摘要:

AbstractThis paper introduces a robust biplot which is related to multivariateM‐estimates. Then × pdata matrix is first considered as a sample of sizenfrom somep‐variate population, and robustM‐estimates of the population location vector and scatter matrix are calculated. In the construction of the biplot, each row of the data matrix is assigned a weight determined in the preliminary robust estimation. In a robust biplot, one can plot the variables in order to represent characteristics of the robust variance‐covariance matrix: the length of the vector representing a variable is proportional to its robust standard deviation, while the cosine of the angle between two variables is approximately equal to their robust correlation. The proposed biplot also permits a meaningful representation of the variables in a robust principal‐component analysis. The discrepancies between least‐squares and robust biplots are illustrated i

ISSN:0319-5724    

DOI:10.2307/3315312

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractSuppose the observations (ti,yi), i = 1,…n, follow the modelwhere gjare unknown functions. The estimation of the additive components can be done by approximating gj,with a function made up of the sum of a linear fit and a truncated Fourier series of cosines and minimizing a penalized least‐squares loss function over the coefficients. This finite‐dimensional basis approximation, when fitting an additive model withrpredictors, has the advantage of reducing the computations drastically, since it does not require the use of the backfitting algorithm. The cross‐validation (CV) [or generalized cross‐validation (GCV)] for the additive fit is calculated in a further 0(n)operations. A search path in the r‐dimensional space of degrees of freedom is proposed along which the CV (GCV) continuously decreases. The path ends when an increase in the degrees of freedom of any of the predictors yields an increase in CV (GCV). This procedure is illustrated on a meteorologic

ISSN:0319-5724    

DOI:10.2307/3315313

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractFor the general linear regression model Y = Xη + e, we construct small‐sample exponentially tilted empirical confidence intervals for a linear parameter 6 = aTη and for nonlinear functions of η. The coverage error for the intervals is Op(1/n), as shown in Tingley and Field (1990). The technique, though sample‐based, does not require bootstrap resampling. The first step is calculation of an estimate for η. We have used a Mallows estimate. The algorithm applies whenever η is estimated as the solution of a system of equations having expected value 0.We include calculations of the relative efficiency of the estimator (compared with the classical least‐squares estimate). The intervals are compared with asymptotic intervals as found, for example, in Hampelet at.(1986). We demonstrate that the procedure gives sensible intervals for sma

ISSN:0319-5724    

DOI:10.2307/3315314

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractWe propose a feasible general method for finding a minimax estimator of an unknown distribution functionFin the nonparametric problem. As an application, some minimax estimators are proposed. Furthermore, some minimax binomial parametric problems are studied.

ISSN:0319-5724    

DOI:10.2307/3315315

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractWe consider the problem of simultaneously estimating k + 1 related proportions, with a special emphasis on the estimation of Hardy‐Weinberg (HW) proportions. We prove that the uniformly minimum‐variance unbiased estimator (UMVUE) of two proportions which are individually admissible under squared‐error loss are inadmissible in estimating the proportions jointly. Furthermore, rules that dominate the UMVUE are given. A Bayesian analysis is then presented to provide insight into this inadmissibility issue: The UMVUE is undesirable because the two estimators are Bayes rules corresponding to different priors. It is also shown that there does not exist a prior which yields the maximum‐likelihood estimators simultaneously. When the risks of several estimators for the HW proportions are compared, it is seen that some Bayesian estimates yield significantly smaller risks over a large portion of the parameter space for small samples. However, the differences in risks become less significant as the sample size gets

ISSN:0319-5724    

DOI:10.2307/3315316

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractWe address the problem of the curtailment or continuation of an experiment or trial at some interim point where sayNobservations are in hand and at leastS>Nobservations had originally been scheduled for a decision. A Bayesian predictive approach is used to determine the probability that if one continued the trial with a further sample of sizeMwhereN +M≥S, one would come to a particular decision regarding a parameter or a future observable. This point of view can also be applied to significance tests if one is willing to admit the calculation as a subjective assessmen

ISSN:0319-5724    

DOI:10.2307/3315317

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractBayesian analysis of predictive values and related parameters of a diagnostic test are derived. In one case, the estimates are conditional on values of the prevalence of the disease; in the second case, the corresponding unconditional estimates are presented. Small‐sample point estimates, posterior moments, and credibility intervals for all related parameters are obtained. Numerical methods of solution are also discusse

ISSN:0319-5724    

DOI:10.2307/3315318

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractFix r ≥ 1, and let {Mnr} be the rth largest of {X1,X2,…Xn}, where X1,X2,… is a sequence of i.i.d. random variables with distribution functionF.It is proved thatP[Mnr≤ uni.o.] = 0 or 1 according as the series Σ∞n=3Fn(un)(log log n)r/nconverges or diverges, for any real sequence {un} such thatn{1 ‐F(un)} is nondecreasing and divergent. This generalizes a result of Bamdorff‐Nielsen (1961) i

ISSN:0319-5724    

DOI:10.2307/3315319

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper develops a conditional approach to testing hypotheses set up after viewing the data. For example, suppose Xiare estimates of location parameters θi, i = 1,…n.We show how to computep‐values for testing whether θ1is one of the three largest θiafter observing that X1is one of the three largest Xi, or for testing whether θ1>θ2>…>θnafter observing

ISSN:0319-5724    

DOI:10.2307/3315320

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY

摘要:

AbstractWe give an example of a nonbinary block design which is better than any binary design with respect to theE‐optimality criterion. This shows that the class of binary designs is not essentially complete, at least with respect to E‐optimal

ISSN:0319-5724    

DOI:10.2307/3315321

出版商:Wiley‐Blackwell    

年代:1992

数据来源: WILEY