bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the nearly nonstationary seasonal time series
Authors: Chan Ngai Hang 
Published: June 2006

AbstractA time series is said to be nearly nonstationary if some of its characteristic roots are close to the unit circle. For a seasonal time series, such a notion of near‐nonstationarity is studied in a double‐array setting. This approach not only furnishes a natural transition between stationarity and nonstationarity, but also unifies the corresponding asymptotic theories in a seasonal‐time‐series context. The general theory is expressed in terms of functionals of independent diffusion processes. The asymptotic results have applications to estimation and testing in a nearly nonstationary situation and serve as a useful alternative to the common practice of seasonal adjustment.
Ordres stochastiques et efficacité asymptotique des L‐estimateurs
Authors: CapÉRAÀ Philippe 
Published: June 2006

AbstractThe efficiency of an estimator depends heavily on the tails of the distribution of the observations. Several partial orders have been defined to compare probability distributions according to their tails. In this paper we show that the asymptotic relative efficiency of two L‐estimators with monotone weight functions is isotonic with respect to the partial orders defined by van Zwet (1964) and Lawrence (1975). We also give results concerning trimmed means.
Robust hierarchical Bayes estimation of exchangeable means
Authors: Angers Jean‐François , Berger James O. 
Published: June 2006

AbstractEstimation of the mean of a multivariate normal distribution is considered. The components of the mean vector θ are assumed to be exchangeable; this is modelled in a hierarchical fashion with independent Cauchy distributions as the first‐stage prior. The resulting generalized Bayes estimator is calculated and shown to be robust with respect to the presence of outlying means. Alternative estimators that have similar behaviour but are cheaper to compute are also derived.
Sensitivity of some posterior summaries when the prior is unimodal with specified quantiles
Authors: Sivaganesan S. 
Published: June 2006

AbstractPrior information is modeled either by (1) a class of unimodal distributions with specified quantiles, or by (2) an ∈‐contamination class with contaminations subject to unimodal and quantile restrictions. We show how the ranges of certain posterior summaries can be found. Using numerical examples, we compare the robustness behaviour under these classes, and assess the effect, in terms of robustness, of specifying a base prior.
Consultant's corner: A consulting problem involving bivariate acceptance sampling by variables
Authors: Hamilton D. C. , Lesperance M. L. 
Published: June 2006

AbstractAcceptance sampling techniques are used to monitor the accuracy of gas meters. Random samples of meters are taken from homogeneous lots, and two accuracy measurements are recorded for each meter. In the past, the two measurements were averaged, and an acceptance sampling test applied to the sample of averages. In 1987, the plan was modified so that virtually the same test is applied to the two measurements individually. This new procedure is more stringent than the old procedure. In a study of data sampled over three years, the new plan rejects more lots than does the old plan, leading to greatly increased costs to the gas industry and therefore to the consumer. Theoretical reasons are given for why this occurs, and an alternative plan is proposed.
An exact decomposition for a class of exponential dispersion models: Application to sequential testing
Authors: Massam Hélène 
Published: June 2006

AbstractWe define the Wishart distribution on the cone of positive definite matrices and an exponential distribution on the Lorentz cone as exponential dispersion models. We show that these two distributions possess a property of exact decomposition, and we use this property to solve the following problem: givenqsamples (yil,… yiNj),i= l,…,q, from a N(μi,Σi,) distribution, testH:Σ1= Σ2= … = σq.Using the exact decomposition property, the classical test statistic forH, involvingqparameters pi= (Ni, ‐ l)/2,i= 1,…,q, is replaced by a sequence ofq‐ l test statistics for the sequence of testsHi,:σ1=σ2= … =σigiven thatHi‐1is true,i= 2,…,q. Each one of these test statistics involves two parameters only, p.i‐1=p1+ … +pi‐1andpi. We also use the exact decomposition property to test equality of the “direction parameters” forqsample points from the exponential distribution on the Lorentz cone. We give a table of critical values for the distribution on the three‐dimensional Lorentz cone. Tables of critical values in higher dimensions can easily be computed following the same method as in dimension three.
Bivariate control charts for testing x data patterns
Authors: Chan Lai K. , Li Guo‐Ying 
Published: June 2006

AbstractA new control chart, called the θ chart, for monitoring the mean of a process with bivariate quality characteristics is proposed. It can identify a rotation, shift or alternation between the subgroups of the process mean. The conventional application of X2 chart to identify a sudden shift of the process mean is also expanded to identify a change of the process mean or a change of the process dispersion. Furthermore, when used together, the θ and X2 charts could provide further insight into the process.
Weak and strong representations for quantile processes from finite populations with application to simulation size in resampling inference
Authors: Shi Xiquan , Wu C. F. J. , Chen Jiahua 
Published: June 2006

AbstractWe prove three results on the weak or strong representations for quantile processes of samples drawn randomly with or without replacement from a finite population. As an application of the strong‐approximation result (Theorem 2), we give an approach for determining the order of B, the number of Monte Carlo simulations required for the accuracy of resampling inference. In typical situations the order of B is between nbn and n2+δ, where n is the original sample size, δ > 0, and (log log n)/bn → 0.
On using the jackknife to estimate quantile variance
Authors: Martin Michael A. 
Published: June 2006

AbstractWe show that the jackknife technique fails badly when applied to the problem of estimating the variance of a sample quantile. When viewed as a point estimator, the jackknife estimator is known to be inconsistent. We show that the ratio of the jackknife variance estimate to the true variance has an asymptotic Weibull distribution with parameters 1 and 1/2. We also show that if the jackknife variance estimate is used to Studentize the sample quantile, the asymptotic distribution of the resulting Studentized statistic is markedly nonnormal, having infinite mean. This result is in stark contrast with that obtained in simpler problems, such as that of constructing confidence intervals for a mean, where the jackknife‐Studentized statistic has an asymptotic standard normal distribution.
Some topics of current interest in clinical trials
Authors: Armitage Peter 
Published: June 2006

AbstractAfter a short review of the development of the modern approach to the design of clinical trials, attention is focused on the wide variety of trials, their ethical constraints, the criteria for stopping trials, and the possible use of Bayesian methods. Brief discussions are then presented of two specific topics: the analysis of categorical data, and the replication of trials with the consequent need for overviews.
Better approximate confidence intervals for a binomial parameter
Authors: BÖHNING Dankmar 
Published: June 2006

AbstractThis paper discusses five methods for constructing approximate confidence intervals for the binomial parameter Θ, based on Y successes in n Bernoulli trials. In a recent paper, Chen (1990) discusses various approximate methods and suggests a new method based on a Bayes argument, which we call method I here. Methods II and III are based on the normal approximation without and with continuity correction. Method IV uses the Poisson approximation of the binomial distribution and then exploits the fact that the exact confidence limits for the parameter of the Poisson distribution can be found through the x2 distribution. The confidence limits of method IV are then provided by the Wilson‐Hilferty approximation of the x2. Similarly, the exact confidence limits for the binomial parameter can be expressed through the F distribution. Method V approximates these limits through a suitable version of the Wilson‐Hilferty approximation. We undertake a comparison of the five methods in respect to coverage probability and expected length. The results indicate that method V has an advantage over Chen's Bayes method as well as over the other three methods.
Protection against outliers in empirical bayes estimation
Authors: Farrell Patrick J. , Macgibbon Brenda , Tomberlin Thomas J. 
Published: June 2006

AbstractThe proven optimality properties of empirical Bayes estimators and their documented successful performance in practice have made them popular. Although many statisticians have used these estimators since the landmark paper of James and Stein (1961), relatively few have proposed techniques for protecting them from the effects of outlying observations or outlying parameters. One notable series of studies in protection against outlying parameters was conducted by Efron and Morris (1971, 1972, 1975). In the fully Bayesian case, a general discussion on robust procedures can be found in Berger (1984, 1985). Here we implement and evaluate a different approach for outlier protection in a random‐effects model which is based on appropriate specification of the prior distribution. When unusual parameters are present, we estimate the prior as a step function, as suggested by Laird and Louis (1987). This procedure is evaluated empirically, using a number of simulated data sets to compare the effects of the step‐function prior with those of the normal and Laplace priors on the prediction of small‐area proportions.
Linear representation of M‐estimates in linear models
Authors: Rao C. Radhakrishna , Zhao L. C. 
Published: June 2006

AbstractConsider the linear regression model, yi = xiβ0 + ei, i = l,…,n, and an M‐estimate β of βo obtained by minimizing Σρ(yi — xiβ), where ρ is a convex function. Let Sn = ΣXiXiXi and rn = Sn½ (β — β0) — Sn 2 Σxih(ei), where, with a suitable choice of h(.), the expression Σ xix(e,) provides a linear representation of β. Bahadur (1966) obtained the order of rn as n→ ∞ when βo is a one‐dimensional location parameter representing the median, and Babu (1989) proved a similar result for the general regression parameter estimated by the LAD (least absolute deviations) method. We obtain the stochastic order of rn as n → ∞ for a general M‐estimate as defined above, which agrees with the results of Bahadur and Babu in the special cases considered by them.
On the identification of ARMA echelon‐form models
Authors: Nsiri Said , Roy Roch 
Published: June 2006

AbstractAn identification procedure for multivariate autoregressive moving average (ARMA) echelon‐form models is proposed. It is based on the study of the linear dependence between rows of the Hankel matrix of serial correlations. To that end, we define a statistical test for checking the linear dependence between vectors of serial correlations. It is shown that the test statistic t̃n considered is distributed asymptotically as a finite linear combination of independent chi‐square random variables with one degree of freedom under the null hypothesis, whereas under the alternative hypothesis, t̃N/N converges in probability to a positive constant. These results allow us, in particular, to compute the asymptotic probability of making a specification error with the proposed procedure. Links to other methods based on the application of canonical analysis are discussed. A simulation experiment was done in order to study the performance of the procedure. It is seen that the graphical representation of t̃N, as a function of N, can be very useful in identifying the dynamic structure of ARMA models. Furthermore, for the model considered, the proposed identification procedure performs very well for series of 100 observations or more and reasonably well with short series of 50 observations.
Goodness of fit for the inverse Gaussian distribution
Authors: O'Reilly Federico J. , Rueda RaÚL 
Published: June 2006

AbstractFor testing the fit of the inverse Gaussian distribution with unknown parameters, the empirical distribution‐function statistic A2 is studied. Two procedures are followed in constructing the test statistic; they yield the same asymptotic distribution. In the first procedure the parameters in the distribution function are directly estimated, and in the second the distribution function is estimated by its Rao‐Blackwell distribution estimator. A table is given for the asymptotic critical points of A2. These are shown to depend only on the ratio of the unknown parameters. An analysis is provided of the effect of estimating the ratio to enter the table for A2. This analysis enables the proposal of the complete operating procedure, which is sustained by a Monte Carlo study.
Penalized minimum‐distance estimates in finite mixture models
Authors: Chen Jiahua , Kalbfleisch J.D. 
Published: June 2006

AbstractWhen finite mixture models are used to fit data, it is sometimes important to estimate the number of mixture components. A nonparametric maximum‐likelihood approach may result in too many support points and, in general, does not yield a consistent estimator. A penalized likelihood approach tends to produce a fit with fewer components, but it is not known whether that approach produces a consistent estimate of the number of mixture components. We suggest the use of a penalized minimum‐distance method. It is shown that the estimator obtained is consistent for both the mixing distribution and the number of mixture components.
On Spiring's normal loss function
Authors: Sun Feng‐Bin , Laramée Jean‐Yves , Ramberg John S. 
Published: June 2006

AbstractLoss functions express the loss to society, incurred through the use of a product, in monetary units. Underlying this concept is the notion that any deviation from target of any product characteristic implies a degradation in the product performance and hence a loss. Spiring (1993), in response to criticisms of the quadratic loss function, developed the reflected normal loss function, which is based on the normal density function. We give some modifications of these loss functions to simplify their application and provide a framework for the reflected normal loss function that accomodates a broader class of symmetric loss situations. These modifications also facilitate the unification of both of these loss functions and their comparison through expected loss. Finally, we give a simple method for determing the parameters of the modified reflected normal loss function based on loss information for multiple values of the product characteristic, and an example to illustrate the flexibility of the proposed model and the determination of its parameters.
Bootstrapping with auxiliary information
Authors: Zhang Biao 
Published: June 2006

AbstractIn the nonparametric setting, the standard bootstrap method is based on the empirical distribution function of a random sample. The author proposes, by means of the empirical likelihood technique, an alternative bootstrap procedure under a nonparametric model in which one has some auxiliary information about the population distribution. By proving the almost sure weak convergence of the modified bootstrapped empirical process, the validity of the proposed bootstrap procedure is established. This new result is used to obtain bootstrap confidence bands for the population distribution function and to perform the bootstrap Kolmogorov test in the presence of auxiliary information. Other applications include bootstrapping means and variances with auxiliary information. Three simulation studies are presented to demonstrate the performance of the proposed bootstrap procedure for small samples.
The robustness of the quasilikelihood estimator
Authors: Lee Y. , Nelder John A. 
Published: June 2006

AbstractThe quasilikelihood estimator is widely used in data analysis where a likelihood is not available. We illustrate that with a given variance function it is not only conservative, in minimizing a maximum risk, but also robust against a possible misspecification of either the likelihood or cumulants of the model. In examples it is compared with estimators based on maximum likelihood and quadratic estimating functions.
Probability and statistics: A tale of two worlds?
Authors: Genest Christian 
Published: June 2006

AbstractThis comparative study of research productivity and publication habits in probability and statistics completes the paper that was published in this Journal at the end of 1997.It is based on a ten‐year survey of eighteen international journals, half of which are specialized in probability theory and the other half in statistics. Paper, author and adjusted page counts yield cursory measures of productivity for countries and institutions that contributed to fundamental research in these two related fields during the period 1986‐1995.These data also reveal significant cultural differences between probabilists and statisticians in the volume of research, the length of papers, coauthorship practices, etc. Canada is seen to be one of the strongest contributors to the development of these two disciplines.
Estimation of noncentrality parameters
Authors: Kubokawa T. , Robert C.P. , Saleh A.K.Md.E. 
Published: June 2006

AbstractWe propose some estimators of noncentrality parameters which improve upon usual unbiased estimators under quadratic loss. The distributions we consider are the noncentral chi‐square and the noncentral F. However, we give more general results for the family of elliptically contoured distributions and propose a robust dominating estimator.
Bayesian analysis of multivariate survival data using Monte Carlo methods
Authors: Aslanidou Helen , Dey Dipak K. , Sinha Debajyoti 
Published: June 2006

AbstractThis paper deals with the analysis of multivariate survival data from a Bayesian perspective using Markov‐chain Monte Carlo methods. The Metropolis along with the Gibbs algorithm is used to calculate some of the marginal posterior distributions. A multivariate survival model is proposed, since survival times within the same group are correlated as a consequence of afrailtyrandom block effect. The conditional proportional‐hazards model of Clayton and Cuzick is used with a martingale structured prior process (Arjas and Gasbarra) for the discretized baseline hazard. Besides the calculation of the marginal posterior distributions of the parameters of interest, this paper presents some Bayesian EDA diagnostic techniques to detect model adequacy. The methodology is exemplified with kidney infection data where the times to infections within the same patients are expected to be correlated.
Restricted tests for testing independence of time to failure and cause of failure in a competing‐risks model
Authors: Dykstra Richard , Kochar Subhash , Robertson Tim 
Published: June 2006

AbstractWe consider the competing‐risks problem without making any assumption concerning the independence of the risks. Maximum‐likelihood estimates of the cause‐specific hazard rates are obtained under the condition that their ratio is monotone. We also consider the likelihood‐ratio test for testing the proportionality of two cause‐specific hazard rates against the alternative that the ratio of these two hazard rates is monotonic. This testing problem is equivalent to testing independence against likelihood‐ratio dependence of the time to failure and the cause of failure in the competing‐risks setup. We allow for random censoring on the right. The asymptotic null distribution of the test statistic is obtained and is found to be of the chi‐bar‐square type. The problem is extended to the case of more than two risks. A numerical example is given to illustrate the procedure.
Goodness‐of‐fit test for uniform stochastic ordering among several distributions
Authors: Park Chul Gyu , Lee Chu‐In Charles , Robertson Tim 
Published: June 2006

AbstractThe likelihood‐ratio test (LRT) is considered as a goodness‐of‐fit test for the null hypothesis that several distribution functions are uniformly stochastically ordered. Under the null hypothesis,H1:F1⪯F2⪯···⪯FN, the asymptotic distribution of the LRT statistic is a convolution of several chi‐bar‐square distributions each of which depends upon the location parameter. The least‐favourable parameter configuration for the LRT is not unique. It can be two different types and depends on the number of distributions, the number of intervals and the significance level α. This testing method is illustrated with a data set of survival times of five groups of male fruit flies.
Generalized linear models for the analysis of quality‐improvement experiments
Authors: Lee Y. , Nelder J. A. 
Published: June 2006

AbstractGeneralized linear models provide a useful tool for analyzing data from quality‐improvement experiments. We discuss why analysis must be done for all the data, not just for summarizing quantities, and show by examples how residuals can be used for model checking. A restricted‐maximum‐likelihood‐type adjustment for the dispersion analysis is developed.
Bayesian variable selection with related predictors
Authors: Chipman Hugh 
Published: June 2006

AbstractIn data sets with many predictors, algorithms for identifying a good subset of predictors are often used. Most such algorithms do not allow for any relationships between predictors. For example, stepwise regression might select a model containing an interactionABbut neither main effectAorB.This paper develops mathematical representations of this and other relations between predictors, which may then be incorporated in a model selection procedure. A Bayesian approach that goes beyond the standard independence prior for variable selection is adopted, and preference for certain models is interpreted as prior information. Priors relevant to arbitrary interactions and polynomials, dummy variables for categorical factors, competing predictors, and restrictions on the size of the models are developed. Since the relations developed are for priors, they may be incorporated in any Bayesian variable selection algorithm for any type of linear model. The application of the methods here is illustrated via the stochastic search variable selection algorithm of George and McCulloch (1993), which is modified to utilize the new priors. The performance of the approach is illustrated with two constructed examples and a computer performance dataset.
Test de différence de contrastes et somme pondérée de khi‐deux
Authors: Bayomog Samuel , Guyon Xavier , Hardouin Cécile , Yao Jianfeng 
Published: June 2006

AbstractAfter recalling the framework of minimum‐contrast estimation, its consistency and its asymptotic normality, we highlight the fact that these results do not require any stationarity or ergodicity assumptions. The asymptotic distribution of the underlying contrast difference test is a weighted sum of independent chi‐square variables having one degree of freedom each. We illustrate these results in three contexts: (1) a nonhomogeneous Markov chain with likelihood contrast; (2) a Markov field with coding, pseudolikelihood or likelihood contrasts; (3) a not necessarily Gaussian time series with Whittle's contrast. In contexts (2) and (3), we compare experimentally the power of the likelihood‐ratio test with those of other contrast‐difference tests.