sampling without recall from a dirichlet process
Authors: Christensen Ronald
Published: June 2006

The problem of sequential sampling without recall from a Dirichlet process is studied. An individual observes a sequential samplep1,p2, … . At each stage the observer can either accept the current valuepior continue sampling. The total cost to the observer is the current value plus a cost for each observation taken after the first. A concrete context for the problem is provided by a shopper who must buy a particular item and can elicit price quotations sequentially but must pay for each quotation. Qualitative properties of optimal search rules are derived which establish that the problem is well behaved. In particular, the reservation‐price property is shown to hold. The results extend those in Christensen (1986).
Empirical bayes estimation of reliability characteristics for an exponential family
Authors: Pensky M. , Singh R. S.
Published: June 2006

This paper considers empirical Bayes (EB) squared‐error‐loss estimations of mean lifetime, variance and reliability function for failure‐time distributions belonging to an exponential family, which includes gamma and Weibull distributions as special cases. EB estimators are proposed when the prior distribution of the lifetime parameter is completely unknown but has a compact (known or unknown) support. Asymptotic optimality and rates of convergence of these estimators are investigated. The rates established here under the compact support restriction are better than the polynomial rates of convergence obtained previously.
A uniform saddlepoint expansion for the null‐distribution of the wilcoxon‐mann‐whitney statistic
Authors: Froda Sorana , Van Eeden Constance
Published: June 2006

The authors give the exact coefficient of 1/Nin a saddlepoint approximation to the Wilcoxon‐Mann‐Whitney null‐distribution. This saddlepoint approximation is obtained from an Edgeworth approximation to the exponentially tilted distribution. Moreover, the rate of convergence of the relative error is uniformly of orderO(1/N) in a large deviation interval as defined in Feller (1971). The proposed method for computing the coefficient of 1/Ncan be used to obtain the exact coefficients of 1/Ni, for anyi. The exact formulas for the cumulant generating function and the cumulants, needed for these results, are those of van Dantzig (1947‐1950).
The run length distributions of the R, s and s2 control charts when is estimated
Authors: Chen Gemai
Published: June 2006

R, s and s2 charts with estimated control limits are widely used in practice. Common practice in control‐chart theory is to estimate the control limits using data from the process and, once the process is determined to be in control, to treat the resulting control limits as though fixed. While there are empirical rules for setting up the control charts using past or trial data, little is known about the run length distributions of these charts when the fact that control limits are estimated is taken into account. In this paper, we derive and evaluate the run length distributions associated with the R, s and s2 charts when the process standard deviation a is estimated. The results are then used to discuss the appropriateness of the widely followed empirical rules for choosing the number m of samples and the sample size n.
A Bayesian approach to some overdispersion models
Authors: Albert James H. , Pepple Patricia A.
Published: June 2006

In fitting a generalized linear model, many authors have noticed that data sets can show greater residual variability than predicted under the exponential family. Two main approaches have been used to model this overdispersion. The first approach uses a sampling density which is a conjugate mixture of exponential family distributions. The second uses a quasilikelihood which adds a new scale parameter to the exponential likelihood. The approaches are compared by means of a Bayesian analysis using noninformative priors. In examples, it is indicated that the posterior analysis can be significantly different using the two approaches.
On the choice of optimality criteria in comparing statistical designs
Authors: Shah K. R. , Sinha B. K.
Published: June 2006

We formulate in a reasonable sense a class of optimality functionals for comparing feasible statistical designs available in a given setup. It is desired that the optimality functionals reflect symmetric measures of the lack of information contained in the designs being compared. In view of this, Kiefer's (1975) universal optimality criterion is seen to rest on stringent conditions, some of which can be relaxed while preserving optimality (in an extended sense) of the so‐calledbalanceddesigns.
On the asymptotic normality of functions of uniform spacings
Authors: Beirlant J. , Janssen P. , Veraverbeke N.
Published: June 2006

A new proof is given for the asymptotic normality of sum functions of spacings, providing an alternative to the method of Le Cam (1958). The result is obtained under an optimal moment condition. The proof is based on a simple decomposition into a leading term, which is asymptotically normal, and a remainder term, which is shown to be negligible.
Testing independence with additional information
Authors: Perron François
Published: June 2006

Let X = (Xj : j = 1,…, n) be n row vectors of dimension p independently and identically distributed multinomial. For each j, Xj is partitioned as Xj = (Xj1, Xj2, Xj3), where pi is the dimension of Xji with p1 = 1,p1+p2+p3 = p. In addition, consider vectors Yji, i = 1,2j = 1,…,ni that are independent and distributed as X1i. We treat here the problem of testing independence between X11 and X13 knowing that X11 and X12 are uncorrected. A locally best invariant test is proposed for this problem.
A multivariate Wald‐Wolfowitz rank test against serial dependence
Authors: Hallin Marc , Puri Madan L.
Published: June 2006

Rank‐based cross‐covariance matrices, extending to the case of multivariate observed series the (univariate) rank autocorrelation coefficients introduced by Wald and Wolfowitz (1943), are considered. A permutational central limit theorem is established for the joint distribution of such matrices, under the null hypothesis of (multivariate) randomness as well as under contiguous alternatives of (multivariate) ARMA dependence. A rank‐based, permutationaily distribution‐free test of the portmanteau type is derived, and its asymptotic local power is investigated. Finally, a modified rank‐based version of Tiao and Box's model specification procedure is proposed, which is likely to be more reliable under non‐Gaussian conditions, and more robust against gross errors.

RÉSUMÉ

Des matrices de covariances croisées fondées sur les rangs, généralisant au cas des séries multivariées les coefficients d'autocorrélation de rangs introduits par Wald et Wolfowitz (1943) sont considérées. Un théorème central‐limite permutationnel est établi pour ces matrices, sous Phypothèse que la sérle sous‐jacente constitue la réalisation d'un bruit blanc multivarié, ainsi que sous des contre‐hypothèses contiguës de dépendance ARMA. Un test de rangs du type portemanteau est également construit, et sa puissance asymptotique locale est explicitement calculée. Enfin, une version fondée sur les rangs de la procédure d'identification de Tiao et Box est proposée. Celle‐ci est plus fiable que la procédure usuelle sous des conditions non gaussiennes, et plus robuste par rapport à la présence de valeurs aberrantes.
Computationally efficient classes of higher‐order kernel functions
Authors: Abdous Belkacem
Published: June 2006

Classes of higher‐order kernels for estimation of a probability density are constructed by iterating the twicing procedure. Given a kernelKof orderl, we build a family of kernelsKmof ordersl(m+ 1) with the attractive property that their Fourier transforms are simply 1 — {1 —$(.)}m+1, where Ǩ is the Fourier transform ofK. These families of higher‐order kernels are well suited when the fast Fourier transform is used to speed up the calculation of the kernel estimate or the least‐squares cross‐validation procedure for selection of the window width. We also compare the theoretical performance of the optimal polynomial‐based kernels with that of the iterative twicing kernels constructed from some popular second‐order kernels.
Robust methods for personal‐income distribution models
Authors: Victoria‐Feser Maria‐Pia , Ronchetti Elvezio
Published: June 2006

Statistical problems in modelling personal‐income distributions include estimation procedures, testing, and model choice. Typically, the parameters of a given model are estimated by classical procedures such as maximum‐likelihood and least‐squares estimators. Unfortunately, the classical methods are very sensitive to model deviations such as gross errors in the data, grouping effects, or model misspecifications. These deviations can ruin the values of the estimators and inequality measures and can produce false information about the distribution of the personal income in a country. In this paper we discuss the use of robust techniques for the estimation of income distributions. These methods behave like the classical procedures at the model but are less influenced by model deviations and can be applied to general estimation problems.
Generalized likelihood‐ratio test of the number of components in finite mixture models
Authors: Chen Jiahua
Published: June 2006

The number of components is an important feature in finite mixture models. Because of the irregularity of the parameter space, the log‐likelihood‐ratio statistic does not have a chi‐square limit distribution. It is very difficult to find a test with a specified significance level, and this is especially true for testing k — 1 versus k components. Most of the existing work has concentrated on finding a comparable approximation to the limit distribution of the log‐likelihood‐ratio statistic. In this paper, we use a statistic similar to the usual log likelihood ratio, but its null distribution is asymptotically normal. A simulation study indicates that the method has good power at detecting extra components. We also discuss how to improve the power of the test, and some simulations are performed.
A Bayesian method for classification and discrimination
Authors: Lavine Michael , West Mike
Published: June 2006

We discuss Bayesian analyses of traditional normal‐mixture models for classification and discrimination. The development involves application of an iterative resampling approach to Monte Carlo inference, commonly called Gibbs sampling, and demonstrates routine application. We stress the benefits of exact analyses over traditional classification and discrimination techniques, including the ease with which such analyses may be performed in a quite general setting, with possibly several normal‐mixture components having different covariance matrices, the computation of exact posterior classification probabilities for observed data and for future cases to be classified, and posterior distributions for these probabilities that allow for assessment of second‐level uncertainties in classification.
A counterexample to a conjecture on random shadows
Authors: Small Christopher G.
Published: June 2006

We construct a counterexample to a conjecture in stereology. It is well known that two convex solid bodies which cast congruent orthographic shadows on any common plane must necessarily be congruent to each other. This characterization fails if the orientations of the shadows are allowed to differ. Such counterexamples as have been constructed for the latter case fail to have the same distribution of random shadows projected onto planes with random orientation. Therefore P. McCullagh has conjectured that two bodies whose random shadows have the same distribution are necessarily congruent. We construct a counterexample to this conjecture. Some implications are drawn for the development of a general theory of stereological reconstruction based upon random projected shadows or images.
Ultrastructural elliptical models
Authors: Arellano‐Valle R.B. , Bolfarine H. , Vilca‐Labra F.
Published: June 2006

Dolby's (1976) ultrastructural model with no replications is investigated within the class of the elliptical distributions. General asymptotic results are given for the sample covariance matrixSin the presence of incidental parameters. These results are used to study the asymptotic behaviour of some estimators of the slope parameter, unifying and extending existing results in the literature. In particular, under some regularity conditions they are shown to be consistent and asymptotically normal. For the special case of the structural model, some asymptotic relative efficiencies are also reported which show that generalized least squares and the method of moment estimators can be highly inefficient under nonnormality.
Conditional maxima and inferences for the truncated exponential distribution
Authors: Bain Lee J. , Gan Gaoxiong
Published: June 2006

This paper derives the conditional distribution of the maximum given the sample total for a random sample from the truncated exponential distribution. Based on that result, the paper develops tests or associated confidence intervals for the truncation parameter θ with another parameter θ assumed unknown.
Sequential importance sampling for nonparametric Bayes models: The next generation
Authors: Maceachern Steven N. , Clyde Merlise , Liu Jun S.
Published: June 2006

There are two generations of Gibbs sampling methods for semiparametric models involving the Dirichlet process. The first generation suffered from a severe drawback: the locations of the clusters, or groups of parameters, could essentially become fixed, moving only rarely. Two strategies that have been proposed to create the second generation of Gibbs samplers are integration and appending a second stage to the Gibbs sampler wherein the cluster locations are moved. We show that these same strategies are easily implemented for the sequential importance sampler, and that the first strategy dramatically improves results. As in the case of Gibbs sampling, these strategies are applicable to a much wider class of models. They are shown to provide more uniform importance sampling weights and lead to additional Rao‐Blackwellization of estimators.
A new method for estimating finite‐population quantiles using auxiliary information
Authors: Mak Tak K. , Kuk Anthony
Published: June 2006

A computationally simple method for estimating finite‐population quantiles in the presence of auxiliary information is proposed. An algorithm is also found for implementing related approaches for estimating quantiles, including that of Rao et al. (1990), obtained from inverting difference‐type estimators of the distribution function. The proposed estimation procedure can be seen as a one‐step iteration of the suggested algorithm and is asymptotically equivalent to the limiting estimator. In particular, the proposed method yields a simple and efficient way of approximating Rao et al.'s estimator. Simulation studies based on two real populations show that the approximation can be very satisfactory even for small to moderate samples.
Tables for the Friedman rank test
Authors: Martin Louise , Leblanc Raymond , Toan Nguyen Ky
Published: June 2006

This note presents tables for Friedman's test for two‐way analysis of variance by ranks. These tables are more accurate than those that are presented in the literature. After intensive simulations, we have found for particular critical values some discrepancies with tables published earlier. The tables are also more extensive than those previously available.
Markov‐chain monte carlo: Some practical implications of theoretical results
Authors: Roberts Gareth O. , Rosenthal Jeffrey S.
Published: June 2006

We review and discuss some recent progress in the theory of Markov‐chain Monte Carlo applications, particularly oriented to applications in statistics. We attempt to assess the relevance of this theory for practical applications.
Fisher information and maximum‐likelihood estimation of covariance parameters in Gaussian stochastic processes
Authors: Abt Markus , Welch William J.
Published: June 2006

The inverse of the Fisher information matrix is commonly used as an approximation for the covariance matrix of maximum‐likelihood estimators. We show via three examples that for the covariance parameters of Gaussian stochastic processes under infill asymptotics, the covariance matrix of the limiting distribution of their maximum‐likelihood estimators equals the limit of the inverse information matrix. This is either proven analytically or justified by simulation. Furthermore, the limiting behaviour of the trace of the inverse information matrix indicates equivalence or orthogonality of the underlying Gaussian measures. Even in the case of singularity, the estimator of the process variance is seen to be unbiased, and also its variability is approximated accurately from the information matrix.
The score function and a comparison of various adjustments of the profile likelihood
Authors: Davison A. C. , Stafford J. E.
Published: June 2006

Several adjustments of the profile likelihood have the common effect of reducing the bias of the associated score function. Hence expansions for the adjusted score functions differ by a term,Dξ, that has small asymptotic order (n−½). The effect ofDξon other quantities of interest is studied. In particular, we find the bias and variance of the adjusted maximum‐likelihood estimate to be relatively unaffected, while differences in the Bartlett correction depend onDξin a simple way.
A bootstrap procedure in linear regression with nonstationary errors
Authors: Yeh Arthur B.
Published: June 2006

In the context of linear regression with dependent and nonstationary errors, the classical moving‐block bootstrap (MBB) fails to capture the nonstationarity of the errors. A new bootstrap procedure called the blocking external bootstrap (BEB) is proposed to overcome the problem. The consistency of the BEB in estimating the variance of the least‐squares estimator is studied in the case of α‐mixing and nonstationary sequence of errors. It is shown that the BEB only achieves partial correction if the block size is fixed. Complete consistency is achieved by the BEB when the block size is allowed to go to infinity. We also study the first‐order consistency of the least squares estimator based on the BEB. A simulation study is carried out to assess the performance of the BEB versus the MBB in estimating the variance of the least‐squares estimator. Finally, some open problems are discussed.
Propriétés statistiques des copules de valeurs extrêmes bidimensionnelles
Authors: Ghoudi Kilani , Khoudraji Abdelhaq , Rivest Et Louis‐Paul
Published: June 2006

Let (X, Y) be a bivariate random vector whose distribution function H(x, y) belongs to the class of bivariate extreme‐value distributions. If F1 and F2 are the marginals of X and Y, then H(x, y) = C{F1(x),F2(y)}, where C is a bivariate extreme‐value dependence function. This paper gives the joint distribution of the random variables Z = {log F1(X)}/{log F1(X)F2(Y)} and W = C{F1{(X),F2(Y)}. Using this distribution, an algorithm to generate random variables having bivariate extreme‐value distribution is présentés. Furthermore, it is shown that for any bivariate extreme‐value dependence function C, the distribution of the random variable W = C{F1(X),F2(Y)} belongs to a monoparametric family of distributions. This property is used to derive goodness‐of‐fit statistics to determine whether a copula belongs to an extreme‐value family.
Estimation in the multipath change point problem for correlated data
Authors: Joseph Lawrence , Vandal Alain C. , Wolfson David B.
Published: June 2006

In many experiments, several measurements on the same variable are taken over time, a geographic region, or some other index set. It is often of interest to know if there has been a change over the index set in the parameters of the distribution of the variable. Frequently, the data consist of a sequence of correlated random variables, and there may also be several experimental units under observation, each providing a sequence of data. A problem in ascertaining the boundaries between the layers in geological sedimentary beds is used to introduce the model and then to illustrate the proposed methodology. It is assumed that, conditional on the change point, the data from each sequence arise from an autoregressive process that undergoes a change in one or more of its parameters. Unconditionally, the model then becomes a mixture of nonstationary autoregressive processes. Maximum‐likelihood methods are used, and results of simulations to evaluate the performance of these estimators under practical conditions are given.
Estimation of a multivariate mean with constraints on the norm
Authors: Marchand Eric
Published: June 2006

Estimation of the mean θ of a spherical distribution with prior knowledge concerning the norm ||θ|| is considered. The best equivariant estimator is obtained for the local problem ||θ|| = λ0, and its risk is evaluated. This yields a sharp lower bound for the risk functions of a large class of estimators. The risk functions of the best equivariant estimator and the best linear estimator are compared under departures from the assumption ||θ|| = λ0.