摘要:

AbstractWe prove the asymptotic validity of bootstrap confidence bands for the influence curve from its usual estimator (the sensitivity curve). The proof is based on the use of Gill's generalized delta method for Hadamard differentiable operators. Some statistical applications, in particular to the estimation of asymptotic variance, are given.

ISSN:0319-5724    

DOI:10.2307/3315546

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractClasses 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

ISSN:0319-5724    

DOI:10.2307/3315548

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractIn the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV‐1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour‐bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumo

ISSN:0319-5724    

DOI:10.2307/3315549

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractCombined Bayesian estimates for equicorrelation covariance matrices are considered. The case of a common equicorrelation p and possibly different standard deviations σl,σkamongkexperimental groups is examined first, and the Bayesian estimation of (σ, σ1,σk) is discussed. Secondly, under the assumption of a common standard deviation and possibly different equicorrelations, the Bayesian estimation of (ρ1,ρk,σ) is con

ISSN:0319-5724    

DOI:10.2307/3315550

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

AbstractRank‐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.RÉSUMÉDes 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 p

ISSN:0319-5724    

DOI:10.2307/3315547

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

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

ISSN:0319-5724    

DOI:10.2307/3315552

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY

摘要:

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 ofX2chart 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 andX2charts could provide further insight into the proces

ISSN:0319-5724    

DOI:10.2307/3315553

出版商:Wiley‐Blackwell    

年代:1995

数据来源: WILEY