bluuebunny/crossref_metadata_2025 huggingface dataset:
Testing retrospective hypotheses
Authors: Maymin Zakhar , Gutmann Sam
Published: June 2006

This paper develops a conditional approach to testing hypotheses set up after viewing the data. For example, suppose Xi are estimates of location parameters θi, i = 1,…n. We show how to compute p‐values for testing whether θ1 is one of the three largest θi after observing that X1 is one of the three largest Xi, or for testing whether θ1 > θ2 > … > θn after observing X1 >X2> … >Xn.
Weak approximations for quantile processes of stationary sequences
Authors: Csörgö Miklós , Yu Hao
Published: June 2006

ABSTRACT By studying the deviations between uniform empirical and quantile processes (the so‐called Bahadur‐Kiefer representations) of a stationary sequence in properly weighted sup‐norm metrics, we find a general approach to obtaining weighted results for uniform quantile processes of stationary sequences. Consequently we are able to obtain weak convergence for weighted uniform quantile processes of stationary mixing and associated sequences. Further, by studying the sup‐norm distance of a general quantile process from its corresponding uniform quantile process, we find that information at the two end points of the uniform quantile process can be so utilized that this weighted sup‐norm distance converges in probability to zero under the so‐called Csörgõ‐Révész conditions. This enables us to obtain weak convergence for weighted general quantile processes of stationary mixing and associated sequences.
A comparison of tests for trend with historical controls in carcinogen bioassay
Authors: Fung Karen Y. , Krewski D. , Smythe R. T.
Published: June 2006

ABSTRACT Tests for trend in tumour response rates with increasing dose in long‐term laboratory studies of carcinogenicity that take into account historical control information are discussed. The theoretical basis for these tests is described, and their small‐sample properties evaluated using computer simulation. The performance of these tests is also evaluated using data from carcinogenicity experiments conducted under the U.S. National Toxicology Program. Based on these results, recommendations are made as to the most appropriate tests in practice. When the assumptions underlying these tests are satisfied, the use of historical control information is shown to result in an increase in power relative to the classical Cochran‐Armitage test that is widely used without historical controls.
When is a curve an outlier? An account of a tricky problem
Authors: Manchester Lise , Blanchard Wade
Published: June 2006

ABSTRACT The analysis of a set of data consisting ofNshort (≤20 observations each) multivariate time series, where the observations are irregularly spaced and where observations for the different components of each multivariate series are observed at different times, is discussed. With the increased use of automatic recording devices in many fields, data such as these, which are of course samples from smooth response curves, are becoming more common. In this application, which was a clinical trial comparing two cements for use in hip replacement surgery, the key to the analysis was in recognizing that the interest lay in the degree to which the five curves representing a patient's vital signs deviated from baseline (i.e., normal for that patient) during surgery. This enabled the statisticians to define appropriate response variables. The analysis included Rosseeuw's (1984) technique for the identification of multivariate outliers and logistic regressions to identify any effects on the process producing the outliers due to treatment or covariates.
The role of probability generating functions for estimation in incompletely observed random walks
Authors: Maki Ellen , Mcdunnough Philip
Published: June 2006

Partial observation of a random walk results in independent convolutions of i.i.d. variables. It is known that under a scheme of sufficiently frequent observation, moments of the random walk can be consistently estimated. In these cases, probability generating functions (p.g.f.'s) can be used to circumvent the difficulties posed by likelihood estimation involving convolutions. Asymptotic properties of the p.g.f. estimates are given, and a comparison is made with the method‐of‐moments estimator, which is also shown to be asymptotically normal. In a parametric context, the p.g.f. estimator is shown to be asymptotically efficient. Monte Carlo experiments demonstrate that there are advantages to using the p.g.f.‐based estimate in small samples as well.
Some results on bootstrap prediction intervals
Authors: Mojirsheibani Majid , Tibshirani Robert
Published: June 2006

We investigate the construction of a BCa‐type bootstrap procedure for setting approximate prediction intervals for an efficient estimator θm of a scalar parameter θ, based on a future sample of size m. The results are also extended to nonparametric situations, which can be used to form bootstrap prediction intervals for a large class of statistics. These intervals are transformation‐respecting and range‐preserving. The asymptotic performance of our procedure is assessed by allowing both the past and future sample sizes to tend to infinity. The resulting intervals are then shown to be second‐order correct and second‐order accurate. These second‐order properties are established in terms of min(m, n), and not the past sample size n alone.
A parametric model for heterogeneity in paired Poisson counts
Authors: Goutis Constantinos , Galbraith Rex F.
Published: June 2006

We present a model for data in the form of matched pairs of counts. Our work is motivated by a problem in fission‐track analysis, where the determination of a crystal's age is based on the ratio of counts of spontaneous and induced tracks. It is often reasonable to assume that the counts follow a Poisson distribution, but typically they are overdispersed and there exists a positive correlation between the numbers of spontaneous and induced tracks in the same crystal. We propose a model that allows for both overdispersion and correlation by assuming that the mean densities follow a bivariate Wishart distribution. Our model is quite general, having the usual negative‐binomial and Poisson models as special cases. We propose a maximum‐likelihood estimation method based on a stochastic implementation of the EM algorithm, and we derive the asymptotic standard errors of the parameter estimates. We illustrate the method with a data set of fission‐track counts in matched areas of zircon crystals.
A note on the scale parameter of the dirichlet process
Authors: Walker Stephen G. , Mallick Bani K.
Published: June 2006

This paper gives an interpretation for the scale parameter of a Dirichlet process when the aim is to estimate a linear functional of an unknown probability distribution. We provide exact first and second posterior moments for such functionals under both informative and noninformative prior specifications. The noninformative case provides a normal approximation to the Bayesian bootstrap.
Box‐Cox transformed linear models: A parameter‐based asymptotic approach
Authors: Chen Gemai , Lockhart Richard A.
Published: June 2006

A Box‐Cox transformed linear model usually has the formy(λ) = μ + β1x1+… + βpxp+ oe, wherey(λ) is the power transform ofy.Although widely used in practice, the Fisher information matrix for the unknown parameters and, in particular, its inverse have not been studied seriously in the literature. We obtain those two important matrices to put the Box‐Cox transformed linear model on a firmer ground. The question of how to make inference on β = (β1,…,βp)Twhen λ; is estimated from the data is then discussed for large but finite sample size by studying some parameter‐based asymptotics. Both unconditional and conditional inference are studied from the frequentist point of view.
Estimation of parameters in survey sampling: Optimality
Authors: Godambe V. P.
Published: June 2006

Some recent works on estimation in survey sampling are analyzed and extended from the perspective of the theory of optimal estimating functions.
Estimation of an exponential quantile under pitman's measure of closeness
Authors: Kourouklis S.
Published: June 2006

We consider the problem of estimating a quantile of an exponential distribution with unknown location and scale parameters under Pitman's measure of closeness (PMC). The loss function is required to satisfy some mild conditions but is otherwise arbitrary. An optimal estimator is obtained in the class of location‐scale‐equivariant estimators, and its admissibility in the sense of PMC is investigated.
Lower bounds on Bayes risks for estimating a normal variance: With applications
Authors: Vidakovic Brani , Dasgupta Anirban
Published: June 2006

Brown and Gajek (1990) gave useful lower bounds on Bayes risks, which improve on earlier bounds by various authors. Many of these use the information inequality. For estimating a normal variance using the invariant quadratic loss and any arbitrary prior on the reciprocal of the variance that is a mixture of Gamma distributions, we obtain lower bounds on Bayes risks that are different from Borovkov‐Sakhanienko bounds. The main tool is convexity of appropriate functionals as opposed to the information inequality. The bounds are then applied to many specific examples, including the multi‐Bayesian setup (Zidek and his coauthors). Subsequent use of moment theory and geometry gives a number of new results on efficiency of estimates which are linear in the sufficient statistic. These results complement earlier results of Donoho, Liu and MacGibbon (1990), Johnstone and MacGibbon (1992) and Vidakovic and DasGupta (1994) for the location case.
Effects of the regulators paclobutrazol and flurprimidol on the growth of terminal sprouts formed on trimmed silver maple trees
Authors: Camacho Fernando , Arron Geoffrey
Published: June 2006

Approximately 500,000 trees, growing near or under electrical distribution lines, are trimmed by Ontario Hydro each year at a cost of about $25 per tree. Several new growth regulators have been identified that are effective in controlling the growth of trimmed trees. Two such regulators are PP333 (paclobutrazol) and EL500 (flurprimidol). This paper presents the analysis of the data from an experiment conducted by Ontario hydro in which trimmed silver maple trees were trunk‐injected with different doses of these growth regulators. It was found that high doses of the growth regulators, particularly PP333 (20 g/L), were effective in retarding sprout growth.
In search of the “best” growth inhibitor
Authors: Lee Hyun Suk , Philips Bob
Published: June 2006

In searching for the “best” growth inhibitor, we decided to consider growth inhibition in terms of the lengths of the terminal sprouts. For it is logical to infer that the trees with the longer sprouts (after a 20‐month period) will most likely be the ones that will need trimming in the future. Additionally, we reasoned that if a particular treatment produced a smaller proportion of “long” sprouts, then it would be a more effective growth inhibitor. It was now necessary to define what was meant by “long”. After consultation with foresters we chose cutoff lengths of 15.0, 25.0 and 35.0 cm. Hence the response variable was chosen to be the proportion of the terminal sprouts on a tree that exceeded a specified cutoff length. By varying the cutoff lengths, we would minimize the effect of the arbitrariness involved in choosing one particular length.
Rank correlation methods for missing data
Authors: Alvo Mayer , Cabilio Paul
Published: June 2006

The subject of rank correlation has had a rich history. It has been used in numerous applications in tests for trend and for independence. However, little has been said about how to define rank correlation when the data are incomplete. The practice has often been to ignore missing observations and to define rank correlation for the smaller complete record. We propose a new class of measures of rank correlation which are based on a notion of distance between incomplete rankings. There is the potential for a significant increase in efficiency over the approach which ignores missing observations as demonstrated by a specific case.
A circular‐cone test for testing homogeneity against a simple tree order
Authors: Conaway Mark , Pillers Carolyn , Robertson Tim , Sconing Jim
Published: June 2006

Several methods exist for the problem of testing the equality of several treatments against the one‐sided alternative that the treatments are better than the control. These methods include Dunnett's test, Bartholomew's likelihood‐ratio test, the Abelson‐Tukey‐Schaafsma‐Smid optimal‐contrast test, and the multiple‐contrast test of Mukerjee, Robertson, and Wright. A new test is proposed based on an approximation of the likelihood‐ratio test of Bartholomew. This test involves using a circular cone in place of the alternative‐hypothesis cone. The circular‐cone test has excellent power characteristics similar to those of Bartholomew's test. Moreover, it has the advantages of being simpler to compute and may be used with unequal sample sizes.
Selection of the splined variables and convergence rates in a partial spline model
Authors: Chen Hung , Chen Keh‐Wei
Published: June 2006

A method based on the principle of unbiased risk estimation is used to select the splined variables in an exploratory partial spline model proposed by Wahba (1985). The probability of correct selection based on the proposed procedure is discussed under regularity conditions. Furthermore, the resulting estimate of the regression function achieves the optimal rates of convergence over a general class of smooth regression functions (Stone 1982) when its underlying smoothness condition is not known.
Modeling heteroscedastic age‐period‐cohort cancer data
Authors: MacNeill I. B. , Mao Y. , Xie L.
Published: June 2006

The extent to which cancer will be a burden on the Canadian health‐care system will be determined by future cancer rates and future population levels in the high‐risk age groups. Parametric models of incidence and mortality rates for various cancers may be used to obtain medium‐term forecasts of rates, which then can be used in conjunction with population projections to obtain forecasts of total incidence and mortality. Age‐period‐cohort cancer data often exhibit marked heteroscedasticity, which complicates the modeling of the data. Methods to allow for the effects of this heteroscedasticity on residual processes are developed and discussed in the context of modeling Canadian female breast‐cancer incidence data.
Inferential estimation, likelihood, and linear pivotals
Authors: Sprott D. A.
Published: June 2006

A linear pivotal is introduced as a generalization of an estimate. The defining feature of a linear pivotal is that it generates a likelihood function in the same way as does a statistic. This allows the efficiency and sufficiency of the pivotal to be examined. The efficient reduction of data to a linear pivotal can often be achieved when it cannot be achieved using an estimate. Maximum‐likelihood estimation can be interpreted as a method of generating approximate sufficient linear pivotals.
Kurtosis and spread
Authors: Balanda Kevin P. , Macgillivray H. L.
Published: June 2006

An increase in kurtosis is achieved through the location‐ and scale‐free movement of probability mass from the “shoulders” of a distribution into its centre and tails. We introduce a coherent structure of ordering and measures, requiring no symmetry assumption, that represent different formalizations of this movement. For this purpose spread functions and spread‐spread plots are defined. The orderings impose growth patterns on the spread‐spread plot of the distributions involved, and the weakest involve both a specific scale‐matching technique and placement of “shoulders”. The role of existing kurtosis orderings and measures in this general context is identified and examples discussed throughout.
Tests for the mean of a multivariate normal population
Authors: Hudon Georges
Published: June 2006

We study the problem of testing: H0: μ ∈ P against H1: μ ∉ P, based on a random sample ofNobservations from ap‐dimensional normal distribution Np(μ, Σ) with Σ > 0 and P a closed convex positively homogeneous set. We develop the likelihood‐ratio test (LRT) for this problem. We show that the union‐intersection principle leads to a test equivalent to the LRT. It also gives a large class of tests which are shown to be admissible by Stein's theorem (1956). Finally, we give the α‐level cutoff points for the LRT.
Comparison of experiments for a class of positively dependent random variables
Authors: Shaked Moshe , Tong Y. L.
Published: June 2006

Using Blackwell's definition for comparison of experiments, it is shown that some sets of positively dependent random variables are less informative than similar sets of independent random variables. It is also shown that the information content of symmetric multivariate normal random vectors with a common known variance increases as the common correlation coefficient decreases. Some results which compare members of two‐parameter exponential families are also included.
The case of the random telephone numbers
Authors: Johnston Bruce
Published: June 2006

An unusual pattern of telephone numbers recorded on suspect credit‐card purchases led to the development of a generalized multinomial distribution. One usage of credit cards included 26 telephone numbers with a pattern of 7 unique numbers: 16 of one kind, 4 of another, 2 of another, and 4 different ones. With the assumption that the probability of any digit appearing in a telephone number is 1/10, the pattern of the 26 telephone numbers is found to have a probability of occurrence on the order of 1/1065. That is, the chance of such a pattern occurring at random is roughly equivalent to winning nine times in a row the popular ottery, LOTO 6/49.
Step‐function covariate effects in the proportional‐hazards model
Authors: Leblanc Michael , Crowley John
Published: June 2006

We describe some computationally efficient methods for building proportional‐hazards models with piecewise constant relative risk functions. The proposed techniques can be used to fit and assess a single step‐function (changepoint) term or as flexible exploratory survival‐data analysis tools. In addition, these tools can be used to include step‐function terms in more general proportional‐hazards models such as tree‐based models. An application to the development of prognostic groups based on data from a clinical trial for myeloma is presented.

Nous décrivons quelques méthodes de calcul efficaces pour construire des modèles de risques proportionnels avec des functions de risque constantes par pièces. Les techniques proposés peuvent ětre utilisées pour ajuster et évaluer un terme fonction par étage/point de changement ou comme un outil d'analyse flexible d'exploration de données de survie. De plus, ces outils peuvent ětre utilisés pour inclure des termes fonctions par étages dans des modèles de risques proportionnels plus généraux tels que les modèles à base d'arbres. Une application au développement de groupes de prognostiques basée sur des données d'une enquète sur le myélome est présentée.
Estimating risk reduction in stein estimation
Authors: Venter J. H. , Steel S. J.
Published: June 2006

It is shown that the unbiased estimator of the risk reduction in Stein estimation is unsatisfactory from a mean‐squared‐error point of view. A truncated form of the unbiased estimator and various empirical Bayes estimators of the risk reduction are shown to perform much better than the unbiased estimator. A simple practical estimator is proposed whose performance is a compromise between that of the truncated and empirical Bayes estimators.
Moments of the sampled autocovariances and autocorrelations for a Gaussian white‐noise process
Authors: Anderson Oliver D.
Published: June 2006

Cumulants, moments about zero, and central moments are obtained for the mean‐corrected serial covariances and serial correlations for series realizations of lengthnfrom a white‐noise Gaussian process. All first and second moments (and some third, fourth, and higher moments) are given explicitly for the serial covariances; and the corresponding moments for the serial correlations are derived either explicitly or implicitly.
The limiting distribution of the least‐squares estimator in nearly integrated seasonal models
Authors: Perron Pierre
Published: June 2006

We consider the least‐squares estimator of the autoregressive parameter in a nearly integrated seasonal model. Building on the study by Chan (1989), who obtained the limiting distribution, we derive a closed‐form expression for the appropriate limiting joint moment generating function. We use this function to tabulate percentage points of the asymptotic distribution for various seasonal periods via numerical integration. The results are extended by deriving a stochastic asymptotic expansion to order Op(T‐l), whose percentage points are also obtained by numerically integrating the appropriate limiting joint moment generating function. The adequacy of the approximation to the finite‐sample distribution is discussed.
Stability theorems for maxima of dependent sequences
Authors: F.Li Michael Z. , Tomkins R. J.
Published: June 2006

Three stability theorems due to Gnedenko (1943), Barndorff‐Nielsen (1963), and Tomkins (1986) are extended to the sample maxima of identically distributed ϕ‐mixing and m‐dependent sequences.
Laws of the iterated logarithm and large deviations for a class of diffusionl processes
Authors: Remillard Bruno , Dawson Donald A.
Published: June 2006

We use the martingale approach to study large deviations and laws of the iterated logarithm for certain multidimensional diffusion processes. The criteria for the validity of these properties are expressed in terms of averaging properties of the coefficients of the infinitesimal generator. In particular we apply our results to diffusion processes with random coefficients.
On the asymptotic distributions of high‐order spacings statistics
Authors: Guttorp P. , Lockhart R. A.
Published: June 2006

Goodness‐of‐fit tests for the uniform distribution based on sums of smooth functions ofm‐spacings are studied. A limiting sum‐of‐weighted‐chi‐squareds approximation is shown to be accurate uniformly inmfor the special cases of analogues of Greenwooďs statistic and Moran's statistic. Asymptotic critical points are provided; theory and Monte Carlo studies show they are accurate for allmprovidednis moderately large.
A consistent nonparametric density estimator for the deconvolution problem
Authors: Liu Ming Chung , Taylor Robert L.
Published: June 2006

The problem of nonparametric estimation of a probability density function when the sample observations are contaminated with random noise is studied. A particular estimator f̌n(x) is proposed which uses kernel‐density and deconvolution techniques. The estimator f̌n(x) is shown to be uniformly consistent, and its appearance and properties are affected by constantsMnandhnwhich the user may choose. The optimal choices ofMnandhndepend on the sample sizen, the noise distribution, and the true distribution which is being estimated. Particular selections forMnandhnwhich minimize upper‐bound functions of the mean squared error for f̌n(x) are recommended.
Robust kernel estimators for additive models with dependent observations
Authors: Bianco Ana , Boente Graciela
Published: June 2006

Robust nonparametric estimators for additive regression or autoregression models under an α‐mixing condition are proposed. They are based on local M‐estimators or local medians with kernel weights, and their asymptotic behaviour is studied. Moreover, diese local M‐estimators achieve the same univariate rate of convergence as their linear relatives.
Convergence de I estimateur a noyau de derivees de Radon‐Nikodym generales dans le cas melangeant
Authors: Bensaid Nadia , Fabre Jean‐Pierre
Published: June 2006

In many situations, nonparametric inference in point‐process theory consists in estimating a Radon‐Nikodym derivative of a nonnegative measure p with respect to another nonnegative measure v, where p and v are intensities of point processes. We consider the case of a mixing andstrictly stationary sequence of point processes and establish convergence results for the kernel estimator.
Normalité asymptotique d'estimateurs convergents du mode conditionnel
Authors: Berlinet Alain , Gannoun Ali , Matzner‐Løber Eric
Published: June 2006

Nous donnons des théorèmes généraux de normalité asymptotique des estimateurs convergents du mode conditionnel, indépendamment de la structure de dépendance des données et les appliquons au cas d'un processus stationnaire α‐mélangeant.
On the nearly nonstationary seasonal time series
Authors: Chan Ngai Hang
Published: June 2006

A 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

The 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

Estimation 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

Prior 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

Acceptance 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

We 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

A 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

We 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

We 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.
An efficiency result for the empirical characteristic function in stationary time‐series models
Authors: Feuerverger Andrey
Published: June 2006

It is shown under general conditions that arbitrarily high asymptotic efficiencies can be obtained when the parameters of a stationary time series are estimated by fitting the characteristic functions of the process to their empirical versions. A consistency and a central limit result are also given.
Estimating the concentration of the Langevin distribution
Authors: Ducharme Gilles R. , Milasevic Philip
Published: June 2006

We propose an estimator of the concentration parameter of the Langevin distribution that is based on the spatial median. We derive its asymptotic distribution, compute its asymptotic efficiency, and show that it possesses some interesting stability properties under contamination.
Some topics of current interest in clinical trials
Authors: Armitage Peter
Published: June 2006

After 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

This 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

The 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

Consider 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

An 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

For 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.
Applications of empirical characteristic functions in some multivariate problems
Authors: Ghosh Sucharita , Ruymgaart Frits H.
Published: June 2006

In this note we extend univariate tests for normality and symmetry based on empirical characteristic functions to the multivariate case.
Penalized minimum‐distance estimates in finite mixture models
Authors: Chen Jiahua , Kalbfleisch J.D.
Published: June 2006

When 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

Loss 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

In 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

The 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

This 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

We 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

This 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

We 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

The 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

Generalized 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

In 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.