Accounting for variability in individual hierarchical clinical trial data

Meta-analytical approaches have been extensively used to analyze medical data. In most cases, the data come from different studies or independent trials with similar characteristics. However, these methods can be applied in a broader sense. In this paper, we show how existing meta-analytic techniques can also be used as well when dealing with parameters estimated from individual hierarchical data. Specifically, we propose to apply statistical methods that account for the variances (and possibly covariances) of such measures. The estimated parameters together with their estimated variances can be incorporated into a general linear mixed model framework. We illustrate the methodology by using data from a first-in-man study and a simulated data set. The analysis was implemented with the SAS procedure MIXED and example code is offered.     

A NEW MEASURE OF ROTATABILITY OF RESPONSE SURFACE DESIGNS

This paper proposes a new measure of rotatability of a response surface design. It is based on a comparison between the design moments of a given design and the design moments of a rotatable design closest to the given design in the least squares sense. This measure is easier to calculate than Khur?s measure. An alternative easier non-geometrical way of deriving Khuri's measure is also presented. Both measures are calculated to illustrate some designs considered by Khuri.     

Conditional estimation of average on the basis of weighting data

LetF(x,y) be a distribution function of a two dimensional random variable (X,Y). We assume that a distribution functionF _x(x) of the random variableX is known. The variableX will be called an auxiliary variable. Our purpose is estimation of the expected valuem=E(Y) on the basis of two-dimensional simple sample denoted by:U=[(X ₁, Y₁)…(X_n, Y_n)]=[X Y]. LetX=[X ₁…X _n]andY=[Y ₁…Y _n].This sample is drawn from a distribution determined by the functionF(x,y). LetX _(k)be the k-th (k=1, …,n) order statistic determined on the basis of the sampleX. The sampleU is truncated by means of this order statistic into two sub-samples: % MathType!End!2!1! and % MathType!End!2!1!.Let % MathType!End!2!1! and % MathType!End!2!1! be the sample means from the sub-samplesU _k,1 andU _k,2, respectively. The linear combination % MathType!End!2!1! of these means is the conditional estimator of the expected valuem. The coefficients of this linear combination depend on the distribution function of auxiliary variable in the pointx _(k).We can show that this statistic is conditionally as well as unconditionally unbiased estimator of the averagem. The variance of this estimator is derived. The variance of the statistic % MathType!End!2!1! is compared with the variance of the order sample mean. The generalization of the conditional estimation of the mean is considered, too.     

A Note on the Predictors of Differenced Sequences

In this note we consider the problems of optimal linear prediction (o.l.p.) and the minimum mean squared error prediction (m.m.s.e.p.) of a sequence X_t, which fits to a stationary and invertible ARMA model through the filter (1 - B^s)^d X_t= Y_t. It is shown that these two predictors are not identical in general from the theoretical point of view. Permitting the degree of differencing d to take any real value, a set of conditions for these commonly applied prediction formulas to be identical is given.     

Vec and vech operators for matrices,with some uses in jacobians and multivariate statistics

The vec of a matrix X stacks columns of X one under another in a single column; the vech of a square matrix X does the same thing but starting each column at its diagonal element. The Jacobian of a one-to-one transformation X → Y is then ∣∣?(vecX)/?(vecY) ∣∣ when X and Y each have functionally independent elements; it is ∣∣ ?(vechX)/?(vechY) ∣∣ when X and Y are symmetric; and there is a general form for when X and Y are other patterned matrices. Kronecker product properties of vec(ABC) permit easy evaluation of this determinant in many cases. The vec and vech operators are also very convenient in developing results in multivariate statistics.     

Quota fulfillment times

An example of the classical occupancy problem is to sample with replacement from an urn containing several colours of balls and count the number of balls sampled until a given number of “quotas” are filled. This and the corresponding random variable for sampling without replacement will be referred to as quota fulfillment times. Asymptotic and exact methods for computing moments and distributions are given in this paper. Moments of quota fulfillment times are related to moments of order statistics of beta and gamma random variables. Most of the results for sampling without replacement and some of the results for sampling with replacement are believed to be new. Some other known sampling-with-replacement results are given for comparative purposes.     

Calibration as estimation

Calibration in macroeconomics involves choosing fre parameters by matching certain moments of simulted models with those of data. We formally examine this method by treating the process of calibration as an econometric estimator. A numerical version of the Mehra-Prescott (1985) economy is the setting for an evaluation of calibration estimators via Monte Carlo methods. While these estimators sometimes have reasonable finite-sample properties they are not robust to mistakes in setting non-free parameters. In contrast, generalized method-of-moments (GMM) estimators have satisfactory finite-sample characteristics, quick convergence, and informational requirements less stringent than those of calibration estimators. In dynamic equilibrium models in which GMM is infeasible we offer some suggestions for improving estimates based on calibration methodology.     

平面板状天线

研究了自由空间下平的面板状天线,用矩量法求解了这种二维天线的电流分布及其输入阻抗,进行了大量的数值计算,把计算二维积分的运算从 N×N 元减少到 N 元,从而缩短了运算,节约机时。对不同尺寸的平面板状天线进行了输入阻抗实验验证,理论与实验较一致。     

On the characteristic function of multivariate Student t-distribution

The characteristic function of the multivariate Student t-distribution is obtained, and it is shown that this characteristic function has the pedogogical virtue of reducing the multivariate problem to the analogous univariate problem. Applications of the characteristic function are discussed.     

基于有理样条死亡假设的分数时点寿险净保费责任准备金

保险责任准备金是保险公司风险管理的重要度量指标,责任准备金的精确合理的测算,将会对保险公司的健康发展起着极其重要的作用。分数时点净保费责任准备金的测算依赖于精算假设,本文在提出一类有理样条死亡假设的基础上,研究了终身寿险的分数时点净保费责任准备金的计算问题。我们得到了其理论计算公式和上下界范围,探讨了调节参数的变化对净保费责任准备金的影响。数据分析表明:分数时点责任准备金对调节参数的变化比较敏感,目前常用的UDD假设下的责任准备金测算值恰是本文方法下的一个边界。所以基于有理样条估计方法的分数时点责任准备金测算在实务中具有很强的灵活性,对保险公司责任准备金风险管理具有重要的指导意义。