Maximum Likelihood Estimation of Isotonic Normal Means with Unknown Variances

To analyze the isotonic regression problem for normal means, it is usual to assume that all variances are known or unknown but equal. This paper then studies this problem in the case that there are no conditions imposed on the variances. Suppose that we have data drawn fromkindependent normal populations with unknown meansμ_i's and unknown variancesσ²_i's, in which the means are restricted by a given partial ordering. This paper discusses some properties of the maximum likelihood estimates ofμ_i's andσ²_i's under the restriction and proposes an algorithm for obtaining the estimates.     

多波长线性回归荧光法同时测定苯酚,间苯二酚和间苯三酚

酚类物质是环保、卫生、医药、食品等行业分析的重要指标，通常只能测定酚的总量［１～３］，最小二乘法［４］、卡尔曼滤波法［５］虽能同时测定各量，但需要用计算机解谱，且只进行了苯酚和间苯二酚两组分的测定．对于结构相似的苯酚、间苯二酚和间苯三酚三组分混合体系...     

Nonparametric tests for bounds on the derivative of a regression function

We consider two tests of the null hypothesis that the k-th derivative of a regression function is uniformly bounded by a specified constant. These tests can be used to study the shape of the regression function. For instance, we can test for convexity of the regression function by setting k=2 and the constant equal to zero. Our tests are based on k-th order divided difference of the observations. The asymptotic distribution and efficacies of these tests are computed and simulation results presented.Research supported by Natural Sciences and Engineering Research Council of Canada Grant OGP0007969.Research supported by National Science Foundation Grant DMS-9306738.     

An optimum tolerance region for multivariate regression

A tolerance region is a map from the sample space of one statistical model to the event space of a second statistical model having the same parameter. This paper derives an optimum β-expectation tolerance region for the multivariate regression model. A measure of power is proposed and evaluated.     

Strong consistency of least squares estimates in multiple regression II

The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors.     

On the robustness of least squares procedures in regression models

The criterion robustness of the standard likelihood ratio test (LRT) under the multivariate normal regression model and also the inference robustness of the same test under the univariate set up are established for certain nonnormal distributions of errors. Restricting attention to the normal distribution of errors in the context of univariate regression models, conditions on the design matrix are established under which the usual LRT of a linear hypothesis (under homoscedasticity of errors) remains valid if the errors have an intraclass covariance structure. The conditions hold in the case of some standard designs. The relevance of C. R. Rao's (1967 In Proceedings Fifth Berkeley Symposium on Math. Stat. and Prob., Vol. 1, pp. 355–372) and G. Zyskind's (1967, Ann. Math. Statist.38 1092–1110) conditions in this context is discussed.     

A methodology for measuring the relative effectiveness of healthcare services

^** Email: giorgio.vittadini{at}unimib.it^*** Email: simona.minotti{at}unicatt.it In this paper we propose a methodology for measuring the ‘relativeeffectiveness’ of healthcare services (i.e. the effectof hospital care on patients) under general conditions, in which:) a healthcare outcome underlies qualitative and quantitativeobservable indicators; ß) we are interested in studyingthe simultaneous dependency of multiple outcomes on covariates(where the outcomes can also be correlated to each other); )the relative effectiveness is adjusted for hospital-specificcovariates; ) we hypothesise a general distribution for randomdisturbances and the random parameters of relative effectiveness.For this topic, a generalisation of the SURE (seemingly unrelatedregression equations) multilevel model is proposed. The solutionsare obtained by means of Bayesian inference methods. Since thereis currently no software available to estimate this model, anSAS procedure based on Markov Chain Monte Carlo methods hasbeen developed by the authors, in line with Goldstein &Spiegelhalter (1996, J. R. Stat. Soc. Ser. A, 159, 385–443),Spiegelhalter et al. (1996, Bayesian Using Gibbs Sampling Manual.Cambridge: MRC Biostatistic Unit, Institute of Public Health)and Albert & Chib (1997, J. Am. Stat. Assoc., 92, 916–925).In addition, a new theoretical result regarding the joint posteriordistribution for the parameters is provided. The model proposedhas been implemented for an effectiveness study of a selectionof Lombard hospitals.     

Improved DOSY NMR data processing by data enhancement and combination of multivariate curve resolution with non-linear least square fitting

The quality of DOSY NMR data can be improved by careful pre-processing techniques. Baseline drift, peak shift, and phase shift commonly exist in real-world DOSY NMR data. These phenomena seriously hinder the data analysis and should be removed as much as possible. In this paper, a series of preprocessing operations are proposed so that the subsequent multivariate curve resolution can yield optimal results. First, the baseline is corrected according to a method by Golotvin and Williams. Next, frequency and phase shift are removed by a new combination of reference deconvolution (FIDDLE), and a method presented by Witjes et al. that can correct several spectra simultaneously. The corrected data are analysed by the combination of multivariate curve resolution with non-linear least square regression (MCR-NLR). The MCR-NLR method turns out to be more robust and leads to better resolution of the pure components than classic MCR.     

Positive Reachability for Diffusion Equations

Counterexamples are constructed for some plausible conjectures. Typical of these: as the Maximum Principle ensures that positive boundary data give a positive state at time T from 0 initial data, one might (plausibly, but falsely) conjecture that all positive terminal states should be approximately reachable in this way, i.e., subject to the requirement that the boundary data stays nonnegative.     

用于细胞及组织培养的中等强度LED生物光源

研制出可用于细胞及组织培养的中等强度发光二极管光源,介绍了光源的光路原理和简要结构,测试了该光源的辐射照度及其强度分布,使用统计分析软件SPSS拟合得到该光源的辐射照度经验公式。