A NONPARAMETRIC TEST OF SYMMETRY VERSUS ASYMMETRY FOR RANKED-SET SAMPLES

This paper introduces a nonparametric test of symmetry for ranked-set samples to test the asymmetry of the underlying distribution. The test statistic is constructed from the Cramér-von Mises distance function which measures the distance between two probability models. The null distribution of the test statistic is established by constructing symmetric bootstrap samples from a given ranked-set sample. It is shown that the type I error probabilities are stable across all practical symmetric distributions and the test has high power for asymmetric distributions.     

Model Selection,Transformations and Variance Estimation in Nonlinear Regression

The results of analyzing experimental data using a parametric model may heavily depend on the chosen model for regression and variance functions, moreover also on a possibly underlying preliminary transformation of the variables. In this paper we propose and discuss a complex procedure which consists in a simultaneous selection of parametric regression and variance models from a relatively rich model class and of Box-Cox variable transformations by minimization of a cross-validation criterion. For this it is essential to introduce modifications of the standard cross-validation criterion adapted to each of the following objectives: 1. estimation of the unknown regression function, 2. prediction of future values of the response variable, 3. calibration or 4. estimation of some parameter with a certain meaning in the corresponding field of application. Our idea of a criterion oriented combination of procedures (which usually if applied, then in an independent or sequential way) is expected to lead to more accurate results. We show how the accuracy of the parameter estimators can be assessed by a “moment oriented bootstrap procedure", which is an essential modification of the “wild bootstrap” of Härdle and Mammen by use of more accurate variance estimates. This new procedure and its refinement by a bootstrap based pivot (“double bootstrap”) is also used for the construction of confidence, prediction and calibration intervals. Programs written in Splus which realize our strategy for nonlinear regression modelling and parameter estimation are described as well. The performance of the selected model is discussed, and the behaviour of the procedures is illustrated, e.g., by an application in radioimmunological assay.     

Changepoint Problems Under Random Censorship

Let X ₁, …, X _[nθ], X _{[nθ] + 1}, …, X _n be a sequence of independent random variables (the “lifetimes”) such that X _j ? F ₁ for 1 ≤ j ≤ [nθ] and X _j ? F ₂ for [nθ] + 1 ≤ j ≤ n, with F ₁ ≠ F ₂ unknown. In this paper we investigate an estimator θ _n for the changepoint θ if the X's are subject to censoring. The rate of almost sure convergence of θ _n to θ is established and a test for the hypothesis θ = 0, i.e. “no change”, is proposed.     

热带假丝酵母产辅酶Q10发酵条件的研究

目的以热带假丝酵母作为辅酶Q10的生产菌,研究不同的发酵条件对辅酶Q10产量的影响, 以获得比较高的辅酶Q10产量。方法用酒精提取,用紫外分光光度法检测。结果葡萄糖是较好的碳源,大豆蛋白胨是较好的氮源,磷酸盐不同的比例对细胞生长及辅酶Q10合成的影响较显著,添加硫酸锰对辅酶Q10的合成有一定的促进作用。发酵初始pH 8.0,接种量为4.0%,250mL三角瓶装液量为40mL,发酵时间为72 h,葡萄糖4.0%, 大豆蛋白胨5.0%,辅酶Q10产量达到70 μg·mL-1。

结论热带假丝酵母作为高产辅酶Q10菌种具有较好的实用性以及进一步提高产量的潜力和广阔的应用前景。     

Partially A-optimal blocked multi-factor designs

In this paper, we propose a partially A-optimal criterion for block designs where multiple factors are arranged. The number of levels of each factor is assumed to be arbitrary and unequal block sizes are allowed. A sufficient condition is derived for a design to be partially A-optimal among all feasible designs. Then the properties of the selected design and its relation with orthogonal arrays are studied. Methods of constructing designs satisfying the sufficient condition are also given.     

Controlling the false-discovery rate by procedures adapted to the length bias of RNA-Seq

In RNA-Seq experiments, the number of mapped reads for a given gene is proportional to its expression level and length. Because longer genes contribute more sequencible fragments than do shorter ones, it is expected that even if two genes have the same expression level, the longer gene will have a greater number of total reads. This characteristic creates a length bias such that the proportion of significant genes increases with the gene length. However, genes with a long length are not more biologically meaningful than genes with a short length. Therefore, the length bias should be properly corrected to determine the accurate list of significant genes in RNA-Seq. For this purpose, we proposed two multiple-testing procedures based on a weighted-FDR and a separate-FDR approach. These two methods use prior information on differential gene length while keeping the false-discovery rate (FDR) controlled at $\alpha$. In the weighted-FDR controlling procedure, we incorporated prior weights for the length of each gene. These weights increase the power when the gene’s length is short and decrease the power when its length is long. In the separate-FDR controlling procedure, we sequentially ordered all genes according to their lengths and then split these genes into two subgroups of short and long genes. The adaptive Benjamini–Hochberg procedure was then performed separately for each subgroup. The proposed procedures were compared with existing methods and evaluated in two numerical examples and one simulation study. We concluded that the weighted $p$-value procedure properly reduced the length bias of RNA-Seq.     

世界男子跳水运动员难度动作位序分析——以第29届奥运会男子单人10米台跳水决赛为例

运用图像分析法、文献资料法、数理统计法等研究方法,对第29届奥运会男子单人跳水决赛前8名运动员难度动作出现的位序与成绩关系进行分析。研究表明,整套难度动作位序布局的合理性、难度系数动作类别组编的均衡性与运动成绩呈正相关,难度动作的选择应与运动员的实际身体素质水平和专业技术水平相吻合,动作才能完成得轻松优美,才能充分展现男子单人10米跳台运动员的个性化特点,难与美的结合仍然是当今跳水制胜的关键。