摘要:

AbstractCoordinate measuring machines (CMMs) are used to check the geometric integrity of component parts. The geometric constraints to which a part must conform, as defined e.g., by The American National Standards Institute, assume the use of some type of gauging system when inspecting the part. Statistical issues arise in interpretting CMM data in the inspection of part tolerances. We consider a set of n planar regions on the surface of a part. The unit vector normal to each plane is estimated by orthogonal least squares. The small‐sample density of this estimator (on the unit sphere S2) is determined asymptotically as the variance of the CMM error approaches 0. To a first‐degree approximation, this density is Fisher‐von Mises. Diagnostics are reviewed to test the geometric constraint that the n planar regions are oriented correctly with respect to one another, and to test the flatness of planar re

ISSN:0319-5724    

DOI:10.2307/3315438

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractWe 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 enqu

ISSN:0319-5724    

DOI:10.2307/3315439

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractThere 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,0against H1‐ H0and H1against H2‐ H1when 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 expression

ISSN:0319-5724    

DOI:10.2307/3315440

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractLikelihood and estimating‐equation methods provide the two most common approaches to parametric inference. With the former there are three main ways to deal with interval estimation or hypothesis testing; roughly speaking, these are based on the likelihood function, the score function, and the maximum likelihood estimator. For estimating equations which, unlike likelihood, do not require the specification of a full probability distribution for the data, there are analogous methods based on the pseudoscore (estimating function) and on the estimator obtained from the estimating equations. Boos (1992) has given a lucid review, with emphasis on problems that involve constraints on parameters (Aitchison and Silvey 1958). The purposes of this paper are to incorporate empirical likelihood (Owen 1988) into this setting, to compare it with the other methods, and to present some simulations which indicate the need for small‐sample corrections in some situations.Les méthodes de vraisemblance et des équations d'estimation sont les deux approches à l'inférence paramétrique les plus répandues. Avec la première méthode, il y a trois principales façons de traiter des estimations par intervalle ou des test d'hypothèses; en gros, ces méthodes sont fondées sur la fonction de vraisemblance, la fonction score, et l'estimateur du maximum de vraisemblance. Avec la méthode des équations d'estimation qui, contrairement à la méthode de vraisemblance, ne nécessite pas la spécification d'une loi de distribution complète pour les données, il y existe des méthodes analogues fondées sur le pseudo score (fonction d'estimation) et sur l'estimateur obtenu des équations d'estimation. Boos (1992) a fait une critique lucide, soulignant les problèmes qui impliquent des contraintes sur les paramètres (Aitchison et Silvey 1958). L'objet de cet article est d'introduire la vraisemblance empirique (Owen 1988) dans ce cadre, de la comparer avec les autres méthodes et de présenter quelques simulations qui révèlent la nécessité de corrections de petits écha

ISSN:0319-5724    

DOI:10.2307/3315441

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractNonparametric regression quantiles provide informative and powerful alternatives and generalizations to the more traditional mean and median. The use of B‐spline approximation in the conditional quantile estimation has been studied recently by He and Shi (1994). The regression quantile splines are given by minimizing n i = 1 ρα(Yi‐ g(Xi))where ρα(t) = |t| ‐ (2α ‐ 1)t is the Czech function and g is taken from the space spanned by normalized B‐splines basis functions. This paper relaxes the independence assumption on the stationary sequence {Xi, Yi}. If the true conditional quantile function is smooth up to order r and the observed sequence is β‐mixing (or absolutely regular), it is shown, under suitable mixing conditions, that the optimal global convergence rates can be achieved by the B‐spline based estimators and their derivatives.Les fractiles de régression non‐paramétriques donnent d'éclairantes et puissantes alternatives et généralisations aux traditionelles moyenne et médiane. L'utilisation d'approximations par B‐splines dans l'estimation conditionnelle du fractile a été étudiée récemment par He et Shi (1994). Les splines des fractiles de régression sont obtenus en minimisant n i = 1 ρα(Yi‐ g(Xi)), o ù ρα(t) = |t| ‐ (2α ‐ 1)t est la fonction de Czech et g est pris dans l'espace généré par une base de fonctions composé de B‐splines normalisées. Cet article affaiblit l'hypothèse d'indépendance de la suite stationnaire {Xi, Yi,}. Si la véritable fonction fractile est lisse d'ordre r et la suite observée est β‐mixante (ou absolument régulière), il est montré, sous des hypothèses appropriées de mixage, que les taux obtimaux de convergence global peuvent ětre o

ISSN:0319-5724    

DOI:10.2307/3315442

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractConsider a family of square‐integrable Rd‐valued statistics Sk= Sk(X1,k1; X2,k2;…; Xm,km), where the independent samples Xi,kjrespectively have kii.i.d. components valued in some separable metric space Xi. We prove a strong law of large numbers, a central limit theorem and a law of the iterated logarithm for the sequence {Sk}, including both the situations where the sample sizes tend to infinity while m is fixed and those where the sample sizes remain small while m tends to infinity. We also obtain two almost sure convergence results in both these contexts, under the additional assumption that Skis symmetric in the coordinates of each sample Xi,kj.Some extensions to row‐exchangeable and conditionally independent observations are provided. Applications to an estimator of the dimension of a data set and to the Henze‐Schilling test statistic for equality of two densities are also

ISSN:0319-5724    

DOI:10.2307/3315443

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractWe develop a saddle‐point approximation for the marginal density of a real‐valued function p(), where is a general M‐estimator of a p‐dimensional parameter, that is, the solution of the system {n‐1ljl(Yl,) = 0}j=1,…,p. The approximation is applied to several regression problems and yields very good accuracy for small samples. This enables us to compare different classes of estimators according to their finite‐sample properties and to determine when asymptotic approximations are usefu

ISSN:0319-5724    

DOI:10.2307/3315444

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractA Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling‐based approach using a Gibbs or Metropolis‐within‐Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly disc

ISSN:0319-5724    

DOI:10.2307/3315445

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractA family of easily computable estimators of the odds ratio of a number of two‐by‐two contingency tables is proposed. It includes the well‐known Mantel‐Haenszel estimator as a special case. A necessary and sufficient condition is given for the strong consistency of the estimators for the case when the tables are sparse and the number of tables becomes large. The condition also ensures the asymptotic normality of this family of estimators. A family of consistent estimators is proposed for the variances of the asymptotic distributions. In the case of the Mantel‐Haenszel estimator, the validity of Breslow's (1981, Biometrika) condition for the consistency and asymptotic normality is questioned. Examples are given to demonstrate that it is neither necessary nor sufficient for the consistency of the Mantel‐Haenszel estimator.Cet article propose une famille d'estimateurs faciles à calculer du rapport‐chance d'un certain nombre de tableaux de contingences deux par deux. Elle comprend le fameux estimateur de Mantel‐Haenszel, comme cas particulier. Une condition nécessaire et suffisante pour la convergence forte des estimateurs est donnée, dans le cas où les tableaux sont clairsemés et le nombre de tableaux devient élevé. Cette condition garantit également la normalité asymptotique de cette famille d'estimateurs. Une famille d'estimateurs convergents est proposée pour les variances des distributions aymptotiques. Dans le cas de l'estimateur de Mantel‐Haenszel, la validité de la condition de Breslow (1981, Biometrika) pour la convergence et la normalité asymptotique est remise en cause. Des examples sont fournis, démontrant qu'elle n'est ni nécessaire ni suffisante pour la convergence de

ISSN:0319-5724    

DOI:10.2307/3315446

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY