摘要:

AbstractPlusieurs méthodes ont été suggérées pour calculer lesMet lesG‐M‐estimateurs de β, le paramètre de la régression, et de σ, le paramètre d'échelle, dans un modèle linéaire. Cet article montre que, pour quelques jeux de données fameux en statistique robuste, les systèmes d'équations nonlinéaires pour l'estimation simultanée de β, à l'aide d'unM‐estimateur ayant une fonction ψ redescendante, et de σ à l'aide de la médiane des valeurs absolues des résidus, ont plusieurs solutions. Cette multiplicité est causée non pas par la présence d'une fonction ψ redescendante qui fait en sorte que β n'est pas toujours bien défini même si σ est connu, mais bien par l'estimation simultanée de β et de σ. Les difficultés mises en lumière dans ce travail peuvent être évitées en employant une méthode de calcul différente, en deux étapes. On estime d'abord σ à l'aide de la médiane des valeurs absolues des résidus obtenus pour en estimateur robuste défini de façon unique tel le “Proposal 2” de Huber ou l'estimateur basé sur la normeL1. On estime ensuite β en résolvant le système nonlinéaire pour leM‐estimateur oú σ prend la valeur calculée à la première étape. Des conditions an

ISSN:0319-5724    

DOI:10.2307/3314844

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractThe problem of constructing confidence limits for a scalar parameter is considered. Under weak conditions, Efron's accelerated bias‐corrected bootstrap confidence limits are correct to second order in parametric familles. In this article, a new method, called the automatic percentile method, for setting approximate confidence limits is proposed as an attempt to alleviate two problems inherent in Efron's method. The accelerated bias‐corrected method is not fully automatic, since it requires the calculation of an analytical adjustment; furthermore, it is typically not exact, though for many situations, particularly scalar‐parameter familles, exact answers are available. In broader generality, the proposed method is exact when exact answers exist, and it is second‐order accurate otherwise. The automatic percentile method is automatic, and for scalar parameter models it can be iterated to achieve higher accuracy, with the number of computations being linear in the number of iterations. However, when nuisance parameters are present, only second‐order accuracy seems o

ISSN:0319-5724    

DOI:10.2307/3314845

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractThe mixed Poisson–inverse‐Gaussian distribution has been used by Holla, Sankaran, Sichel, and others in univariate problems involving counts. We propose a Poisson–inverse‐Gaussian regression model which can be used for regression analysis of counts. The model provides an attractive framework for incorporating random effects in Poisson regression models and in handling extra‐Poisson variation. Maximum‐likelihood and quasilikelihood‐moment estimation is investigated and illustrated with an example involving motor‐i

ISSN:0319-5724    

DOI:10.2307/3314846

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractTwo approximations to theF‐distribution are evaluated in the context of testing for intraclass correlation in the analysis of family data. The evaluation is based on a computation of empirical significance levels and a comparison betweenp‐values associated with these approximations and the corresponding exactp‐values. It is found that the approximate methods may give very unsatisfactory results, and exact methods are therefore recommended for genera

ISSN:0319-5724    

DOI:10.2307/3314849

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractWe derive twoC(α) statistics and the likelihood‐ratio statistic for testing the equality of several correlation coefficients, fromk≥ 2 independent random samples from bivariate normal populations. The asymptotic relationship of theC(α) tests, the likelihood‐ratio test, and a statistic based on the normality assumption of Fisher'sZ‐transform of the sample correlation coefficient is established. A comparative performance study, in terms of size and power, is then conducted by Monte Carlo simulations. The likelihood‐ratio statistic is often too liberal, and the statistic based on Fisher'sZ‐transform is conservative. The performance of the twoC(α) statistics is identical. They maintain significance level well and have almost the same power as the other statistics when empirically calculated critical values of the same size are used. TheC(α) statistic based on a noniterative estimate of the common correlation coefficient (based on Fisher'sZ‐transfor

ISSN:0319-5724    

DOI:10.2307/3314850

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractIf two parameters ψ and λ, are orthogonal, λψ, the maximum‐likelihood estimate of λ for given ψ, varies only slowly with ψ in the neighbourhood of the overall maximum‐likelihood point. The same is true if ψλ is replaced by a nonlinear functionh(ψλ). The detailed form of the variation of ψλ with ψ is studied, and a basis suggested for choosing a particular functionh(ψλ) that shows the dependence in the least

ISSN:0319-5724    

DOI:10.2307/3314851

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractSuppose we havenobservations fromX=Y+Z, whereZis a noise component with known distribution, andYhas an unknown densityf. When the characteristic function ofZis nonzero almost everywhere, we show that it is possible to construct a density estimatefnsuch that for allf, Iimn||=0.

ISSN:0319-5724    

DOI:10.2307/3314852

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractForn≥ 1, letXnl,…,Xnnbe independent integer‐valued random variables, and defineSn=Xnl+···+Xnn. In a recent paper, we obtained a simple proof for the convergence of the distribution ofSnto a Poisson distribution under very general conditions. In this paper, we extend that result to the multidimensio

ISSN:0319-5724    

DOI:10.2307/3314853

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY

摘要:

AbstractWe prove a central limit theorem for the quadratic variation process of some Lévy‐Baxter‐type Gaussian random fi

ISSN:0319-5724    

DOI:10.2307/3314854

出版商:Wiley‐Blackwell    

年代:1989

数据来源: WILEY