摘要:

AbstractWe consider the problem of reconstructing a convex body from samples of lower‐dimensional projections, or shadows. Such problems have been studied using mean cross‐sectional measures of convex sets. We develop new methods based upon inner and outer estimates of the convex body, for which rates of convergence are obtained. These asymptotic results for the inner and outer estimates are compared with each other as well as those based upon Cauchy's form

ISSN:0319-5724    

DOI:10.2307/3315425

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractLet X1,., Xn, be i.i.d. random variables with distribution functionF, and letY1,.,.,Ynbe i.i.d. with distribution function G. For i = 1, 2,.,., n set δi, = 1 if Xi≤ Yi, and 0 otherwise, and Xi, = min{Xi, Ki}. A kernel‐type density estimate off, the density function ofFw.r.t. Lebesgue measure on the Borel o‐field, based on the censored data (δi, Xi),i= 1,.,.,n, is considered. Weak and strong uniform consistency properties over the whole real line are studied. Rates of convergence results are established under higher‐order differentiability assumption onf. A procedure for relaxing such assumptions is also

ISSN:0319-5724    

DOI:10.2307/3315426

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractIn a model for rounded data suppose that the random sampleX1,.,.,Xn,. i.i.d., is transformed into an observed random sample X1Δ,.,.,XnΔ, where XiΔ= 2vΔ ifXi, ∈ (2vΔ ‐ Δ, 2vΔ + Δ), for i = 1,.,.,n. We show that the precision Δ of the observations has an important effect on the shape of the kernel density estimator, and we identify important points for the graphical display of this estimator. We examine the IMSE criteria to find the optimal window under the rounde

ISSN:0319-5724    

DOI:10.2307/3315427

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractLet X1be a strictly stationary multiple time series with values in Rdand with a common densityf. Let X1,.,.,Xn, benconsecutive observations of X1. Letk = kn, be a sequence of positive integers, and letHnibe the distance from Xito itskth nearest neighbour among Xj,ji. The multivariate variable‐kernel estimate fn, offis defined by\documentclass{article}\pagestyle{empty}\begin{document}$$ f_n ({\bf x}) = n^{ - 1} \sum\limits_{i = 1}^n {H_{ni}^{ - d} K} \left( {\frac{{{\bf X}_i - {\bf x}}}{{H_{ni} }}} \right), $$\end{document}whereKis a given density. The complete convergence of fn, to f on compact sets is established for time series satisfying a dependence condition (referred to as the strong mixing condition in the locally transitive sense) weaker than the strong mixing condition. Appropriate choices ofkare explicitly given. The results apply to autoregressive processes and bilinear time‐series mod

ISSN:0319-5724    

DOI:10.2307/3315428

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractAn example is given of a uniformly most accurate unbiased confidence belt which yields absurd confidence statements with 100% occurrence. In several known examples, as well as in the 100%‐occurrence counterexample, an optimal confidence belt provides absurd statements because it is inclusion‐inconsistent with either a null or an all‐inclusive belt or both. It is concluded that confidence‐theory optimality criteria alone are inadequate for practice, and that a consistency criterion is required. An approach based upon inclusion consistency of belts[C(x)CC C(x), for somex, impliesγ ≤ γfor confidence coefficients] is suggested for exact interval estimation in continuous parametric models. Belt inclusion consistency, the existence of a proper‐pivotal vector [a pivotal vectorT(X, θ)such that the effective range ofT(x,.)is independent ofx], and the existence of a confidence distribution are proven mutually equivalent. This consistent approach being restrictive, it is shown, using Neyman's anomalous 1954 example, how to determine whether any given parametric function can be estimated consistently and exactly or whether a consistent nonexact solution mus

ISSN:0319-5724    

DOI:10.2307/3315429

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractA Bayesian approach to modeling a rich class of nonconjugate problems is presented. An adaptive Monte Carlo integration technique known as the Gibbs sampler is proposed as a mechanism for implementing a conceptually and computationally simple solution in such a framework. The result is a general strategy for obtaining marginal posterior densities under changing specification of the model error densities and related prior densities. We illustrate the approach in a nonlinear regression setting, comparing the merits of three candidate error distributions.

ISSN:0319-5724    

DOI:10.2307/3315430

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractScore statistics utilizing historical control data have been proposed to test for increasing trend in tumour occurrence rates in laboratory carcinogenicity studies. Novel invariance arguments are used to confirm, under slightly weaker conditions, previously established asymptotic distributions (mixtures of normal distributions) of tests unconditional on the tumor response rate in the concurrent control group. Conditioning on the control response rate, an ancillary statistic, leads to a new conditional limit theorem in which the test statistic converges to an unknown random variable. Because of this, a subasymptotic approximation to the conditional limiting distribution is also considered. The adequacy of these large‐sample approximations in finite samples is evaluated using computer simulation. Bootstrap methods for use in finite samples are also proposed. The application of the conditional and unconditional tests is illustrated using bioassay data taken from the literature. The results presented in this paper are used to formulate recommendations for the use of tests for trend with historical controls in practic

ISSN:0319-5724    

DOI:10.2307/3315431

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractThe asymptotic distribution of the stopping timeNin a time‐sequential procedure for the estimation of the mean exponential survival time given by Gardiner, Susarla, and van Ryzin (1986) is obtained. The same techniques used to obtain this asymptotic distribution ofNare used to obtain the asymptotic distribution of the statistic representing the time‐on‐test expended per unit item in the

ISSN:0319-5724    

DOI:10.2307/3315426.n

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractLet μ be a positive measure concentrated on R+generating a natural exponential family (NEF)Fwith quadratic variance functionVF(m), mbeing the mean parameter ofF.It is shown that v(dx) = (γ+x)μ(γ ≥ 0) (γ ≥ 0) generates a NEF G whose variance function is of the form l(m)Δ+cΔ(m), wherel(m)is an affine function of m, Δ(m) is a polynomial in m (the mean of G) of degree 2, andcis a constant. The family G turns out to be a finite mixture ofFand its length‐biased family. We also examine the cases whenFhas cubic variance function and show that for suitable choices of γ the family G has variance function of the formP(m)+ Q(m)m whereP, Qare polynomials inmof degree m2 while Δ is an affine function of m. Finally we extend the idea to two dimensions by considering a bivariate Poisson and bivariate gamma mixtu

ISSN:0319-5724    

DOI:10.2307/3315433

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY

摘要:

AbstractWe considernpairs of random variables(X11,X21),(X12,X22),…(X1n,X2n)having a bivariate elliptically contoured density of the form\documentclass{article}\pagestyle{empty}\begin{document}$$ K(n)|\Lambda |^{ - n/2} g\left\{ {\sum\limits_1^n {({\bf x}_{1j} - \theta _1 ,\,{\bf x}_{2j} - \theta _2 )\Lambda ^{ - 1} ({\bf x}_{1j} - \theta _1 ,\,{\bf x}_{2j} - \theta _2 )^{\rm T} } } \right\}, $$\end{document}where θ1θ2are location parameters and Δ = ((λik)) is a 2 × 2 symmetric positive definite matrix of scale parameters. The exact distribution of the Pearson product‐moment correlation coefficient betweenX1and X2is obtained. The usual case when a sample of sizenis drawn from a bivariate normal population is a special case of the abovemention

ISSN:0319-5724    

DOI:10.2307/3315434

出版商:Wiley‐Blackwell    

年代:1991

数据来源: WILEY