摘要:

AbstractA regular supply of applicants to Queen's University in Kingston, Ontario is provided by 65 high schools. Each high school can be characterized by a series of grading standards which change from year to year. To aid admissions decisions, it is desirable to forecast the current year's grading standards for all 65 high schools using grading standards estimated from past year's data. We develop and apply a Bayesian break‐point time‐series model that generates forecasts which involve smoothing across time for each school and smoothing across schools. “Break point” refers to a point in time which divides the past into the “old past” and the “recent past” where the yearly observations in the recent past are exchangeable with the observations in the year to be forecast. We show that this model works fairly well when applied to 11 years of Queen's University data. The model can be applied to other data sets with the parallel time‐series structure and short history, and can be extended in several ways to more compl

ISSN:0319-5724    

DOI:10.2307/3314857

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY

摘要:

AbstractConfidence regions for generalized least squares are commonly derived from a measure of departure calculated on the tangent plane at the MLE or on the tangent plane at the true value; the first gives approximate confidence regions, the second exact. For surfaces with curvature, indeed with varying curvature, the exact regions typically are not likelihood regions and can include parameter values of highest and of lowest likelihood. This paper develops an alternative approach to deriving exact confidence regions and uses both surface curvature and distance from the surface as supporting ingredients. For this, conditionality is invoked in two ways beyond that supported by the usual conditionality principle. For the case of normal error the ordinary chi‐squared departure is replaced by a Von Mises‐type angular (or cosine) departure which is assessed using curvature properties in the data direction and radial distance of the data from the regression surface. For the usual linear model (constant curvature equal to zero) the method coincides with the ordinary tests and confidence regions; for the case of constant nonzero curvature, the method generalizes to spheres and sphere‐cylinders the Fisher (Statistical Methods and Scientific Inference, 1956) analysis of a rotationally symmetric normal on ℝ2with mean constrained to a circle. The effects of conditioning are indicated by a computer plot for obtaining 95% con

ISSN:0319-5724    

DOI:10.2307/3314858

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY

摘要:

AbstractMeasures of centrality that generalize the univariate median are studied and applied to multivariate and directional distributions. A standard example is developed for general multivariate settings, and the uniqueness of the median proved for distributions satisfying certain regularity conditions. In the presence of weaker regularity, this median is shown to be of codimension 2. Conditions are also provided for these measures of centrality to be equivariant under transformations on the sample space. The equivariance of the usual univariate median under monotone transformations is seen as a special case.

ISSN:0319-5724    

DOI:10.2307/3314859

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY

摘要:

AbstractNonparametric tests are proposed for the equality of two unknownp‐variate distributions. Empirical probability measures are defined from samples from the two distributions and used to construct test statistics as the supremum of the absolute differences between empirical probabilities, the supremum being taken over all possible events. The test statistics are truly multivariate in not requiring the artificial ranking of multivariate observations, and they are distribution‐free in the generalp‐variate case. Asymptotic null distributions are obtained. Powers of the proposed tests and a competitor are examined by Monte Carlo techn

ISSN:0319-5724    

DOI:10.2307/3314860

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY

摘要:

AbstractConsider a given sequence {Tn} of estimators for a real‐valued parameter θ. This paper studies asymptotic properties of restricted Bayes tests of the following form: rejectH0:θ ≤ θ0in favour of the alternative θ>θ0ifTn≤Cn, where the critical pointCnis determined to minimize among all tests of this form the expected probability of error with respect to the prior distribution. Such tests may or may not be fully Bayes tests, and so are calledTn‐Bayes. Under fairly broad conditions it is shown that\documentclass{article}\pagestyle{empty}\begin{document}$$ c_n = \theta _0 + a_n b(\theta _0)\bar \mu + 0(a_n) $$\end{document}and theTn‐Bayes risk\documentclass{article}\pagestyle{empty}\begin{document}$$ B_n (c_n) = a_n b(\theta _0)p(\theta _0)p(\theta _0)\int_{ - \infty }^\infty {|x - \bar \mu |dF(x) + 0(a_n)} $$\end{document}whereanis the order of the standard error ofTn, ‐ is the prior density, andμis the median ofF, the limit distribution of (Tn– θ)/anb(θ). Sever

ISSN:0319-5724    

DOI:10.2307/3314861

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY

摘要:

AbstractUniform stochastic orderings of random variables are expressed as total positivity (TP) of density, survival, and distribution functions. The orderings are called uniform because each is a stochastic order that persists under conditioning to a family of intervals—for example, the family consisting of all intervals of the form (‐∞,x]. This paper is concerned with the preservation of uniform stochastic ordering under convolution, mixing, and the formation of coherent systems. A general TP2result involving preservation of total positivity under integration is presented and applied to convolutions and mixtures of distribution and survival functions. Log‐concavity of distribution, survival, and density functions characterizes distributions that preserve the various orderings under convolution. Likewise, distributions that preserve orderings under mixing are characterized by TP2distribution and survival fu

ISSN:0319-5724    

DOI:10.2307/3314862

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY

摘要:

AbstractThe effects of missing observations in a designed experiment are reviewed. Conditions are determined for a design to retain equal information, i.e. the same generalized variance of unknown parameters, when either any single or any pair of observations is lost. Some examples of designs with this property are given. Although there are many designs which retain equal information for the loss of exactlytobservations, wheret= 1,2,3,…, it is shown that it is not possible to obtain any design which retains equal information when any one and any two and also any three observations are missin

ISSN:0319-5724    

DOI:10.2307/3314863

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY

摘要:

AbstractLetXi, 1 ≤i≤n, be independent identically distributed random variables with a common distribution functionF, and letGbe a smooth distribution function. We derive the limit distribution of□{ρα(Fn, G) ‐α(F, G)}, whereFnis the empirical distribution function based onX1,…,Xnandαis a Kolmogorov‐Lévy‐type metric between distribution functions. For α ≤ 0 and two distribution functionsFandGthe metric pαis given by pα(F, G) = inf {ϵ ≤ 0:G(x‐ αϵ)

ISSN:0319-5724    

DOI:10.2307/3314864

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY

摘要:

AbstractThe least‐squares estimate θn=Xn+ynof the parameter θ in the linear modelYn=Xnθ + ϵnmay not be consistent, but there may be directionsusuch thatu'θntends tou'θ in some sense. This set of directionsuhas been characterized in two different papers: Drygas (1976) and Wu (1980). The conditions for consistency appear to be different in the two papers. The purpose of this note is to show that the two conditions are equivalent and that they both show that the consistent directions depend upon the geometry of the row vectorsvi, i= 1,…,n, ofXnwith respect to the d

ISSN:0319-5724    

DOI:10.2307/3314865

出版商:Wiley‐Blackwell    

年代:1987

数据来源: WILEY