单李代数不可约表示的标记

对于n秩单李代数g,当采用Dynkin关于素根的分类时,其不可约表示可以用n个非负整数Λ_(αi)标记,也可通过初等表示的权用数组li来标记。利用Cartan逆矩阵,我们给出了计算Λ_(α_i)与li之间关系的方法。对于B_n、C_n、D_n和F_4,利用Cartan逆矩阵证明了这些li是与采用Cartan关于素根的分类时的Λi是一致的。     

1998年狮子座流星暴的一些预测

1998年狮子座流星暴是本年度最重要的天象之一。而广东省处于观测的最有利位置,为了不错过这次十分难得的机会,本文叙述了狮子座流量暴的本质及其观测工作的意义,求出了该流星暴母体的部分轨道根数;对1998年狮子座流星暴作了一些预测;对观测方法提出了一些建议,本次预测虽用的是天文专业的方法,但为了使更多的观测员理解,本文尽可能使用最基础的知识。     

青岛一套表的实践与经验

 企业统计一套表一直是统计制度方法改革和实践中的焦点问题。本文通过对青岛市统计局企业一套表制度实施情况的案例分析,系统界定了企业一套表的概念和内涵,全面展现了企业一套表的运作过程,客观分析了制约企业一套表实施的主要原因,并提出了在现阶段实施企业统计一套表的条件和要求。     

Unifying CRM and EWOC designs for phase I cancer clinical trials

The main goal of phase I cancer clinical trials is to determine the highest dose of a new therapy associated with an acceptable level of toxicity for the use in a subsequent phase II trial. The continual reassessment method (CRM) [O’Quigley, J., Pepe, M., Fisher, L., 1990. Continual reassessment method: a practical design for phase I clinical trials in cancer. Biometrics 46, 33–48] and escalation with overdose control (EWOC) [Babb, J., Rogatko, A., Zacks, S., 1998. Cancer phase I clinical trials: efficient dose escalation with overdose control. Statist. Med. 17 (10), 1103–1120] are two model-based designs used for phase I cancer clinical trials. A few modifications of the (original) CRM and EWOC have been made by many authors. In this paper, we show how CRM and EWOC can be unified and present a hybrid design. We study the characteristics of the approach of the hybrid design. The comparisons of the three designs (CRM, EWOC, and the hybrid design) are presented by convergence rates and overdose proportions. The simulation results show that the hybrid design generally has faster convergence rates than EWOC and smaller overdose proportions than CRM, especially when the true maximum tolerated dose (MTD) is above the mid-level of the dose range considered. The performance of these three designs is also evaluated in terms of sensitivity to outliers.     

Linear models that allow perfect estimation

The general Gauss–Markov model, Y = Xβ + e, E(e) = 0, Cov(e) = σ ² V, has been intensively studied and widely used. Most studies consider covariance matrices V that are nonsingular but we focus on the most difficult case wherein C(X), the column space of X, is not contained in C(V). This forces V to be singular. Under this condition there exist nontrivial linear functions of Q′Xβ that are known with probability 1 (perfectly) where ${C(Q)=C(V)^\perp}$ . To treat ${C(X) \not \subset C(V)}$ , much of the existing literature obtains estimates and tests by replacing V with a pseudo-covariance matrix T = V + XUX′ for some nonnegative definite U such that ${C(X) \subset C(T)}$ , see Christensen (Plane answers to complex questions: the theory of linear models, 2002, Chap. 10). We find it more intuitive to first eliminate what is known about Xβ and then to adjust X while keeping V unchanged. We show that we can decompose β into the sum of two orthogonal parts, β = β ₀ + β ₁, where β ₀ is known. We also show that the unknown component of X β is ${X\beta_1 \equiv \tilde{X} \gamma}$ , where ${C(\tilde{X})=C(X)\cap C(V)}$ . We replace the original model with ${Y-X\beta_0=\tilde{X}\gamma+e}$ , E(e) = 0, ${Cov(e)=\sigma^2V}$ and perform estimation and tests under this new model for which the simplifying assumption ${C(\tilde{X}) \subset C(V)}$ holds. This allows us to focus on the part of that parameters that are not known perfectly. We show that this method provides the usual estimates and tests.     

Weighted local linear composite quantile estimation for the case of general error distributions

It is known that for nonparametric regression, local linear composite quantile regression (local linear CQR) is a more competitive technique than classical local linear regression since it can significantly improve estimation efficiency under a class of non-normal and symmetric error distributions. However, this method only applies to symmetric errors because, without symmetric condition, the estimation bias is non-negligible and therefore the resulting estimator is inconsistent. In this paper, we propose a weighted local linear CQR method for general error conditions. This method applies to both symmetric and asymmetric random errors. Because of the use of weights, the estimation bias is eliminated asymptotically and the asymptotic normality is established. Furthermore, by minimizing asymptotic variance, the optimal weights are computed and consequently the optimal estimate (the most efficient estimate) is obtained. By comparing relative efficiency theoretically or numerically, we can ensure that the new estimation outperforms the local linear CQR estimation. Finite sample behaviors conducted by simulation studies further illustrate the theoretical findings.     

A structured framework for assessing sensitivity to missing data assumptions in longitudinal clinical trials

The objective of this research was to demonstrate a framework for drawing inference from sensitivity analyses of incomplete longitudinal clinical trial data via a re‐analysis of data from a confirmatory clinical trial in depression. A likelihood‐based approach that assumed missing at random (MAR) was the primary analysis. Robustness to departure from MAR was assessed by comparing the primary result to those from a series of analyses that employed varying missing not at random (MNAR) assumptions (selection models, pattern mixture models and shared parameter models) and to MAR methods that used inclusive models. The key sensitivity analysis used multiple imputation assuming that after dropout the trajectory of drug‐treated patients was that of placebo treated patients with a similar outcome history (placebo multiple imputation). This result was used as the worst reasonable case to define the lower limit of plausible values for the treatment contrast. The endpoint contrast from the primary analysis was ? 2.79 (p = .013). In placebo multiple imputation, the result was ? 2.17. Results from the other sensitivity analyses ranged from ? 2.21 to ? 3.87 and were symmetrically distributed around the primary result. Hence, no clear evidence of bias from missing not at random data was found. In the worst reasonable case scenario, the treatment effect was 80% of the magnitude of the primary result. Therefore, it was concluded that a treatment effect existed. The structured sensitivity framework of using a worst reasonable case result based on a controlled imputation approach with transparent and debatable assumptions supplemented a series of plausible alternative models under varying assumptions was useful in this specific situation and holds promise as a generally useful framework. Copyright © 2012 John Wiley & Sons, Ltd.     

Empirical Likelihood Inference for the Parameter in Additive Partially Linear EV Models

In this article, we consider empirical likelihood inference for the parameter in the additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distribution without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct the confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions.